Net Foreign Assets, Productivity and Real Exchange Rates in Constrained Economies

Abstract

Empirical evidence suggests that real exchange rates (RER) behave differently in developed and developing countries. We develop an exogenous 2-sector growth model in which RER determination depends on the country's capacity to borrow from international capital markets. The country faces a constraint on capital inflows. With high domestic savings, the country converges to the world per capita income and RER only depends on productivity spread between sectors (Balassa-Samuelson effect). If the constraint is too tight and/or domestic savings too low, RER depends on both net foreign assets (transfer effect) and productivity. We then analyze the empirical implications of the model and find that, in accordance with the theory, RER is mainly driven by productivity and net foreign assets in constrained countries and exclusively by productivity in unconstrained countries.

Full text

Page 1

University of Kent
School of Economics Discussion Papers


Net Foreign Assets, Productivity and Real Exchange
Rates in Constrained Economies


Dimitris K. Christopoulos, Karine Gente and
Miguel A. León-Ledesma

December 2010

KDPE 1011

Page 2

Net Foreign Assets, Productivity and Real Exchange
Rates in Constrained Economies∗
Dimitris K. Christopoulos?, Karine Gente§†
and Miguel A. Le´ on-Ledesma‡
?Panteion University,§DEFI, University of Aix-Marseilles,
‡University of Kent
November 30, 2010
Abstract
Empirical evidence suggests that real exchange rates (RER) behave differently in
developed and developing countries. We develop an overlapping generations two-sector
exogenous growth model in which RER determination may depend on the country’s
capacity to borrow from international capital markets. The country faces a constraint
on capital inflows. With high domestic savings, the RER only depends on productivity
spread between sectors (Balassa-Samuelson effect). If the constraint is too tight and/or
domestic savings too low, the RER depends on both net foreign assets (transfer effect)
and productivity. We then analyze the empirical implications of the model and find
that, in accordance with the theory, the RER is mainly driven by productivity and net
foreign assets in constrained countries and by productivity in unconstrained countries.
JEL Classification: E39; F32; F41.
Keywords: Real exchange rate; capital inflows constraint; overlapping genera-
tions.
∗We wish to thank Menzie Chinn, Mike Devereux, Vasco Gabriel, Peter McAdam, Gian-Maria Milesi-
Ferretti, Michel Normandin, Marcelo Sanchez, Volker Wieland, Alpo Willman, an anonymous referee, an
associate editor, and seminar participants at Uiversity of New South Wales, Australian National University,
Macquarie University, Joint Bundesbank-ECB-CFS Lunchtime Seminars, University of Aix-Marseilles, Uni-
versity of Reading, University of Surrey and the 2010 ASSET Conference for their helpful comments. All
errors remain our own.
†Corresponding author: Karine Gente, DEFI, University of Aix-Marseilles, Chteau Lafarge, Route
des Milles, 13290 Aix-en-Provence, FRANCE, Tel : 33-4-42 93 59 66, Fax : 33-4-42 38 95 85, e-mail:
karine.gente@univmed.fr.
1

Page 3

1Introduction
A recurrent question in International Macroeconomics concerns the main long-run determi-
nants of real exchange rates (RER). There is, however, no consensus yet on this question.
Among the most often quoted determinants we can find productivity, terms of trade and
net foreign assets (NFA) [see Chinn (2006)]. Empirical evidence suggests that these deter-
minants change significantly as we vary periods and countries considered. This is especially
relevant in recent times, since the resolution of global economic imbalances can lead to large
readjustments of external wealth with important consequences for equilibrium RERs and
exchange rate policies of emerging markets.
The empirical literature on the Balassa-Samuelson (BS) effect shows that RER appre-
ciation may be related to productivity growth but not systematically. It seems to have
special relevance for countries like Japan, some OECD countries [Canzoneri et al. (1999)]
and transition economies [´Egert et al 2003, 2006]. Ito et al. (1999) show that RER and
growth are positively correlated in Japan, Korea, Taiwan, Hong Kong whereas the corre-
lation remains negative for Indonesia, Thailand, Malaysia, Philippines and China. Hong
Kong, Taiwan and Singapore combine a high growth rate and a small appreciation. For
other Asian countries except China, Singapore, Taiwan and Thailand, Chinn (2000a) finds
that productivity explains RER only when public spending and oil prices are taken into
account. Chinn (2000b), using panel data, finds that the RER requires around 5 years to
converge to the level predicted by BS. Bergin et al (2006) also report that the BS effect is
not stable through time, but it appears to have become more important in recent decades.
The fit of the standard BS theory to explain RER changes seems to be very poor and largely
country- and period-specific.1
In line with the theory that emphasizes the role of foreign assets for equilibrium RERs,
Lane and Milesi-Ferretti (2004) have developed a model that highlights the transfer effect -
which relates RER to NFA. Using a database that covers 64 industrial and less developed
countries between 1970 and 1998, they show that a rise in NFA appreciates the RER, es-
pecially for countries that have low income, low openness, or foreign exchange restrictions.
The theoretical model they present links international payments to the RER through an ad-
justment of labor supply2. However, their model does not address why developing countries
experiment higher transfer effects than others.
Linking together this diverse set of results, our study contributes to this literature in two
1See Garc´ ıa-Solanes and Torrej´ on-Flores (2009) for further evidence on the different importance of the
BS effect for rich and poor countries. Chong et al (2010) provide new evidence based on a local projections
approach.
2Obstfeld and Rogoff (1995) and Galstyan (2007) also develop models in which international payments
affect the relative price of the non-traded good through a labor supply adjustment.
2

Page 4

ways. First, it presents a model that reconciles these empirical findings in which RER deter-
mination depends on the country’s capacity to borrow from international capital markets.
Second, it analyzes whether the behavior of RER data is consistent with the main results
of the model, focusing on whether the long-run relationship between the RER and its main
determinants depends on the financial constraints faced by countries.
As emphasized by Rogoff (1992) and De Gregorio et al. (1994), imperfect factor mobility
is a necessary condition in a two-sector model for the real exchange rate to be determined by
factors other than technological conditions. We relax the assumption of perfect capital mo-
bility using an overlapping generations setting of a two-sector economy with a capital inflows
constraint. We assume that the amount the country can borrow on the international capital
market is an exogenous fraction of per-capita income.3This fraction represents the trust
of foreign investors about local institutions, creditworthiness, and the ease of cross-border
financial transactions. Using such a specification, we are able to determine analytically the
threshold level of the constraint below (above) which the country converges to a financially
constrained (unconstrained) steady state. If the constraint is not too tight - or if there are
high domestic savings - the constrained economy will become unconstrained in the long-run.
Otherwise, if investors are not confident - or there are low domestic savings - the country
will converge to the constrained steady state. We investigate the consequences of a foreign
transfer and a productivity shock in this setting. The RER behavior differs widely between
those two kinds of steady states.
Two main conclusions arise from this model regarding the behavior of the RER. In
the unconstrained steady state, the RER will exclusively be determined by the Balassa-
Samuelson effect. Conversely, in the constrained steady state, the RER will depend on
supply and demand of non-traded goods. In this case, a productivity shock operates through
a demand effect and not only through the Balassa-Samuelson effect. In the same way, an
international transfer from abroad will appreciate the RER, whereas this is not the case in
the unconstrained steady state. This transfer effect is higher in less open economies. This
is consistent with Lane and Milesi-Ferretti’s (2004) empirical results.
We then test the long-run implications of the model for RER behavior. The econometric
specification used arises from the expression for the RER from a linearized version of the
model. We estimate separate RER models for financially constrained and unconstrained
economies, selected using the Chinn and Ito (2007) measure of external financial openness.
The findings are supportive of the implications of the model in the long-run, with the RER
driven mainly by productivity in financially open countries and by both productivity and
3Gente (2006) introduces a [2x2] setting in the Obstfeld and Rogoff (1996) constrained economy model,
but with a constraint depending on wages. Calibrating of the constrained steady state, Gente (2006) shows
that productivity growth combined with fertility decline may explain the RER depreciation experienced by
Asian countries.
3

Page 5

NFA for countries with restricted access to international finance.
The paper is organised as follows. Section 2 presents the theory model. Section 3 analyses
the steady state solution of the model for constrained and unconstrained economies. Section
4 presents the econometric evidence, and Section 5 provides some conclusions.
2The model
The model is a variant of Obstfeld and Rogoff (1996) constrained economy overlapping
generations model in which there are two production sectors: a tradable sector and a non
tradable sector. In this setting, the real exchange rate R denotes the relative price of non
tradable to tradable goods. The constraint the country faces on capital inflows is4
Bt+1≥ −ηNtyt
(1)
where Bt+1denotes the NFA of the domestic country in terms of traded goods, and η > 0
is the proportion of total income (Ntyt) the domestic country can borrow, where Nt is
total population and yt is per capita income. The η parameter reflects the ease of access
the country has to international capital flows and may be related to institutional features
such as restrictions to capital and current account transactions5. The smaller η the more
constrained the country is to capital inflows. Because of the way the constraint is specified,
a RER appreciation attracts capital flows6and may fill in a lack of domestic savings that
accelerates growth temporarily or increases permanently long-run income per capita. In
the model we present below, agents live for two periods and only work in their first period
of life. Making use of overlapping generations, our model allows the steady state to be
constrained or unconstrained. The credit constraint we impose can not only slow down
absolute convergence7but also prevent it from occurring even in the long-run.
4As mentioned above, Gente (2006) assumes that the constraint on capital inflows only depends on the
wage and not on total income. We use a more general specification (See Section 2.2 for further details).
5Our purpose in this paper is not to explain or estimate the η parameter. This constraint may be
the consequence of some capital market imperfections such as sovereign risk. We view our constraint as a
reduced form of a more complete model. However, it serves our purpose of emphasizing the role of financial
constraints for RER determination.
6In Rodrik (2008), capital inflows are related to traded inputs and a real appreciation also increases
capital inflows as in our model.
7As it would have been the case with an infinite horizon agent [Barro, Mankiw and Sala-i-Martin (1995),
Lane (2001)].
4

Page 6

2.1Individuals
The economy consists of a sequence of individuals who live for two periods. In the second
period of her 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 Ntidentical individuals who
make decisions concerning consumption and savings.
The intertemporal preferences of an individual belonging to generation t are represented
by
U?cY
t,co
t+1
?= β lncY
t+ (1 − β)lnco
t+1
(2)
where cY
sumption when old; β ∈ (0,1) denotes individuals’ thrift.
Let cNand cTbe, respectively, the spending allocated into non-traded and traded goods.
Instantaneous preferences are defined according to a Cobb-Douglas aggregator:
tand co
t+1are respectively composite consumption when young and composite con-
u(cT,cN) = cα
Tc1−α
N , 0 < α < 1(3)
Following Obstfeld and Rogoff (1996), the small economy faces a constraint on capital inflows
(1). The consequence of this assumption is that the domestic return on capital may be higher
than the world return. The budget constraints for each generation are
πtcY
t+ (1 + n)kt+1+ (1 + n)bt+1= wt
t+1=?1 + rd
(4)
πt+1co
t+1
?(1 + n)kt+1+ (1 + ¯ r)(1 + n)bt+1, (5)
where kt+1 is total capital stock per young agent in terms of traded good prices kt+1 =
Kt+1/Nt+1, bt+1 are net foreign assets per young agent bt+1 ≡ Bt+1/Nt+1, wt are wages
earned when young, and n is the rate of population growth. The price of the tradable good
is normalized at unity and πtis the consumer price index.The domestic return on capital is
the market interest rate rd
economy assumption. The maximization problem of an individual born in period t under
the constraints (4), (5) (1) gives8
?
πt+1co
t+1
t+1whereas the world return ¯ r is fixed according to the small open
πtcY
t= βwt−rd
t+1− ¯ r
1 + rd
?wt−?rd
t+1
(1 + n)bt+1
?
(6)
t+1= (1 − β)??1 + rd
t+1− ¯ r?(1 + n)bt+1
?
(7)
cT= απc
RcN= (1 − α)πc
(8)
8The maximization program is solved in two steps: first, the individual chooses πtctand bt+1to maximize
lifetime utility, and then chooses the optimal composition of consumption between cT and cN to maximize
instantaneous utility.
5

Page 7

From equations (6) and (7), individuals consume a proportion β of their life-cycle income
during the first period of life and the remaining in the second. Life-cycle income consists of
• the wage w,
• the capital gain agents may realize borrowing at world rate ¯ r to invest in domestic
capital whose return rdis higher than ¯ r.
Equations (8) gives the allocation of total consumption spending between the two goods
at each period, where the price index is π = φ(α)R1−α, with φ(α) ≡ α−α(1 − α)α−1.
2.2Production Sectors
Investment transforms instantaneously a unit of tradable good into a unit of installed capital:
Kt+1= Itand capital fully depreciates after one period (δ = 1). The representative firm
produces in the two sectors, the traded (T) and the non-traded (N) sector.
Max
It,KTt,LTtF (KTt,LTt) + RH (KNt,LNt) − wLt− It
s.t. Kt+1= It
KTt+ KNt= Kt
(9)
LTt+ LNt= Lt
(10)
with Ltbeing total labor supply, and Kiand Lithe amount of capital stock and labor supply
used in sector i = T,N respectively. F(·) and H(·) are the traded and non-traded sector
production functions. Dropping time indices, optimal allocation of factors is given by
aTf?(kT) = aNRh?(kN)(11)
aT[f (kT) − kTf?(kT)] = aNR[h(kN) − kNh?(kN)]
where ki ≡ Ki/(liL) is the capital-labor ratio, and the share of labor used in sector i
is li = Li/L, i = T,N. The intensive form production functions are F (kT,1) ≡ f (kT),
H (kN,1) ≡ h(kN). Finally, ai is the total factor productivity level of sector i = T,N.
According to (11) and (12), kNand kTdepend only on RER whereas the allocation of labor
depends both on the capital-labor ratio and the RER. Hence, kN ≡ kN(aT,aN,R) and
kT≡ kT(aT,aN,R), while lN≡ lN(aT,aN,k,R) and lT≡ lT(aT,aN,k,R). From (9), (10),
(11) and (12), the optimal factor allocation implies
(12)
∂kN
∂R
∂kT
∂R
=
aTf
R2aNh??(kN− kT)
RaNh
f??aT(kN− kT)
(13)
=
6

Page 8

Similarly, ∂lN/∂k ? 0 if kN? kT and ∂lN/∂R > 0. When the tradable sector is capital in-
tensive, a real appreciation leads to an increase in both capital intensities kNand kTwhereas
labor moves from the traded to the non-traded sector. These factor movements reflect that
a real appreciation makes the non-tradable sector more attractive. Assuming perfect inter-
sectoral mobility, the returns on capital rd= aTf?(kT(aT,aN,R)) − 1 ≡ rd(aT,aN,R) and
labor w = aT[f (kT(aT,aN,R)) − f?(kT(aT,aN,R))kT(aT,aN,R)] ≡ w(aT,aN,R) only de-
pend on the RER (R) and productivity. A RER appreciation, profitable to the non-traded
sector which is labor intensive, will increase wage and reduce the domestic interest rate9.
An exogenous rise in traded (non-traded) sector productivity increases (decreases) domestic
interest rates and reduces (increases) wages when the traded sector is capital intensive. Un-
less otherwise stated, we will omit the productivity terms (ai) when there is no productivity
change so that: kT≡ kT(R),kN≡ kN(R),lN≡ lN(k,R),rd≡ rd(k,R),w ≡ w(k,R).
Per capita total income depends on both the RER and per capita capital stock: y ≡
?1 + rd(R)?k + w ≡ y (R,k) with
∂k= 1 + rd
∂y
∂R= Rh(kN(R))lN(k,R)
Notice that a RER appreciation and a rise in per capita capital stock both exert a positive
effect on total income and relaxes the constraint. Equations (1) and (14) mean that a rise in
domestic savings allows the country to borrow more on international capital markets. This
is due to the way the constraint is specified because the amount the country can borrow
depends on per-capita income instead of only the wage as in Gente (2006), where only the
RER appreciation may relax the constraint.
∂y
(14)
(15)
2.3The temporary equilibrium in the constrained case
We will focus on the case where the capital inflows constraint binds, at least initially, with
a capital intensive traded sector. This creates a gap between domestic and world returns
on capital. This gap - in a similar way as a risk premium10- reflects the fact that many
developing countries do not have full access to international capital markets: the return on
domestic capital rd
perceived risky return due to, for instance, a restrictive capital account regime.
The period-t temporary equilibrium conditions are as follows:
(i) Capital market equilibrium.Given the optimal intersectoral factor allocation
t+1must be higher than the world market interest rate ¯ r to offset the
9In a similar fashion as a Stolper-Samuelson effect.
10Similar results could potentially be obtained by considering country-risk.
7

Page 9

kT(R) and kN(R), net foreign assets per capita are given by
bt+1= −ηy (Rt,kt)
1 + n
(16)
Let Γ(Rt+1) ≡ η?rd(Rt+1) − ¯ r??1 + rd(Rt+1)?−1be the arbitrage premium which depends
on the interest rate gap between domestic and world capital markets and on proportion η
of the income agents can borrow. The higher Γ the higher the capital gain agents realize.
Therefore, capital per worker is
kt+1= [1 − β + η − βΓ(Rt+1)]w(Rt)
1 + n+ [η − βΓ(Rt+1)]1 + rd(Rt)
1 + n
kt
(17)
(ii) Labor market equilibrium. The inelastic labor supply Ntis equal to the labor
demand Lt. Given the capital market equilibrium, the wage w equalizing labor supply and
demand is defined by
w(Rt) ≡ f (kT(Rt)) − kT(Rt)f?(kT(Rt))(18)
(iii) Non-tradable goods market equilibrium. There are Ntyoung agents and Nt−1
old agents. Hence, the equilibrium on the non tradable goods market is
(1 − α)?NtπtcY
t+ Nt−1πtco
t
?= RtYN(Rt,kt)(19)
with YN(Rt,kt) ≡ lN(Rt,kt)Nth(kN(Rt)). Consumption spending is given by equations (6)
and (7).
Equation (17) describes the allocation of saving between both assets. It offers a first
dynamic relationship between the RER and the capital-labor ratio. Using (16), (18) and
(19), with consumption spending given by (6) and (7), we get a second dynamic relationship
between R and k.
The intuition behind the dynamics is the following. In such a constrained economy, the
amount the country can borrow on world market is limited to a fraction of total income. In
this 2-sector 2-factor model, total income does not only depend on the capital-labor ratio
but also depends on RER. A RER appreciation - or an increase in the capital-labor ratio -
increases total income in terms of traded good and then loosens the constraint. The country
can borrow more, increases its capital stock and total output, loosening the constraint again.
This mechanism will help the country converging to an unconstrained steady state if non-
traded consumption is sufficiently high and if the constraint is not too tight (if η not too
small). Otherwise the country will remain constrained in the long-run11.
11When the tradable sector is labor intensive, it is the RER depreciation that helps the country converge
to an unconstrained steady state. We do not focus on this case in what follows because it is less frequently
observed and corresponds to a preliminary stage of development [Ito, Isard and Symanski (1999)].
8

Page 10

In the existing literature, there are constrained economy models like Barro, Mankiw and
Sala-i-Martin (1995) or Lane (2001) that focused on the convergence speed issue. Indeed, in
those constrained economy models the country systematically converges to an unconstrained
steady state and the question of interest is to know at what speed. In our model, the
country may converge in the long-run to a steady state that could either be constrained or
unconstrained12. Hence, the important question here is to study the relationship between
NFA and RER in both types of equilibrium.
3Steady state
There are two kinds of steady state: constrained and unconstrained. However, these two
steady states do not exist simultaneously13. The country may converge to an unconstrained
steady state if the constraint is not to severe (high η), domestic saving is high (low β) or
if agents consume enough non-traded goods (low α). The relationship between RER, NFA
and productivity depends on the kind of steady state the economy converges to.
3.1Constrained or unconstrained?
We now aim at determining the threshold level of the constraint, ˜ η such that if η < ˜ η, the
country will remain constrained in the long-run (see Appendix B). We will then proceed
into three stages. First, we describe the constrained steady state. Second, we describe the
unconstrained steady state. Third, we determine the threshold level of the constraint ˜ η.
3.1.1A constrained steady state
The constrained steady state is denoted by a ∗. If the country remains constrained even in
the long-run, the steady state (k∗,R∗) is defined14by the following system
k∗=w(R∗)
1 + n
1 − (η − βΓ(R∗))1+rd(R∗)
?
Equation (20) gives the long-run allocation of saving. In this constrained economy, capital
per capita k is financed by domestic saving plus capital inflows. Equation (21) is the long-
run non-traded good market clearing condition. Both the long-run capital-labor ratio and
(1 − β) + η − βΓ(R∗)
1+n
(20)
β +1 + rd(R∗)
1 + n
(1 − β)
??
w(R∗) +rd(R∗) − ¯ r
1 + rd(R∗)ηy (R∗,k∗)
?
=yN(R∗,k∗)R∗
1 − α
(21)
12This is due to the presence of overlapping generations and the fact that there is no need for the time
preference rate to equalize the world interest rate.
13We can show, using a simple Cobb-Douglas example, that, when the unconstrained steady state exists,
the constraint is no longer respected and then the constrained steady state does not exist.
14To guarantee potential existence, we assume that η < (1 + n)/(1 + ¯ r).
9

Page 11

RER are determined by those two conditions. Then, the constraint gives net foreign assets:
b∗= −ηy (R∗,k∗)/(1 + n).
3.1.2An unconstrained steady state
An over-bar denotes the unconstrained steady state. It is the standard steady state that
occurs in a two-sector two-factor small open economy model. The country has perfect access
to the international capital market so that
rd?¯R?= ¯ r(22)
That is, domestic return on capital converges to the world one. Equation (22) deter-
mines the long-run RER that depends only on the world interest rate15. The long-run RER
determines the wage and hence the demand for non-traded goods (left hand side of equation
(23)). Domestic capital¯k clears the non-traded good market
?
Finally, the net foreign assets fill the gap between domestic capital¯k and domestic saving
¯b =w?¯R?
In this unconstrained steady state the standard Balassa-Samuelson effect holds since the
RER depends only on the supply side of the model.
β +(1 + ¯ r)(1 − β)
1 + n
?
w?¯R?=yN
?¯R,¯k?¯R
1 − α
(23)
1 + n(1 − β) −¯k(24)
3.1.3The threshold level
The level of the constraint, η, is exogenous and could be interpreted as the penalty imposed
by international investors to a country because of lack of creditworthiness and institutional
restrictions to financial flows. We take this penalty as given and determine whether this
η−penalty is severe enough to allow the developing country to converge to the unconstrained
steady state. We focus on the case where k0<¯k. Let ˜ η be the threshold level of the constraint
such that
- when η ≥ ˜ η, the country converges to the unconstrained steady state and we recover
the standard small open economy setting
- when η < ˜ η, the country converges to the constrained steady state and remains con-
strained in the long-run.
15The RER is also determined here by the productivity spread between sectors: rd(aN,aT,R) = ¯ r with
∂rd/∂aN< 0,∂rd/∂aT> 0 when the traded sector is capital intensive.
10

Page 12

A special case of this model would be η = 0 where the country would be so constrained
that net foreign assets would be zero. This case would correspond to a closed economy
setting.
A rise in ˜ η makes convergence to the constrained steady state more likely to occur. We
can characterize the threshold level ˜ η in a simple Cobb-Douglas case.
Example: The Cobb-Douglas case. We assume Cobb-Douglas technologies in both sec-
tors. Let the long-run propensity to consume the non-traded good be
Ψ = (1 − α)[β + (1 − β)(1 + ¯ r)/(1 + n)]
After a bit of algebra (see Appendix B) we can show that
˜ η =
1+n
1+¯ r[ν + Ψ(ρ − ν)] − (1 − β)(1 − ν)
1 + Ψ(ρ − ν)
Where ρ and ν are the elasticities of output with respect to capital in the traded and
non-traded sectors respectively. We assume that the total propensity to consume the
non-traded good Ψ is lower than unity and that the traded sector is capital intensive.
This means that 1+Ψ(ρ − ν) > 0. This implies that a rise in Ψ enhances convergence to
the unconstrained steady state16. The intuition behind this result is simply that a rise
in non-traded goods consumption tends to appreciate the RER. This RER appreciation
relaxes the constraint and helps the country reaching the unconstrained steady state.
In the same way, the threshold level ˜ η depends on n and β since population growth
and time preference influence both propensity to consume Ψ and savings.17
Calibration. We assume that half of the consumption is spent on non-traded goods. As-
suming that each generation lives for 25 years, the world interest factor is 1+ ¯ r = 1.37
which means that the world real interest rate is about 1.25% per year, and n = 0.6, cor-
responding to a rate of population growth of 1.9% per year. In accordance with Beine
et al. (2001), let β = 0.6 to have a domestic rate of time preference of around 3.56%.
Using those figures, the threshold level is ˜ η = 0.129 which means that a steady-state
constrained economy cannot borrow more than 13% of GDP. Figure 1 represents the
long-run equilibrium. The constrained steady state is represented for η = 0.1 and the
unconstrained steady state for η = 0.2. In the constrained steady state, the domestic
real interest rate exceeds the world interest rate and more resources are allocated to the
production of the traded good. Since domestic interest rate and RER are negatively
related, the RER is lower in the constrained steady state than in the unconstrained
16Since η < (1 + n)/(1 + ¯ r), we have ∂˜ η/∂Ψ < 0.
17We have that ∂˜ η/∂n > 0, and ∂˜ η/∂β > 0.
11

Page 13

one. We choose the elasticities of output with respect to capital per capita for the
two sectors to match empirical evidence: 40% of total output is traded with 37% of
labor being employed in that sector [Mahbub Morshed and Turnovsky (2004)]. With
ν = 0.4 and ρ = 0.2 the traded sector is capital intensive. Then, we have l∗
and¯lT = 37.70% whereas y∗
constrained steady state, production factors are over-allocated in the traded sector:
the lower the RER, the higher the return on traded production.
T= 39.24%
T/y∗= 43.51% and ¯ yT/¯ y = 41.62% (See Table 1). In the
[Figure 1]
[Table 1]
3.2Net Foreign Assets and the RER
The relationship between NFA and RER, the so-called transfer effect, will depend on the
nature of the steady state the economy converges to. Let Ttdenote a transfer received from
abroad. Then capital market equilibrium becomes
st+ Tt= (1 + n)[bt+1+ kt+1]
We can consider T as an unrequited transfer from the rest of the World. Like savings, this
transfer will be used for asset accumulation.
3.2.1Unconstrained steady state
Long-run equilibrium is given by equations (23) and (22). The introduction of the transfer
changes NFA accumulation
¯b = T +w?¯R?
A transfer will increase NFA. Since RER is exclusively determined by productivity and world
interest rates: there is no transfer effect and NFA do not affect the RER.
1 + n(1 − β) −¯k (25)
3.2.2 Constrained steady state
In the constrained steady state, long-run equilibrium is given by equations (20) and (21) and
the constraint still binds
b∗= −ηy (R∗,k∗)
The introduction of the transfer T changes equation (20) that becomes
1 + n
k∗=
w(R∗)
1+n[(1 − β) + η − βΓ(R∗)] +
1 −1+rd(R∗)
T
1+n
?
1+n
?
η − βηrd(R∗)−¯ r
1+rd(R∗)
12

Page 14

A transfer will have two kinds of effects
(i) a direct effect: a rise in T increases the capital-labor ratio. Since the non-traded
sector is labor intensive, this rise in capital reduces non-traded output and leads to a RER
appreciation.
(ii) an indirect effect: a transfer increases total production and loosens the constraint. As
a result, capital stock increases more and this reinforces the RER appreciation. The higher
η - the more the country is allowed to borrow on international markets - the higher the RER
appreciation.
As in Lane and Milesi-Ferretti (2004), the transfer effect increases with the size of the
non-traded sector: the less open (low α) the country, the higher the direct effect. However,
our model shows analytically that the transfer effect depends also on the country’s access
to external borrowing. It holds only in the constrained economy case, that is, when η < ˜ η.
Conversely, when η ≥ ˜ η the transfer effect does not hold.
Calibration: The transfer effect An international transfer can be considered as an ex-
ogenous increase in savings. Figure 2 depicts the consequences of a transfer on steady
state. The transfer shifts the (CM) curve upwards. In the unconstrained steady state,
it does not affect domestic interest rate -because the equilibrium lies at the intersection
between (WIR) and (CM). In the constrained steady state, the domestic interest rate
increases and more resources are allocated to the production of the non-traded good. It
follows that in this case, RER appreciates whereas RER is not affected by the transfer
in the unconstrained steady state18.
[Figure 2]
3.3Productivity and the RER
In this 2x2 model total output increases not only with the capital-labor ratio and total factor
productivity but also with RER appreciation [See equations (14) and (15)]. However, the
relationship between the RER and productivity still depends on the nature of the steady
state the economy converges to.
3.3.1 Unconstrained steady state
The long-run equilibrium is given by equations (23) and (24). The RER is exclusively
determined by the world interest rate and productivity spread between sectors according to
rd(aT,aN,R) = ¯ r(26)
18The transfer also relaxes the constraint moving the equilibrium to the left part of the Figure. If the
transfer is high enough, it can help the constrained economy reach an unconstrained steady state.
13

Page 15

with ∂rd/∂aT> 0. An increase in traded productivity will directly generate a RER appre-
ciation (Balassa-Samuelson effect).
3.3.2 Constrained steady state
RER and the capital-labor ratio clear the non-traded goods market and the long-run equi-
librium is given by
b∗= −ηy (aT,R∗,k∗)
k∗=w(aT,R∗)
1 + n
1 − (η − βΓ(aT,R∗))1+rd(aT,R∗)
with ∂w/∂aT< 0 and ∂rd/∂aT> 0,∂Γ/∂aT> 0. The constraint always binds so that NFA
are determined by output. The Balassa-Samuelson effect does not hold here in the sense
that equation (26) no longer applies. The RER does not only depend on productivity and
world interest rate but instead results from the interaction between demand and supply of
non-traded output. A rise in traded goods productivity aTleads to changes in both demand
and supply of non-traded goods and will generate:
(i) an ambiguous effect on non-traded goods demand19due to a rise in domestic return
on capital combined with a wage decrease.
(ii) a decrease in non-traded output
(iii) an ambiguous effect on total output
The third effect will affect the country’s capacity to borrow on international markets. A
rise in total output will relax the constraint, increase capital stock, and decrease non-traded
output. Conversely, a decrease in total output will tighten the constraint, reducing capital
stock and increasing non-traded output. Since this third effect is ambiguous, the relationship
between traded productivity and RER is difficult to characterize in this constrained steady
state. For economies with high rate of time preference and/or not allowed to borrow enough
on international markets, the Balassa-Samuelson effect may be reversed: a rise in traded
productivity may lead to a RER depreciation. Otherwise (high β and/or high η), the RER
still appreciates as in the unconstrained case but operating here through a demand effect and
not only through a productivity channel as in the unconstrained case. It is hence possible that
productivity can have an ambiguous effect on the RER for financially constrained countries.
1 + n
(1 − β) + η − βΓ(aT,R∗)
1+n
19With a simulation exercise, we can show that, in the vast majority of cases, demand for non-traded
goods will decrease.
14