International Capital Flows and Long-Run
Convergence
Frédéric Gannon (University of Le Havre)
Gilles Le Garrec (Sciences Po - OFCE)
Vincent Touzé (Sciences Po - OFCE)
March 2015
Abstract
This paper analyses how the economic and demographic dierences between
two regions -one developed and called the North, the other emerging and called
the South- explains the world economic equilibrium and the international capital
flows. We develop a simple two-period OLG model. We compare closed economy
to open economy equilibrium. We consider that openness facilitates convergence
of economic and demographic factors in the South towards those prevailing in the
North. We examine successively the consequences of a technological catching-up,
a demographic transition and an institutional convergence of pension schemes. We
determine the analytical solution of the dynamics of the world interest rate and
deduce the evolution of the current accounts. These results are completed by numerical simulations. They show that the technological catching-up alone leads to
a welfare loss for the North in reason of capital flows to the South. If we add to
this first change a demographic transition, the capital demand is reduced in the
South whereas its saving increases in reason of a higher life expectancy. These two
eects contribute to reduce the capital flows from the North to the South. Finally,
an institutional convergence of the two pension schemes reduces saving rate in the
South which increases the capital flow from the North to the South. Keywords:
International capital flows, OLG, economic convergence, demographic transition.
JEL codes: D91, F15, J10, O33.
1
Introduction
The world population is aging, but at dierent paces, and according to the UN (2008)
demographic projections, this phenomenon should go on until the end of the century. This
generalized but unequal aging process is occurring in a world of increasing capital mobility
and technological transfers, which can oer new opportunities for exchanges amongst
regions. Moreover, this aging process increases the demographic dependency putting the
unfunded pension schemes under pressure in developped countries, which in turn induces
countries to change their rules of sharing of resources between generations, which infers
on the individual choices of savings. Conversely, in the emerging countries, the unequal
sharing of growth benefits and a longer life expectancy could encourage government to
settle or improve unfunded pension schemes and smooth the dierences of welfare across
generations. How in a globalized economy these antagonistic problematics resolve?
The UN forecasts (table 1) show that the length of the life expectancy at birth has
increased, between 1960 and 2010, by 9 years in the North and 21 years in the South,
dramatically crushing the North-South gap from 24 to 8 years. This trend illustrates a long
run convergence process which is to be linked to economic growth (Aghion et al, 2010).
Moreover, in the same period, the current fertility rate in the South lies just below that of
the North in 1960, reducing the gap from 3 to 0.9. The microeconomic (Becker, 1991) and
microdemographic (Caldwell, 1976) rationale for the number of children by family focuses
on the quality-quantity tradeo. In this theoretical framework, the economic growth
improves standards of life, putting pressure on the fertility rate by favouring quality over
quantity. As to the resulting population growth, it has been strongly reduced (divided by
3.4) in the North but it stays at a positive rate because the lengthening of life expectancy
has largely oset an insucient fertility rate (1.64 instead of 2.1 for maintaining the 1:1
ratio between generations). In the South, the population growth has significantly reduced
but it stays at higher rate than the one observed in the North in 1960. Between 1960 and
2010, the share of the North in the world population has been roughly divided by two.
In the future, if the South population rate does not converge towards that of the North,
i.e. zero (if a stable population is assumed), the relation between economic growth and
demographic evolution will be only explained by South characteristics.
These demographic changes in both South and North took place along with an impressive economic growth. Between 1960 and 2008, the GDP per capita has been more
2
Figure 1: Past and forcasted evolution of the South population in percent of the World
population (United Nations, 2013)
than tripled in the North and quintupled in the South (table 2). The per capita wealth
in the South has increased by about 50% implicitly illustring a technological catching-up.
years
North
Life
Total fertility
Annual
expectancy
(children
population
at age 18
per woman)
growth (%)
1950 1980 2010 1950 1980 2010 1950 1980 2010
53
56
60
2.8
1.9
1.7
1.2
0.6
0.3
South 41
50.5
55
6.1
4.6
2.7
2.1
2.1
1.3
Table 1. Demographic transition (United Nations, 2013)
years
1980s 1990s 2000s
2010
South (% of North) 9.5
10.1
12.7
15.4
Table 2. GDP per capita convergence (2005 PPP USD; source: Wang et al. (2011)
based on World Development Indicators of the World Bank).
A representation of the world economy based on an overlapping generations framework
is particularly well adapted to examine how such economic and demographic changes can
aect the mechanisms of economic equilibrium.
Two-country OLG theoretical models of the world economy, represented as a closed
3
system, have first been proposed by Fried (1980) and Buiter (1981). Eaton (1987), Galor
and Lin (1994), Obstfeld and Rogo (1996) also used two-country OLG models to study
trade and related issues. Eaton (1987) studies the international trade in a context of
specific-factors. The two-sector OLG model developped by Galor (1992) was extended to
a two-country framework by Mountford (1998), Guilló (2001), Jelassi and Sayan (2004),
S. Sayan (2005), Naito and Zhao (2009) and Yakita (2012). These studies focus mainly on
the consequences of the economic openess on the sectorial specialization and on welfare
considerations. Excepted Jelassy and Sayan (2001), Sayan (2005), Naito and Zhao (2009)
and Yakita (2012), neither of these articles have investigated systematically the demographic issues. Moreover, neither of these studies deals explicitly with the technological
dierences in the process of catching-up.
Applied versions of multi-regional OLG model have been developed by INGENUE
(2002), Börsch-Supan et al. (2002), Fehr et al. (2003, 2005), Aglietta et al. (2007)
and Marchiori (2011). With the notable exception of INGENUE (2002), Fehr et al.
(2005), Aglietta et al. (2007) and Marchiori (2011), the analyses are generally focused on
developed regions.
The purpose of this paper is to investigate how the demographic and economic dierences between countries and their changes, notably their reduction resulting from realistic
convergence process, aect the world market equilibrium, and how each domestic characteristic explains the internal equilibrium.
In this paper, we develop a multi-country OLG model where we suppose a strong
heterogeneity among the countries. This heterogeneity focuses on the demographic and
economic characteristics. Also, we suppose that each region has specific levels of demographic growth, life expectancy, social security size and total factors productivity. The
analytical approach adopted in the paper allows to detail the weight of the various components of world economic growth. The world economy is divided into two regions: one
developed and called the North, the other emerging and called the South. We compare
closed to open economies in a two-region framework. In the case of open economy, global
convergence of economic, demographic and institutional factors are considered successively. The transitory dynamics is determined by regional dierences whereas the long
run equilibrium is induced by global convergence.
The paper is organized as follows. Section 1 presents the model and the properties of
4
the equilibrium in closed economy. Section 2 compares the equilibrium in open economy
with the previous one. Section 3 investigates three types of convergence. First, we examine
a technological catching-up process. Then, we suppose this process is completed by a
demographic transition. Finally, institutional convergence in the pension scheme is added.
1
The Model
Each region is made of three categories of economic agents: the households, the firms,
and an unfunded pension scheme.
The household sector is made of two overlapped generations of adults. Each individual
is a member of a generation. His duration of life is two periods. In the first period, each
household works, consumes, saves and does not value leisure. The second period breaks
into two subperiods. The first subperiod is dedicated to work and consumption while the
second subperiod is retirement time when he consumes his savings and his pension income.
The households are supposed to maximize life-cycle utility. Their savings are invested into
one financial asset, which is an ownership title in the firms’ productive capital.
The productive sector is modeled as a set of perfectly competitive firms which produce
a single good with a technology using capital and labor. It can be consumed or invested.
At the optimum of production, the factors of production are remunerated at the marginal
productivity. The good and the financial asset are freely traded on perfectly competitive
markets.
The public sector is reduced to an unfunded pension scheme which finances pension
benefits of retired people by taxing earnings of contemporaneous workers.
1.1
Households
Individuals live for two periods: they are successively denoted "young" and "old". At
each period t and for a given region i, growth of the number of young is characterized by:
Ni,t
= Gi,t
Ni,t1
(1)
where Ni,t is the number of young people. Besides, old people live only a fraction of the
second period (life expectancy) denoted i,t+1 .
5
When young in t, they work, they consume and they save income for the second period
of their life. In addition, they contribute to a PAYG retirement system. Their first period
budget constraint is then:
Ci,t + Si,t = (1   i,t ) · wi,t
(2)
where Ci,t is the consumption when young, Si,t is the savings, wi,t the wage and  the
contribution rate.
When old in t + 1, they continue to work a fraction li,t+1 of the second period of life
(mandatory length of work/legal of age of retirement) and they consume all their income
which corresponds to their savings with interest, their net wage during the period they
work and their pension the rest of their life. The second period budget constraint is then:


i,t+1 · Zi,t+1 = (1   i,t+1 ) · wi,t+1 · li,t+1 + Ri,t+1 · Si,t + i,t+1  li,t+1 · Pi,t+1
(3)
where Zi,t+1 is the consumption when old in t + 1, Rt+1 the world interest factor, Pi,t+1
the pension and li,t+1  i,t+1 .
Individuals young in t are characterized by the following lifetime utility function:
ln Ci,t +  · i,t+1 · ln Zi,t+1
(4)
Let us consider:
i,t = (1   i,t ) · wi,t + (1   i,t+1 ) · li,t+1 ·
wi,t+1
Ri,t+1


+ i,t+1  li,t+1 ·
Pi,t+1
Rt+1
(5)
the lifetime income of an individual young in t, his consumption which is obtained by
maximization of (4) under (2) and (3) is then characterized by Ct =
i,t
,
1+·i,t+1
and it
follows according to (5) that savings is:
Si,t = (1   i,t ) · wi,t 
i,t
1+·i,t+1
(6)
= si,t · (1   i,t ) · wi,t  (1  si,t ) ·
where si,t =
·i,t+1
1+·i,t+1
(1 i,t+1 )·li,t+1 ·wi,t+1 +(i,t+1 li,t+1 )·Pi,t+1
Ri,t+1
is the marginal propensity to save the current income and (1  si,t )
is the marginal propensity to consume the future income. Notice that marginal propensity
to save is an increasing function of life expectancy.
6
1.2
PAYG retirement system
Assume that the budget of the retirement system is balanced at each period, it follows
that:


(Ni,t + Ni,t1 · li,t ) ·  i,t · wi,t = i,t  li,t · Ni,t1 · Pi,t .
(7)
When considering the population evolution process characterized by (1), the pension is
defined as:
Pi,t =
1.3
Gi,t +li,t
i,t li,t
·  i,t · wi,t .
(8)
Firms
There is a single homogenous good in the world produced by firms in each region according
to a Cobb-Douglas technology:

Yi,t = Ai,t · Ki,t
· L1
i,t
(9)
where Yi,t is the output, Ai,t is the total factor productivity (TFP), Ki,t is the capital
stock and Li,t is the labor.
Assuming that the depreciation of the capital is total during the period and that the
production sector is perfectly competitive implies that:
where ki,t =
1.4

wi,t = Ai,t · (1  ) · ki,t
(10)
1
Ri,t = Ai,t ·  · ki,t
(11)
Ki,t
.
Li,t
Closed-economy equilibrium
If considering closed economies, in each region and at each period, labor markets must
clear at equilibrium:
Li,t = Ni,t + Ni,t1 · li,t = (Gi,t + li,t ) · Ni,t , i, t
7
(12)
as also must financial markets:
Ki,t+1 = Ni,t · Si,t , i, t.
(13)
From eqs. (6), (10), (11) and (12) we can then show that in each region the dynamic
general equilibrium is characterized i and t by:
where i,t =


Ri,t+1 = Ri,t
· 1
i,t
(1+Âi,t+1 )·[·(Gi,t+1 +li,t+1 )+(1)·(1si,t )·(li,t+1 +Gi,t+1 · i,t+1 )]
(1)·si,t ·(1 i,t )

(14)
and
Ai,t+1
Ai,t

1
= 1 + Âi,t+1
.
i,t captures the regional relative tension between demand (numerator) and supply (denominator) of capital.
At the steady state, we have:

 [ · (G + l ) + (1  ) · (1  s ) · (l + G ·  )]
i
i
i
i
i
i
, i.
Ri = 1 + Âi ·
(1  ) · si · (1   i )
(15)
To calculate the steady state interest rates in the closed economies, let us assume that
a period corresponds to 30 years. If we assume that individuals enter in the job market
at age 18 and following demographic features of 2010 (see Table 1), we set N = 1 in the
North, i.e. corresponding with a life expectancy at age 18 of 60 years. Thereafter, as life
expactancy at age 18 is 55 years in the South, we set
1+S
2
=
55
60
and then S = 0.83. If
we assume an annual discount time factor equal to 0.98,  = 0.9830  0.55. As usual
we set the capital’s share in output to 0.3. If we assume that the demographic transition
is achieved in the North then we set GN = 1. The net annual population growth in
the South compared to the North in 2010, i.e. 1.3  0.3 = 1%, correspond then to an
increase of 34.8% over 30 years, (1 + 0.01)30 = 1.348. As the population in the South


at any date t corresponds anything else being equal to Nt + S · Nt1 = Nt · 1 + GSS ,
the factor of growth in the South population
Nt +S ·Nt1
Nt1 +S ·Nt2
is then equal to
Nt
Nt1
= GS ,
and we set accordingly GS  1.348. To reproduce the structure of the world population
in 2010, i.e. a share S of the world population in the South equal to 82%, we set
NN,0 = 20 and NS,0 = 113. We then consider the social security spendings towards old
people. In the North (OECD average in 2005), they represent 8.5% of GDP (Old Age,
Survivors and Health programs), i.e. approximately 12% of the wage bill:  N = 12%.
As to the South, lacking reliable data, we set  S = 4%, which is roughly consistent for
China and India. We consider in the North a legal age of retirement equal to 65 years,
8
i.e. lN =
17
30
= 0.57, and we assume for simplicity in the South that individuals work also
such that lS = 0.57. Finally, if we assume that there is no technological inovation in the
North and no technological convergence of the South to the North, the interest factor is
equal to 3.59 in the North and 4.16 in the South, which corresponds respectively to an
annual rate of 4.4% and 4.9%.


North (N) 0.3 0.55
South (S)

G
N0
1
1
20

l
Â
0.12 0.57
0
0.3 0.55 0.83 1.348 113 0.04 0.57
0
Table 3. Calibration parameters
Considering this calibration, we can observe that both North and South are characterized by an interest rate higher that the economic growth rate. This is obvious for the
North. As we consider no technological growth and no population growth, the economic
growth is nil. In the South, we have also considered no technological growth, but the
population is growing. The economic growth is then equal to the population growth, but
it is lower than the interest rate: rS,annual = 4.9% > gS,annual = 1.37%. As we will see,
this feature is important to analyse the impact of openness on both economies.
2
Openess and globalized finance
We consider now a financial globalized economy. The good and the financial asset are
freely traded on perfectly competitive world markets. Workers are not mobile; hence the
labor market is a local one. The capital market must clear at each date at equilibrium
such as:

i
Ki,t+1 =

i
Ni,t · Si,t , t.
(16)
From eqs. (6), (10), (11), (12) and (16), we can show that the world dynamic general
equilibrium is characterized by a unique interest factor.
Proposition 1: At the general equilibrium, the unique interest factor can be expressed
as a geometric average of the past interest factor and the weighted arithmetic average of
the regional tension between demand and supply of capital:
9
Rt+1 = Rt · 1
t
where t = (t · N,t + (1  t ) · S,t ) , t =
sN ·(1 N )·N,t
1
1
i si ·(1 i )·i,t ·Ai

(17)
 (0, 1] and i,t =
is the share of the region i in the world population.
N
 i,t
i Ni,t
t captures an international tension between demand and supply of capital.
Corollary 1: Starting from closed-economy steady states, everything else being equal,
openness yields:
t = t · RN + (1  t ) · RS
where RN and RS denote the closed-economy steady-states values of the interest factor
respectively in the North and in the South, and
1

1
1
1
1
R0 =  · RN + (1  ) · RS
where  =
(1+lN )·N,0
1
1
(1+lN )·N,0 +(GS +lS )·(1N,0 )·AS,0
 [0, 1].
If variables in the model are fixed, i.e. xi,t = xi t, where x = G, l, s,  , A, this
dynamics is rewritten as follows:
Rt+1 = Rt · [t · RN + (1  t ) · RS ]1
(18)
As the population is growing in the South while the North has already achieved its
transition and reached a steady state, it yields the limit case: lim N,t = 0 and then
t+
lim t = 0.
t+
As the interest rate in the South was higher than in the North, when financial markets
are liberalized, capital immediately flows from the North to the South to reach around
0.9% of South GDP as illustrated in Fig. 2. As a consequence, everything else being equal,
the world interest rate jumps to an intermediary level R0 =, i.e. on an annual basis (Fig.
). It increases regarding North, it decreases regarding South. As both closed economies
were dynamically ecient, it follows that the welfare in the South increases while it
decreases in the North. To evaluate the importance in the welfare change and avoid any
10
Figure 2: Openess without convergence
11
scale eect, we have computed the equivalent consumption eci,t which is the equivalent
constant consumption over the life cycle when considering no life expectancy change:


ln Ci,t +·i,t+1 ·ln Zi,t+1
ln eci,t +  · i,0 · ln eci,t = ln Ci,t +  · i,t+1 · ln Zi,t+1  eci,t = exp
,
1+·
i,0
t  0. We then observe on Fig that the equivalent consumption at date 0 increases by
2% in the South and decreases by 1% in the North. As the share of the South in the world
population is growing, if there is no technological growth and no institutional convergence,
the world interest rate progressively increases up to reaching the interest rate formerly
encountered in the South before openness. In such a case, it follows from (18) and from
our calibration that the world interest factor converges monotonously to one of the South
when closed: R = RS = 4.16. Therefore, the positive eect of openness on the welfare
in the South decreases with time up to reaching zero and the negative eect in the North
continue to increase up to stabilizing at 3.5% of equivalent consumption (Fig. 2).
However, we can have reasonable doubts about the relevancy of such a scenario to
describe the long term convergence of the world economy for at least three reasons. Firstly,
we can think that the world population and especially the South population will not
indefinitly grow. In that spirit, the United Nations (2004) has . Secondly, the present
scenario exhibits no wealth convergence from the South towards the North. Indeed, in
the world with globalized finance, we can show that the relative GDP per head in the
South compared with the North at date t  0 can be expressed simply.
Proposition 2: Openness, everything else being equal, yields:
YS,t
P opS,t
YN,t
P opN
lS
AS,t 1 + Gs,t 1 + N
=

AN 1 + lN 1 + GS,t
S,t
(19)
and therefore no wealth convergence from the South towards the North.
Therefore, if considering that AS,t = AS , GS,t = GS and S,t = S t  0,
YS,t
P opS,t
YN,t
P opN
is
a constant. By contrast, studies from Maddison (2008) and Wang et al. (2011) show
that estimate . As a demographic transition characterized with a decrease in GS and
an increase in s yields a decrease in the relative wealth of the South with respect to

the North,
YS,t
P opS,t
YN,t
P opN
GS

 0 and
YS,t
P opS,t
YN,t
P opN
S
 0, a converging wealth of the South to the North
requires then a technological catching-up. Thirdly, there is no institutional convergence,
 S,t =  S t. However, . In the following, we then study more satisfyingly the dynamics of
12
the world economy considering the global convergence in the three components mentioned
above, technological, demographic and institutional.
3
Global convergence
Assume now that openness goes with a global convergence. If we assume that the North
region has already converged to its final model of society, a global convergence means
that the South region will converge towards the North model of society characterized by
its technology, its population features (life expectancy and total fertility) and its social
protection here characterized by a PAYG pension scheme. From eq. (17) we can then
observe that a global convergence is characterized by the North interest rate:
R=
[ · (1 + l1 ) + (1  ) · (1  s1 ) · (l1 +  1 )]
(1  ) · s1 · (1   1 )
(20)
and as a consequence in the long run it has no impact on the North welfare. In order to
characterize the transition path from closed economies to fully converged economies, we
then need to specifiy the dierent processes of convergence linked to the technology, the
demography and the social protection.
To characterize the technological catching up, the North is assumed to be the technological leader and its economy is characterized by a stationary growth. In our calibration,
we assumed that the TFP in the North was AN = 1, higher than the TFP of the South,
AS when capital markets are opened, such as
AS,0
AN
= 23%. We now assume that openness
permits free technological transfers and, consequently, goes with a technological catchingup of the South to the North according to a process with decreasing return  A < 1 such

 A
AS,t
N
that AS,t1
= AA
for t  1. Note that  A characterizes also the speed of technoS,t1
logical convergence. Following this process, the TFP of the South converges progressively
towards that of the North. Similarly, to characterize the demographic transition in the
South, we assume that both its mortality rate and its fertility converge towards those
of the North which have already achieved its transition. Here, GS,t corresponds to the
fertility rate divided by two because each household is assumed to be composed of two
parents, and 1 + S,t is the life expectancy. The increase of the life expectancy in the
South is then described by
follows:
GS,t
GS,t1
S,t
S,t1


= S,t1
and the decrease of its fertility rate evolves as
G
= GS,t1
for t  1,   and  G being respectively the convergence speed of
13
life expectancy and fertility. Finally, we assume that the contribution rate converges to

 
 S,t
N
with   being
the one of the North and its dynamics is described by  S,t1 =  S,t1
the speed of institutional convergence.
Starting at date 0 from the observed world population in 2010 with N,0 = 18%, we
calibrate   =  G = 0.63 such that N,1 = and N, = 86.7% which are the structure
of the world population expected by the United Nations respectively in 2040 and in the
very long term when the world population would reach its stationary level (UN 2004).
Afterward, following eq. (19), we calibrate the speed of technological convergence  A such
that the relative GDP per capita in the South compared to the North reaches . It gives
us  A = 0.4. Finally, the speed of institutional convergence is set such that in 2040 . This
way we obtain a transition path from closed economies towards fully open and converged
economies. However, as this transition path results from the interaction of 4 dierent
processes of convergence, we assume a fictional convergence pattern such that the technological catching-up goes first, the demographic transition goes second and the institional
convergence goes third. Indeed, openness is first a sharing of ideas and knowledge which
means for the South and through trade exchanges a technological catching-up. Second,
the technological catching-up allows a reduction in mortality rates through medecine improvement. It leads also to a reduction of the fertility which with the moratlity reduction
characterizes the demographic tansition. Finally, through urbanization and social pressure, social protection follows. This way, we can decompose the transition pattern starting
from the technological catching-up.
3.1
Technological catching-up
Figure 2 presents the changes with respect to the simulations obtained in the economic openness configuration when no convergence of any type is assumed, i.e. only with
globalized finance. Unsurprisingly, in such a scenario the increase of the TFP in the
South boosts the demand for capital in the South. In addition, due to consideration of
life cycle, young workers in the South have first a lower saving rate with respect to the
previous simulation because they anticipate the increase of their future income due to the
stronger economic growth. The resulting eect is a higher world interest rate and, as a
14
Figure 3: Technological catching-up (changes wrt the scenario with globalized finance)
15
consequence, more capital flows from the North to the South. However, as the growth
rate of the TFP in the South slows down during the technological catching-up process, an
initially weaker saving rate in the South then becomes higher and eventually converges to
the same level as before. This higher saving rate in the South associated with the growing
share of South in the world population explains why capital flows going from the South
to the North is reduced and become even slightly negative. And finally, when the relative
population of the North becomes negligible, the world interest rate converges towards the
one of the South closed economy and capital flows as a percentage of the world production
become also negligible.
3.2
3.2.1
Demographic transition
Mortality reduction
Now, we consider that the technological diusion results in a medical progress which yields
a reduction in the mortality rate in the South. As evidenced by our simulations, people
in the South save more with respect to the previous case with economic openness and
technological catching-up because they tend to live longer. On the world capital market,
this eect has a negative impact on the interest rate. In return, people in the North save
less. Obviously, the capital flows to the South is firstly reduced. However, for the same
reason as in the previous section, when the relative population of the North becomes
negligible, capital flows as a percentage of the South production become also negligible.
As the social security size is less developed in the South, the interest rate converges to an
intermediate level between South and North closed economies.
3.2.2
Fertility transition
We consider now that the technological diusion results also in a "higher" education of
people which allows a better control of births, hence to a reduction in fertility rate. This
phenomenom associated with the mortality reduction illustrates the concept of demographic transition. Assuming  G = 0.63, we observe that the South population reaches
its steady state level after 15 periods. Compared with the previous scenario, we observe
that at steady state the share of South in the world population is 17% lower (Fig 3a),
which corresponds to 87% of the world population as estimated by the United Nations
(2004) in the very long term. From an economic perspective, as the growth of the working
16
Figure 4: Mortality transition (changes wrt the scenario with technological catching-up)
17
Figure 5: Fertility transition (changes wrt to the scenario with technological catching-up
and mortality transition)
18
population in the South is reduced, the demand of capital there is weaker. The interest
rate decreases to stabilize at % (on an annual ), i.e. minus approximatively 0.4% compared with the previous scenario (Fig ). Despite the weaker demand of capital in the
South, we observe that capital inflows to South in % of GDP (?) increases in the first
two periods. However, it characterizes the sharp decrease in the South saving rate as
exhibited in Fig (1.5% compared to the previous scenario) and a more intense decrease
in GDP than in capital inflows. Finally, following eq. (), the decrease in the working
population share in the South results in less wealth convergence such that the GDP per
capita in the South is more than 3% lower compared with the North GDP per capita in
the previous scenario.
3.3
Institutional convergence
We suppose now that this economic development (technological progress and demographic
transition) is associated with a social pressure for a better share of income between young
and old because, otherwise, old people would benefit less of growth than young people. A
higher social security size (via a higher contribution rate) reduces the savings in the South
with respect to the previous scenario. This reduction mimics the progressive increase of
the social security size. It follows that the net demand of capital is higher in the South.
On the world capital market, the interest rate is pushed up and the people in the North
save more. As a result, the capital flows from the North to the South are higher.
19
Figure 6: Institutional convergence (changes wrt the scenario with technological catchingup and demographic transition)
20
4
Welfare analysis
One important aspect on the economic consequences of openness is its impact on the
welfare of each generation. The figures 5a and 5b present respectively, for the North and
the South, the changes in the time path of their welfare with respect to their level in
closed economy.
The gross eect when we suppose no convergence is necessarily negative in the North
because of the property of dynamic eciency.
However, when it is assumed that openness can generate positive externalities on
the growth of TFP in the South through for instance technological transfers, the global
impact could be positive during the first periods of the transition path if a higher interest
rate would generate a strong positive income eect for old people. But our choice of
parameters does not allow to evidence this property. Conversely, a higher TFP in the
South attracts more capital from the North, leading to a weaker production in the North.
With our calibration, this eect is always dominating. Of course, if we suppose non stable
population in the South, the long run interest rate will be this one obtained in the South
closed economy, which leads to permanent negative eect on the welfare in the North
as previously discussed. In the South, an improved productivity of labor leads to higher
welfare.
In addition, if a demographic transition towards a stationnary population with higher
life expectancy is triggered, the direction of the net flows of capital reverse so that, finally,
the North receive transfers of capital from the South. Consequently, we observe a positive
gain in welfare after 5 periods. Of course, as people in the South are less numerous than
in a context of growing population and lives longer, they benefit of a higher welfare.
Moreover, if the South adopts the North social security standards, the South saves
less and globally there is less productive capital in both the North and the South and
consequently, in both regions, people benefit from a weaker welfare with respect to the
previous scenario. In the long run, the welfare levels in the North and the South converge
to the same level as the one observed in the North closed economy because the two regions
are identical.
21
22
Conclusion
This paper develops a tractable two-period two-region OLG model. We give the analytical solution of the dynamics of the world interest rate. This analytical approach exposes
clearly the existing interactions between the dierent regional components of world equilibrium, contributing to a better understanding of the main mechanisms implicated in
globalization.
This result is completed by numerical simulations. In a context of large domestic
dierences, our study allows to analyse global consequences from trade between the developed and emerging regions. The calibration set mimics the North-South opposition
as described by macroeconomic and demographic empirical data bases (UN, 2008; CepiiCHELEM, 2010). Precisely, we investigate three types of convergence associated with
economic openness. Our results show that the technological catching-up alone leads to
the maximum welfare loss for the North. If we add to this first change a demographic
transition, the gain of wefare is maximum in the South and the North obtains positive
welfare gain in a finite horizon. Finally, an institutional convergence of the two pension
schemes reduces saving rate in the South and induces loss of welfare in the North for any
subsequent period.
The advantages of our approach rooted in an analytical framework are multifold.
First, tractability allows to evidence clear-cut transitory dynamics. Second, it gives way to
possible investigations of general analytical properties. And last, the following extensions
may be contemplated: "true" spatial setting (several countries or regions more precisely
or realistically dierentiated) ; mobile workforce (migration) ; the taking into account
of workers’ qualifications; the linking of development issues to the economic geography
literature (Krugman, 1991; Abdel-Rahman et al., 2005).
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Mathematical Appendix
From eqs. (11) and (12) we have:

i
Ki,t+1 =

(Gi,t+1 + li,t+1 ) · Ni,t · ki,t+1 .
1

i
(21)
From (10) and (11), it follows that wage in each region depends on the world interest
rate:

1
1
· (1  ) ·  1 · Ri,t
.
wi,t = Ai,t
From eqs. (6) and (8), we have:
26
(22)
Si,t = si,t · (1   i,t ) · wi,t  (1  si,t ) · (li,t+1 + Gi,t+1 ·  i,t+1 ) ·
wi,t+1
.
Rt+1
(23)
From eq (22) it follows that:
Si,t = si,t · (1   i,t ) · wi,t  (1  si,t ) · (li,t+1 + Gi,t+1 ·  i,t+1 ) ·
1

· ki,t+1 .
(24)
It follows that:

i
Ni,t · Si,t
=


i Ni,t · si,t · (1   i,t ) · wi,t  (1  si,t ) · (li,t+1 + Gi,t+1 ·  i,t+1 ) ·
.
1

· ki,t+1
(25)

Following eqs. (16) and (11), the dynamic general equilibrium can be characterized
by:
Rt+1 = Rt ·

1

1
i [·(Gi,t+1 +li,t+1 )+(1)·(1si,t )·(li,t+1 +Gi,t+1 · i,t+1 )]·i,t ·Ai,t+1
1

1
(1)· i si,t ·(1 i,t )·i,t ·Ai,t
1
(26)
and at the steady state, the interest factor is:
R=
with  i =

Ai
A1
1
 1

i )·(li +Gi · i )]·i · i
i [·(Gi +li )+(1)·(1s

(1)·
i si ·(1 i )·i · i
.
Sensitivity analysis
27
(27)
Figure 7: Sensitivity techno
28
Figure 8: Sensitivity mortality
29
Figure 9: Sensitivity Ferti
30
Figure 10: Sensitivity Social Security
31