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The Balassa-Samuelson e¤ect in a
developing country�
Karine Gentey
�I wish to thank two anonymous referees, M. Aloy, P. Bacchetta, B Decreuse, J. De Melo, M. Devereux,
M. Leòn Ledesma and participants to OLG seminars in Marseilles for their helpful comments. The usual
disclaimer applies.yCEDERS, University of Aix-Marseilles II, 14 avenue Jules Ferry, 13621 Aix-en-Provence, FRANCE,
Tel : 33-4-42 91 48 26, Fax : 33-4-42 91 48 29, e-mail: [email protected].
1
Abstract Some Asian countries experience small real exchange rate appreciations or
even a real depreciation despite a fast growth in tradable productivity. A key-
characteristic of these countries is that they are constrained on capital in�ows. Is
the Balassa-Samuelson theory still valid in those countries? Are there other factors
likely to explain real exchange rate (RER) changes? To address these questions we
develop a two-sector model in which a small open economy faces a constraint on
capital in�ows. In this setting, the RER does not only depend on productivity but
also on other factors like the rate of time preference, the age dependency ratio or
the level of the external constraint. A calibration of the constrained economy model
seems to match at least qualitatively empirical evidence for China, Hong Kong,
Indonesia, Malaysia, Thailand and Singapore between 1970 and 1992.
Key-words: Real exchange rate; capital in�ows constraint; overlapping generations; pro-
ductivity shock.
Classi�cation J.E.L.: E39; F00; F20.
2
1 Introduction
How does the real exchange rate (RER) react to changes in factor productivity?
The usual answer to this question hinges on Balassa (1964) and Samuelson (1964)
analyses. They analyze the RER determination in a two-sector economy - tradable and
non-tradable goods- with international capital mobility and perfect factor mobility be-
tween sectors. They obtain two main conclusions. First, the RER is fully determined by
the supply side of the economy. Second, an increase in tradable productivity leads to a
real appreciation.
The traditional Balassa-Samueslon (BS) theory is often considered as relevant to ex-
plain the real appreciation experienced by developing countries. However, most of the
time in such countries, international factor mobility is imperfect because foreign investors
require risk premia. The empirical evidence is not always in accordance with the BS analy-
sis. Surveying the empirical papers, Section 2 shows that the BS theory works for OECD
countries and especially for Japan. Nevertheless, in developing countries the growth in
tradable productivity seems unable to explain the RER appreciation.
Some Asian countries experience small RER appreciations or even a RER depreciation
despite a fast growth in tradable productivity. Considering these controversial empirical
results, this article aims at studying the RER reaction to a tradable productivity shock
when key-characteristics of developing countries are taken into account. In particular,
what would happen if a risk premium was explicitly spelled out, that is if capital was
not perfectly mobile? Would the Balassa Samuelson theory still be valid? Are there any
factors other than productivity likely to explain RER changes?
To address these issues, this article deals with the case of a developing country which
faces a constraint on capital in�ows1. We build an OLG model as Obstfeld and Rogo¤
(1996) where it is assumed that for exogenous reasons - such that political risk or high
in�ation for example - the developing country under study can only borrow up to a given
amount of capital on the world market. In this setup, we introduce a two-sector/two-
3
factor structure and investigate the RER reaction to a rise in tradable productivity. The
model encompasses both the constrained case where the domestic interest rate exceeds
the world interest rate, and the traditional BS case, where the domestic and world returns
on capital converge.
In the constrained case, the RER results from supply and demand mechanisms: it
depends not only on growth but also on preferences and age pyramid. As in the BS case,
the rise in tradable productivity leads to a new factor allocation between sectors. This
partial equilibrium mechanism a¤ects the returns on each factor: the domestic interest
rate increases while the wage decreases. Hence, unlike the BS case, the rise in tradable
productivity lowers aggregate demand through these factor returns changes and the RER
may depreciate.
Several theoretical papers have already explained that the RER departs from the level
predicted by the BS analysis. Grafe and Wyplosz (1997) and Mahbub Morshed and
Turnovsky (2004) introduce an imperfect allocation of factors between sectors, whereas
Devereux (1999) considers that the PPP on tradable does not hold due to the existence
of a distribution sector.
Considering imperfect labor mobility, Grafe and Wyplosz (1997) show that transition
countries require a real appreciation - exogenous - to promote economic growth. Thus,
the BS e¤ect is reversed: the rise in tradable productivity, endogenous, is a reaction to
the real appreciation.
Mahbub Morshed and Turnovsky (2004) introduce intersectoral adjustment cost on
capital in a dependent economy. Out of the steady state, the model explains the RER
dynamics2from both supply and demand factors as public spending for example. Never-
theless, in the long-run, the BS analysis holds: an increase in tradable productivity always
leads to a real appreciation.
Finally, Devereux (1999) considers three di¤erent sectors: the tradable one, the non
tradable one and the distribution services sector where monopolistic competition is as-
sumed. Due to the existence of the distribution sector, the �nal goods price of traded
4
commodities contains non-traded elements. As in the BS theory, faster tradable produc-
tivity growth leads to a rise in the price of non-traded goods. However, the domestic price
of the traded goods - which is a combination of the (exogenous) world price of tradable
goods and the price of the distribution services - may decrease. This fall in the domestic
price of traded goods generates a fall in the RER despite higher productivity growth in
the traded sector. Devereux (1999) provides thus an explanation of the real depreciation
experienced by Asian countries.
The constrained economy we develop is an alternative: a rise in tradable productivity
may theoretically lead to a real depreciation too. However, the theoretical global e¤ect
of a rise in tradable productivity remains indeterminate. A calibration of the model
shows that the RER still appreciates after a rise in tradable productivity but less than
predicted by the BS theory. In this way, the Balassa-Samuelson e¤ect remains valid in
a constrained economy but productivity is not the only determinant of the RER. Some
other factors have to be considered when the country is constrained on capital in�ows.
When we consider the high growth rates and the fall in age dependency ratios, key-
characteristics of Asian countries during these last thirty years, the Balassa-Samuelson
e¤ect is partly o¤set: the RER experiences a small appreciation or even a depreciation.
The model seems to match empirical evidence at least qualitatively for China, Hong Kong,
Indonesia, Malaysia, Thailand and Singapore between 1970 and 1992.
Among this literature, the model we present in the next section departs from the
standard BS analysis considering that the world capital markets are imperfect. Section 2
surveys the empirical literature. Section 3 introduces the model, the temporary equilib-
rium and the steady state. Section 4 presents the impact of a rise in tradable productivity
in a general case compared with the special BS issue and confront the model to empirical
evidence. Section 5 provides some conclusions.
5
2 Empirical literature
We review brie�y the BS analysis before surveying the empirical literature. Empirical
evidence o¤ers little support to the BS theory, especially in developing countries.
The BS analysis states that an increase in tradable productivity leads to a RER appre-
ciation when there are both perfect international capital mobility and perfect intersectoral
factor mobility. Consider a two-sector static economy. Assume that production in the
tradable and in the non-tradable sectors resulting from two neoclassical production tech-
nologies, respectively F and H, using two inputs, labor L, and capital K. Both inputs
are perfectly mobile between the two sectors provided that
KT +KN = K (1)
LT + LN = L (2)
where Ki and Li, i = T;N , are the quantities of capital and labor used by sector i. Let
ki � Ki=Li be the capital intensity of sector i and li � Li=L be the share of labor demand
allocated to sector i. The mobility of factors implies
kT lT + kN lN = k (3)
lT + lN = 1 (4)
We adopt the following intensive notation for production f (kT ) � F (kT ; 1), h (kN) �
H (kN ; 1). Let also R be the relative price between non-traded and traded goods: R �
PN=PT . Pro�t maximization and competition among �rms imply that production factors
are paid their marginal product
aTf0 (kT ) = RaNh
0 (kN) (5)
aT [f (kT )� kTf 0 (kT )] = RaN [h (kN)� kNh0 (kN)] (6)
where aT (resp. aN ) denotes tradable (resp. non-tradable) productivity.
6
These conditions lead to a factor allocation which only depends3on the relative price
between the non-tradable and the tradable good: kN � kN (R; aT ; aN), kT � kT (R; aT ; aN) :
Perfect international capital mobility implies
aTf0 (kT (R; aT ; aN)) = �r (7)
where �r is the world interest rate. Di¤erentiating (7), we �nally get
_R
R=_aTaT� � _aN
aN(8)
with4� > 1 when the tradable sector is capital intensive5i.e., when kN < kT ; an assumption
we consider satis�ed hereafter. According to equation (8), the BS theory points out that
faster growth in tradable productivity aT leads to a rise in the relative price of the non-
traded goods. We review hereafter the econometric tests of equation (8).
The empirical literature usually proceeds in two stages. First, the linkage between
the logarithm of the e¤ective RER qt and the relative price between non tradable and
tradable goods, logR = pN � pT , where pN (resp. pT ) is the logarithm of the price index
of the sector non-tradable (resp. tradable), is tested. Second, the relationship between
the RER and the productivity spread between sectors is tested.
Let the aggregate price index for the home country be a combination of the prices of
the two types of goods: pt = (1� �) pNt + �pTt, where � 2 (0; 1) denotes the share of
traded goods in the price index. The global price index for the foreign country stands for
p�t = (1� �) p�Nt+�p�Tt. Let st be the logarithm of the exchange rate, de�ned as the foreign
currency price of domestic currency. Using the de�nition of the RER, qt � st+pt�p�t , the
relationship between the RER and the relative prices between non-tradable and tradable
goods is
qt = (st � p�Tt + pTt) + (1� �) [(pNt � pTt)� (p�Nt � p�Tt)] (9)
As a �rst step, the PPP on tradable goods is tested, that is st = p�Tt� pTt: If the PPP on
tradable holds, the RER is highly correlated with the di¤erence between the relative price
between non-traded and traded goods in domestic and foreign countries. The evidence is
7
mixed. First, empirical evidence assembled by Engel (1993), Lapham (1995), Engel and
Rogers (1996), and Knetter (1997) show that there are large deviations from the law of
one price for many traded goods in disaggregated price data. Engel (1999) shows that
the variance of changes in the international relative price of traded goods - i.e., the �rst
term of equation (9) - account for 90% of the overall variance of RER changes in variance
decompositions of RER on the USD exchange rate against currencies of high-income
countries. Nevertheless, Engel said that �the evidence (...) suggests that the relative
price of non-traded goods has little importance for understanding US RER movements
over the short and medium-run�. This conclusion points out that in the long-run we
should follow Engel (1996) since his results show that the second term of equation (9)
accounts for about half of the variance of the RER. Moreover, evidence suggests that the
�rst component of equation (9) is small for developing countries.
Second, using a database of 13 OECD countries between 1960 and 1993, Canzoneri
et al. (1999) conclude that the null hypothesis of no mean reversion can be rejected on
panel data. Finally, Betts and Kehoe (2001) show, using bilateral RER of 52 countries
between 1980 and 2000, that the relative price of non-traded goods and the RER are
closely related. The relative price of non-tradable goods accounts for one third of all real
exchange rate �uctuations and is higher when trade intensity between countries increases
or when the RER has low variability.
However, these controversial results legitimate to think that in the long-run, especially
in developing countries, relative price of non-tradable goods and RER are closely related
and deviations from PPP seems to be temporary, resulting from monetary phenomena.
In our theoretical model we will use a real OLG model which enables us to focus on a
long-run horizon. Hence, in the next section the RER is assumed to be the relative price
of the non-tradable good R - a rise in R means a real appreciation.
According to (8), the relative price of non-traded goods should re�ect the productivity
spread between sectors and countries
qt = (1� �) [(aT � aN)� (a�T � a�N)] (10)
8
The second step of most econometric analysis consists of estimating a long-run relationship
between RER and productivity spread. According to Ito et al. (1999), real exchange rates
and growth are positively correlated in Japan, Korea, Taiwan, Hong Kong whereas the
correlation remains negative for Indonesia, Thailand, Malaysia, Philippines and China.
Hong Kong, Taiwan and Singapore combine a high growth rate and a small appreciation.
There is a consensus that, in Japan, the BS theory holds ( "It is well known in the literature
that the postwar Japanese record has been a prime example of the BS hypothesis (Ito an
al., 1999) "). For other Asian countries except China, Singapore, Taiwan and Thailand,
Chinn (2000a) �nds that the productivity explains RER only when public spending and
oil prices are taken into account. Chinn (2000b) �nds with a panel data test that the RER
requires around 5 years to converge to the level predicted by BS. In contrast, there is no
mean reversion considering only time series data. Finally, Canzoneri et al. (1999) provide
similar results on OECD countries. To sum up, the BS theory seems to be empirically
validated on panel data while it cannot be when tested on time series.
All these empirical papers suggest that except for Japan there is no consensus on
the validity of the BS theory. Moreover, productivity spread seems to provide a better
explanation for RER changes in developed countries. In developing countries, especially
for China, capital markets are not fully liberalized and recent changes in the structure of
exports lead to an imperfect intersectoral labor mobility. Hence, the �t of the BS theory
to explain RER changes seems to be very poor.
The model we present in the next section departs from the standard analysis by
considering that the world capital markets are imperfect. Equation (7) does not hold and
hence, there is a gap between the world and domestic returns on capital.
3 The model
The model is a variant of the small open economy overlapping generations model of
Obstfeld and Rogo¤ (1996) in which we introduce two production sectors.
9
3.1 Individuals
The economy consists of a sequence of two-period lived individuals. In the second period
of his life, each individual gives birth to 1 + n others so that the per period rate of
population growth is n. At time t, each generation consists of Nt identical individuals
who make decisions concerning consumption and savings.
Intertemporal preferences of an individual belonging to generation t are represented
by
U (ct; dt+1) = � ln ct + (1� �) ln dt+1 (11)
where ct and dt+1 are respectively composite consumption when adult and composite
consumption when old; � 2 (0; 1) denotes individuals�thrift.
Let x = c; d denote individual consumption at each period of life, xN and xT be respec-
tively the spending allocated to non-traded and traded goods. Instantaneous preferences
are de�ned according to:
u (xT ; xN) = x�Tx
1��N , 0 < � < 1 (12)
As in Section 1, the relative price of the non-traded good in terms of the traded good R
is the real exchange rate.
Following Obstfeld and Rogo¤, the small economy faces a constraint on capital in�ows
Bt+1 � ��Ntwt (13)
where Bt+1 denotes the net foreign assets of the domestic country in terms of traded goods
and � > 0 is the proportion of the wage bill6(Ntwt) the domestic country can borrow.
The consequence of this assumption is that the domestic return on capital may be higher
than the world one.
During the �rst period of life, individuals o¤er labor inelastically and distribute their
earnings wt among own consumption spending �tct and savings
�tct + (1 + n) kt+1 + (1 + n) bt+1 = wt (14)
10
where kt+1 is the whole capital stock per young agent in terms of traded goods and
bt+1 = Bt+1=Nt+1 the net foreign assets per young. The price of the tradable good is
normalized at unity. We denote the composite consumption good by x � x�Tx1��N with
x = c; d to specify the same preferences among the two goods at each life period and
�t the consumer price index. National savings can be held into two forms, capital stock
and net foreign assets. Since the returns on these stocks are di¤erent, the agents choose
both the amount of their savings st and its allocation between the two assets. To take
into account this arbitrage, we assume following Obstfeld and Rogo¤ that the constraint
on capital in�ows works at the microeconomic level. This assumption means that banks
cannot lend more than �wt to each individual at the world market interest rate �r. Agents
know both the world and domestic returns on capital. A spread between these two returns
is a new potential source of income for them: they can borrow from the world market to
lend on the domestic market and realize a capital gain.
When old, individuals are retired and consume the proceeds of their savings according
to
�t+1dt+1 =�1 + rdt+1
�(1 + n) kt+1 + (1 + �r) (1 + n) bt+1 (15)
The domestic return on capital is the market interest rate rdt+1 whereas the world return
�r is �xed according to the small open economy assumption.
The maximization program of an individual born in period t solves in two steps. First,
the individual chooses �tct and bt+1 to maximize life-cycle utility (11) under the budget
constraints (14), (15) and the capital in�ows constraint
bt+1 � ��wt1 + n
(16)
Second, he shares his consumption spending (�x) between the two goods xN and xT to
maximize instantaneous utility (12) under the spending constraint �x = RxN+xT . Hence,
the allocation of total consumption spending between the two goods at each period is
xT = ��x
RxN = (1� �)�x
11
where the price index is � = � (�)R1��, with � (�) � ��� (1� �)��1.
Young and old agents�consumption functions are
�tct = �
�wt �
rdt+1 � �r1 + rdt+1
(1 + n) bt+1
�(17)
�t+1dt+1 = (1� �)��1 + rdt+1
�wt �
�rdt+1 � �r
�(1 + n) bt+1
�(18)
Individuals consume a proportion � of their life-cycle income during the �rst period of
life and the remaining when old. Life-cycle income consists of the wage w and the capital
gain they may realize borrowing at world rate �r to invest in domestic capital whose return
rd is higher than �r.
3.2 Production Sectors
The production side is the same as in Section 2. Investment transforms instantaneously a
unit of tradable good in a unit of installed capital: Kt+1 = It and capital fully depreciates
after one period.
The allocation of factors between sectors is de�ned by (5) and (6). This means that
kN and kT depend only on RER whereas the allocation of labor depends both on capital
intensity and RER. Hence, kN � kN (R) and kT � kT (R), while lN � lN (k;R) and
lT � lT (k;R). From (3), (4), (5) and (6), the optimal factor allocation satis�es
dkNdR
=aTf
R2aNh00 (kN � kT )(19)
dkTdR
=RaNh
f 00aT (kN � kT )(20)
Similarly, @lN=@k S 0 if kN S kT and @lN=@R > 0. When the tradable sector is capital
intensive, a real appreciation leads to an increase in both capital intensities kN and kT
whereas labor moves from the traded to the non-traded sector. These factor movements
re�ect that a real appreciation makes the non-tradable sector more attractive. Assuming
perfect intersectoral mobility, the returns on capital rd � aTf 0 (kT (R)) = rd (R) and labor
w � aT [f (kT (R))� f 0 (kT (R)) kT (R)] = w (R) only depends on the RER R.
12
We depart from the BS theory by assuming that there is a constraint on capital
in�ows and thus equation (7) may not hold. Hence, factor movements a¤ect both returns
on factors and hence agents�income.
3.3 The temporary equilibrium in the constrained case
We study the temporary equilibrium in the case where the capital in�ows constraint
binds. This creates a gap between domestic and world returns on capital. This gap - in
accordance with risk premia phenomenon - re�ects that developing countries do not have
access to perfect international capital markets: the return on domestic capital rdt+1 must
be higher than the world market interest rate �r to o¤set bad economic conditions in these
countries.
The period-t temporary equilibrium conditions are
(i) Capital market equilibrium. Given the optimal intersectoral factor allocation
kT (R) and kN (R), net foreign assets per capita are given by
bt+1 = ��w (Rt)
1 + n(21)
Let � (Rt+1) � ��rd (Rt+1)� �r
� �1 + rd (Rt+1)
��1be the arbitrage premium which de-
pends on the interest rate gap between domestic and world capital markets and on pro-
portion � of the wage bill agents can borrow. The higher � the higher the capital gain
agents realize. Therefore, capital per worker is
kt+1 = [1 + � � � (1 + � (Rt+1))]w (Rt)
1 + n(22)
(ii) Labor market equilibrium. The inelastic labor supply Nt is equal to the labor
demand Lt. Given the capital market equilibrium, the wage w equalizing labor supply
and demand is de�ned by
w (Rt) � aT [f (kT (Rt))� kT (Rt) f 0 (kT (Rt))] (23)
(iii) Non-tradable goods market equilibrium. There are Nt young agents and
13
Nt�1 old agents. Hence, the equilibrium on the non tradable goods market is
(1� �) (Nt�tct +Nt�1�tdt) = RtYN (kt; Rt) (24)
where consumption spending is given by equations (17) and (18) and YN (kt; Rt) �
aN lN (kt; Rt)Nth (kN (Rt)) :
Equation (22) describes the allocation of savings between the two assets. It o¤ers a
�rst dynamic relationship between RER and capital intensity. Using (21), (23) and (24),
with consumption spending given by (17) and (18), we get a second dynamic relationship
between RER and capital intensity:
(1 + � (Rt+1)) �w (Rt)+1� �1 + n
(1 + � (Rt))�1 + rd (Rt)
�w (Rt�1) =
aN lN (kt; Rt)Rth (kN (Rt))
1� �(25)
Given K0, and L0, the dynamic system made of equations (22) and (25) yields the paths
of the two variables kt and Rt. Then, given B0, equation (21) determines the path of the
current account.
3.4 Steady state in the constrained case
The country faces a credit constraint7and, even in the long-run, the domestic return on
capital is higher than the world return i.e., the arbitrage premium remains positive. Thus,
solving long-run steady state is equivalent to �nding (k�; R�) such that
k� =w (R�)
1 + n[1 + � � � (1 + � (R�))] (CA)
R�yN (k�; R�)
1� � = w (R�) (1 + � (R�))
�� +
1� �1 + n
�1 + rd (R�)
��(NM)
where yN � YN=Nt is the non-tradable production per worker. Equation (CA) is the
long-run capital accumulation condition. It de�nes an increasing locus between k and R
since dw=dR > 0 and drd=dR < 0. Equation (NM) is the long-run non-tradable market
clearing condition. The slope of the corresponding locus is ambiguous.
Hereafter, we assume that there exists a unique steady-state (k�; R�). This implies the
slope of (NM) is lower than the slope of (CA) in (k�; R�). Formally, consider the function
14
� � (�1; �2) such that
�1 (k;R) = k �w (R)
1 + n[1 + � � � (1 + � (R))] (26)
�2 (k;R) =RyN (k;R)
1� � � w (R) (1 + � (R))�� +
1� �1 + n
�1 + rd (R)
��(27)
The steady-state solves � (k�; R�) = 0. Let J denote the Jacobian matrix of function �
evaluated in equilibrium. We assume for uniqueness that8detJ > 0 i.e.,������@�2(k
�;R�)@R
R�aNh
kN�kT
����� >�����@�1 (k�; R�)@R
���� (28)
The key-characteristic of this economy is the presence of � in equations (26) and (27)
With a constraint on capital in�ows, equation (7) does not hold and the level of the RER
depends not only on sectoral productivity spread but also on the rate of time preference,
the rate of population growth, and the share of non-tradable goods in consumption. A
fall in the domestic rate of time preference � leads to higher savings, higher wealth and
higher non-tradable consumption, entailing a real appreciation. A fall in the share of
traded goods in consumption � leads to a rise in the consumption of non-traded good
and hence to a RER appreciation. A fall in the rate of population growth n means that
population is getting older. Since young agents save and old agents consume the proceeds
of their savings, a fall in n leads to a rise in non-tradable good consumption and hence a
RER appreciation.
This model provides thus new potential sources of RER appreciation. Indeed, in such
a constrained economy, demographic transition going together with development may lead
to a real appreciation. At the opposite to the Balassa-Samuelson analysis, the sectoral
productivity growth is not here the only determinant of the long-run RER. This model
enables to understand why empirical studies are sometimes forced to take into account
other determinants of the RER like public spending9to validate the Balassa-Samuelson
e¤ect. We could also argue that Hong Kong, Taiwan and Singapore experienced only a
small real appreciation despite a high growth rate because changes in tradable productivity
when together with changes in n or �. Figure 1 plots the age dependency ratios for some
15
Asian countries. Hereafter we will always refer to these countries because according to
Ito and Symansky (1999), the BS analysis does not hold (see Section 2). It depicts a
decreasing trend for all countries. This fall in the age dependency ratio comes from a
rising size of the working age population, resulting from an increasing participation of
women in the labor market. The model we develop suggests that the fall in n tends to
depreciate the RER. This depreciating e¤ect may have partly o¤set the real appreciation
generated by growth.
[INSERT Figure1 Here]
Does this empirical evidence explain the real depreciation experienced by China, Indone-
sia, Malaysia and Thailand despite the rise in productivity? What becomes in such an
economy the Balassa-Samuelson e¤ect?
4 An increase in tradable productivity
In this section, we study the steady-state e¤ects of a tradable productivity increase. First,
we show the BS analysis may not always hold in the constrained economy (CE). Second,
we calibrate the model to show that even if underlying mechanisms are very di¤erent to
those pointed out by the Balassa-Samuelson analysis, the RER still appreciates when the
country is credit constrained. Finally, we show that the CE model matches empirical
evidence when we consider both growth and a fall in the age dependency ratio.
4.1 Theoretical e¤ects
To highlight the dependency vis-à-vis aT , let w� � w (R�; aT ), rd� � rd (R�; aT ), �� �
� (R�; aT ), k�i � ki (R�; aT ), l�i � li (k
�; R�; aT ), i = N; T , and y�N � yN (k�; R�; aT ). We
have @w�=@aT < 0, @rd�=@aT > 0, @��=@aT > 0, @y�N=@aT < 0 if kN < kT . The RER
reaction to an increase in tradable productivity is given by
dR�
daT=
�1detJ
�� R�aNh
(kN � kT ) (1� �)@�1@aT
� @�2@aT
�(29)
16
We know from the uniqueness condition (28) that the determinant of the Jacobian matrix
J is positive and @�1=@aT T 0 when kN S kT , while @�2=@aT remains indeterminate.
An increase in tradable productivity may lead to a RER depreciation when kN < kT if
@�2=@aT < 0.
In the BS case, the arbitrage premium vanishes, since according to equation (7) do-
mestic and world returns on capital converge, we have �� = 0: As a result, an increase
in tradable productivity always gives rise to a RER appreciation. Indeed, the rise in aT
leads to a real appreciation since @rd�=@R < 0; @rd�=@aT > 0 and rd� = �r:
The main di¤erence between the constrained economy (CE) and the BS case is that
equation (7) does not hold. Hence, in the CE the arbitrage premium �� is positive because
there is a gap between domestic and world returns on capital. As a result, R� is not fully
determined by the supply side. It depends, as k� does, on both supply and demand
variations. Consequently, we recover in the CE the BS e¤ect on factor movements, but
the RER reaction depends on additional demand e¤ects due to changes in factor returns.
On the supply side, as in the BS case, an increase in tradable productivity leads to a
new factor allocation: capital and labor move from the non-traded to the traded sector
exerting a negative e¤ect on non-traded good production.
On the demand side, the domestic return on capital rd increases while the wage w
decreases. These changes in factor returns a¤ect the demand for non-tradable goods.
The mechanisms are the following:
- a fall in w reduces the agents�income and the amount the country can borrow on
the world capital market.
- a rise in rd increases the arbitrage premium and hence the capital gain agents can
realize from borrowing at �r and lending to domestic �rms at rd (�� > 0):
Let the consequences of this rise in rd (drop in w) on consumption spending be the
positive interest rate e¤ect (negative wage e¤ect). The negative wage e¤ect lowers savings
and the amount the country can borrow. Finally, the global capital intensity k� is reduced
and since @y�N=@k� < 0 the supply of non-traded goods may increase as the capital stock
17
decreases.
Through equation (29), the global long-run e¤ect on the RER depends both on these
supply and demand variations. It follows the RER may depreciate when non-tradable
production �nally increases and non-tradable consumption decreases, or when the fall in
non-tradable production exceeds the fall in non-traded goods demand. Nevertheless, the
global e¤ect of such a productivity shock remains theoretically indeterminate. Hereafter,
we illustrate it using a calibration exercise.
4.2 Calibration
We calibrate the model assuming Cobb-Douglas production functions. Let the production
functions be f (kT ) = (kT )� and h (kN) = (kN)
�. Table 1 reports the value of parameters
used in the calibration.
[INSERT Table 1 Here]
We assume as in Mahbub Morshed and Turnovsky (2004) that the productivity is higher in
the traded sector and that half of consumption is spent on non-traded good. We choose
the elasticities of substitution between labor and capital for the two sectors to match
empirical evidence10: 40% of total output11is traded with 37% of labor being employed
in that sector. With � = 0:2 and � = 0:65; the tradable sector is capital intensive and
we have lT = 35:98% whereas YT=Y is1256%: If each period represents 25 years, �r = 0:37
means that the world real interest rate is about 1:25% per year. In accordance with Beine
et al. (2001), let � be 0:5 to have a domestic rate of time preference of around 3:7%. The
choice of a numerical value for parameter n is motivated by the following �gures.
[INSERT Table 2 Here]
Table 2 collects the age dependency ratios (the ratio of dependents to working age popu-
lation) in some developing countries. To be consistent with these �gures, the dependency
ratio13should be around 63% (so that n ' 0:58). Assuming that each generation lives 25
years, n = 0:6 corresponds to a rate of population growth about 1:9% a year.
18
Finally, the key-parameter of our model is �: First, � indicates the capacity for a
country to borrow from the rest of the world. Second, � is a determinant of agents
income as it measures the magnitude of arbitrage premia. From (21), the constraint is
binding. Thus, we evaluate the parameter � on the basis of � = �B=(0:75Y ) with 0:75Y
the labor income share of GDP14. Figure 2 shows that very often � � 0:3
[INSERT Figure 2 Here]
As � increases, the long-run domestic return on capital converges to the world return on
capital. Indeed, the higher �; the higher the life-cycle income and non-tradable consump-
tion, the more appreciated the RER. When the tradable sector is capital intensive, the
domestic return on capital is a decreasing function of �: Thus, there exists �� > 0 such
that rd = �r: When � < �� the country is credit constrained and the RER results from
demand and supply on non-tradable goods. Otherwise, we recover the Balassa-Samuelson
(BS) case and the RER only depends on productivity spread between sectors. In this
calibration, �� > 4:9.
[INSERT Table 3 Here]
Table 3 gives the reaction of the long-run RER in the traditional BS case - that is with
perfect capital mobility (�� = 0)- and in the CE - that is rd (R�) > �r (�� > 0)- after a
30% increase in tradable productivity. I reported domestic interest rates and wages too
to check that rd�i > �r i = 0; 1 is always ful�lled. Let 0 denote the initial steady state and
1 the steady state with a higher tradable productivity. We could notice that the domestic
interest rate shows very low �uctuations15while the wage increases. A rise in aT exerts a
positive direct e¤ect and a negative indirect e¤ect (through the rise in kT ) on rd: Since,
the rise in aT leads to an increase in tradable production the wage increases even if the
domestic interest rate is constant.
We observe that the behavior of the RER is very similar in the CE case and in the BS
setting. Hence, the presence of a credit constraint does not a¤ect the qualitative result:
the RER still appreciates after a productivity shock. Nevertheless, this real appreciation
19
results from a rise in non-tradable demand that overcomes the rise in non-tradable supply.
In contrast, in the BS case the real appreciation results only from factor movements
between sectors. Figure 3 plots the RER reaction to a 30% rise in aT for di¤erent levels
of the constraint � and in the BS case. The level of the constraint is reported near each
point while the BS case is depicted by the larger line.
[INSERT Figure 3 Here]
We observe that � a¤ects the RER reaction to a rise in aT . Indeed, a rise in aT leads
to a new factor allocation between sectors. These factors�movements do not depend on
the level of the credit constraint � whereas the long-run global capital intensity k� does.
According to equation CA, the higher � the larger is the negative wage e¤ect. The more
the country can borrow on the international capital market, the larger the fall in k� which
results from the productivity shock and hence the larger the rise in the production of
non-traded good. It follows that the real appreciation is milder when the country is less
constrained since the production of non-traded good increases more after a productivity
shock. We can notice that the RER appreciation predicted by the CE model even with
� = 0 remains lower than the RER appreciation predicted by the BS analysis.
Finally, the Balassa-Samuelson analysis seems to be still valid in the presence of a
credit constraint. However, the CE model suggests that RER changes experienced by
Asian countries do not only result from productivity shocks but also from other structural
parameters. In the BS case, the RER appreciation could only be explained by a faster
growth in tradable productivity. In the CEmodel, the real appreciation could be explained
by a faster growth in tradable productivity or by a fall in the birth rate, a fall in the rate
of time preference or a slackening of the credit constraint as suggested by Figure 4. Figure
4 depicts the locus (CA)-(NM) for the mentioned values of the parameters �; � and �:
Long-run RER (R�), such that (CA)=(NM), is on the horizontal axis.
[INSERT Figure 4 Here]
The lower16� the more the RER appreciates following a productivity shock. The lower �
20
the higher the domestic return on capital, the higher the arbitrage premia and so does
the life-cycle income. On one side, a lower � tends to increase demand on non-tradable
goods. On the other side, a lower � tends to increase capital accumulation which a¤ects
negatively the non-tradable supply when non-tradable sector is labor intensive. These
two e¤ects imply that the real appreciation is higher for a more stringent constraint.
To confront the CE model with empirical evidence, we calibrate the model for Asian
countries. We analyze a productivity shock combined with a fall in the age dependency
ratio. Results are summarized in Table 4. We refer to the 1970-1992 period because we
use Ito et al. (1999) data for RER changes.
[INSERT Table 4 Here]
Table 4 provides some calibrations of the CE model considering the changes in the
age dependency ratio. We use a CES utility function U (ct; dt+1) = � (1� �)�1 c1��t +
(1� �) (1� �)�1 d1��t+1 , � > 0 instead of (11). We examine the two extreme cases for in-
tertemporal elasticity of substitution ��1 = 1 and ��1 = 0:1. Results are more able to
�t changes of RER observed between 1970 and 1992 in a CE than in the BS case. The
reason is that the real appreciation coming from productivity is partly o¤set by a fall in
the age dependency ratio. In such an OLG model, consumption spending decreases when
the share of working agents in total population increases, exerting a depreciating e¤ect
on the RER.
5 Conclusion
The analysis above shows that the Balassa-Samuelson (BS) theory must be enriched
to explain the real exchange rate (RER) appreciation in developing countries. Indeed,
investors on world capital markets require risk premia for developing countries, and capital
cannot be considered a perfectly mobile factor. As a result, there is a long lasting stage
of development during which the domestic return on capital exceeds the world return and
hence the BS analysis does not necessarily hold.
21
This article complements the traditional analysis questioning the e¤ects of an increase
in tradable productivity during this stage of development. Since capital is imperfectly
mobile, we must consider both supply and demand factors as determinants of the RER.
In this way, an increase in tradable productivity involves some additional e¤ects on the
demand side compared to those pointed out by the BS analysis. A calibration of the
model seems to match empirical evidence: the RER depreciates or experiences a low
appreciation despite high growth rates because the working age population has increased
in Asian developing countries since 1970.
22
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25
Notes :
1. Another investigation of a productivity shock with �nancial frictions on capital
markets is Mendoza and Smith (2002). They do not consider the RER in their one-sector
open economy model.
2. In this model, the capital uses non-traded good in order to preserve dynamics with-
out introducing adjustment cost in the capital accumulation. Only the capital reallocation
between sectors is costly.
3. This is a general property: Jones and Easton (1983) demonstrate that in a 2x2
structure (2 mobile factor, 2 sectors) with constant returns to scale, returns to factors
and factor allocation are not relied on the initial factor endowment.
4. If we consider a Cobb-Douglas example as the one developed in Section 4, then we
have � = (1� �) (1� �)�1 and � > 1 when the tradable sector is capital intensive.
5. According to Ito et al. (1999) the tradable sector is capital intensive in an adavanced
stage of development. It could be the case for emerging Asian countries for example.
6. This assumption follows Obstfeld and Rogo¤. There are two justi�cations. First,
the international capital market is imperfect and the amount that banks lend to agents is
a function of their current income. Since only the young agents can borrow, the constraint
depends on the wage. Second, it is easier for lenders to seize labor income than physical
capital income.
7. The BS analysis is a special case of this model when the domestic return on capital
converges to the world one.
8. This condition is satis�ed in the Cobb-Douglas case described in the following
section.
9. If we include public spending on non-tradable goods in the model, a rise in public
spending would lead to real appreciation.
10. Mahbub Morshed and Turnovsky (2004) used these empirical features for their
calibration.
11. Total output is in the model expressed in units of tradable goods: Y = YT +RYN
26
with YT (kt; Rt) � aT lT (kt; Rt)Ntf (kT (Rt)) :
12. The share of traded output is high but seems in accordance with evidence in Asian
countries, especially export-oriented.
13. The dependency ratio Nt�1=Nt is (1 + n)�1 in such an OLG setting.
14. B corresponds to the Net Foreign Assets (current LCU) and Y to the Gross
Domestic Product at market prices (current LCU).
15. We observe rd�1 � rd�0 = �1:10�9:
16. This mechanism holds for � � ��:
27
