This paper examines the response of real exchange rate to capital flow movements. It shows that countries with a large tradable sector will face smaller variability on their real exchange rate for a given level of capital flows and thus they will need smaller reallocations of real resources.

Rodrigo Cerda

English

Research Papers in Economics

Documento de Trabajo
ISSN (edición impresa) 0716-7334
ISSN (edición electrónica) 0717-7593
Capital Flows, Openess and Real 
Exchange Rate Variability.
Rodrigo Cerda
Nº 205
   Marzo 2002
www.economia.puc.clCapital Flows, Openess and Real Exchange Rate
Variability
Rodrigo Cerda∗
December, 1st 2001
Abstract
This paper examines the response of real exchange rate to capital ﬂow
movements. It shows that countries with a large tradable sector will face
smaller variability on their real exchange rate for a given level of capital
ﬂows and thus they will need smaller reallocations of real resources.
1. Introduction
Highly protected countries, when they decide to liberalize their economies, face
as a central issue if they liberalize ﬁrst their commercial policy or their capital
movements. This question has been named as the sequencing issue on the in-
ternational economics literature (See McKinnon, 1982 and Frenkel, 1983 among
others). This paper addresses the eﬀect of capital movements under trade re-
strictions and it shows that larger movements on real exchange rate (RER) and
hence larger reallocations of resources will be required on economies with trade
restrictions.
2. The model
This section develops a simple competitive equilibrium model for a small open
economy facing freely capital ﬂows but with restrictions on its trade policy. The
economy has three diﬀerent goods at each period of time. Those goods are a
non tradable good, an importable good and an exportable good. There is a
representative individual consuming importable and non-tradable goods and ﬁrms
∗ The University of Chicago and Pontiﬁcia Universidad Catolica de Chile. Correspondence
address: 5125 S. Kenwood ave., #407, Chicago, IL. 60615; e-mail:r-cerda@uchicago.eduproducing non tradable and exportable goods. Finally, there is a government that
taxes the transactions on the tradable sector and uses its revenue to purchase non
tradable goods.
2.1. The individual
There is a representative individual in this economy. The basic description of her
problem is the following. She lives from period t=0 to inﬁnity. At the beginning
of each period of time she is endowed with L units of time that are inelastically
supplied to the labor market. The individual must allocate those units of time
between labor supplied to the non tradable sector (Lnt) and labor supplied to
the exportable sector (Lxt). The wage rate are wnt and wxt respectively. Also,
she is endowed with some units of physical capital, kt, and some units of foreign
assets, bt. Those two types of assets may be used as perfect substitutes on the
capital market and they are inelastically supplied on the capital market to the
non tradable and exportable sector. Hence kxt units of physical capital and bxt
units of foreign capital are supplied to the exportable sector. Both units have a
return equal to rxt. I nt h en o nt r a d a b l es e c t o rt h en o t a t i o nw i l lb ek nt,bnt and
wnt for physical capital, foreign capital and wage rate, respectively. The main
diﬀerence between physical capital and foreign capital is that kt is built on the
non tradable sector while bt depends on the tradable.
The income obtained from the labor and capital market is spent on consump-
tion goods (importable and non-tradable), foreign assets to carry over to the next
period and investment on physical capital. Finally, other prices faced by the in-
dividual are Pnt and Pmt(1-τm). Pnt is the price of non tradable goods at time t,
including consumption and investment on physical capital (Int)w h i l eP mt(1-τm)
is the price of good bought on the tradable market, namely consumption on im-
portables and foreign assets, where τm is a tax levied by the government on the
importable sector.
The representative individual consumes non tradable goods and importable
goods. She has the following CES instantaneous utility function:
u(Cmt,C nt)=A[αC
−ρ
nt +( 1− α)C
−ρ
mt]
−1
ρ
Where Cmt and Cnt are consumption of importable and non tradable goods
while A,α > 0a n d∞ > ρ > −1 are parameters of the utility function. As usual
1
1+ρ is the elasticity of substitution between Cnt and Cmt. Given this utility
function the problem faced by the representative agent is:
max
Cmt,Cnt,Int,bt+1,Lxt,Lnt,kxt,knt,bxt,bnt
∞ X
t=0
βtA[αc
−ρ
nt +( 1− α)c
−ρ
mt]
− 1
ρ (1)
2s.t
PntCnt + g PmtCmt + PntInt + g Pmtbt+1 =
(1 + rxt)(bxt + kxt)+( 1+rnt)(bnt + knt)+wxtLxt + wntLnt
kt = knt + kxt
bt = bnt + bxt
L = Lxt + Lnt
kt+1 = Int + kt
limλtbt ≥ 0
t→∞
Where g Pmt =Pmt(1-τm). Notice that the constraint holds for any t and the last
condition is a transversality condition that eliminate the possibility of a Ponzi-
game, where λt be the shadow price of the budget constraint. We can characterize
the basic properties of the individual’s problem through the ﬁrst order conditions.
Some properties are the followings:
g Pmt
Pnt
=(
Cmt
Cnt
)−(ρ+1)(
1 − α
α
)( 2 )
wxt = wnt,r xt = rnt (3)
λtPnt = λt+1(1 + rnt)=λt+1(1 + rxt)=λt g Pmt (4)
Equation 2 is the usual equality between marginal rate of substitution and
ratio of prices. The conditions on 3 are just arbitrage conditions on the labor
market and the capital market while the conditions on 4 are the ﬁrst order con-
ditions of physical capital and foreign asset level accumulation1.I n s u m m a r y ,
the individual problem relates relative prices (RER) with the marginal rate of
substitution and it provides arbitrage conditions on the labor and capital market
plus conditions on foreign asset accumulation.
2.2. The ﬁrms
In the non tradable sector and the exportable sector there are a large num-
ber of ﬁrms with constant return to scale on labor and total capital. The
production function on the exportable and non-tradable sector are F(Kd
xt,Ld
xt)
1Notice that equation 4 implies that λtPnt = λtg Pmt or relative price of importable good
measured in terms of non tradable goods equal to one. However, if in fact λtPnt > λtg Pmt, the
individual does not accumulate physical asset and there are incentives to accumulate foreign
asset instead. If λtPnt < λtg Pmt, the individual has incentives to disaccumulate foreign assets.
3and H(Kd
nt,Ld
nt), where the superscript ”d” indicates ”demand” and K indi-
cates aggregate capital used on the ﬁrms. Also FK,FL,FLK,HK,HL,HKL>0a n d
FKK,FLL,HLL,HKK < 0.
The exportable sector faces a tax imposed by the government at rate τx, hence
its problem is:
max
Kd
xt,Ld
xt
Pxt(1-τx)F(Kd
xt,Ld
xt) − rxtKd
xt − wxtLd
xt
The non tradable sector faces a similar problem but there are not taxes in
this sector. Hence we have:
max
Kd
nt,Ld
nt
PntH(Kd
nt,Ld
nt) − rntKd
nt − wntLd
nt
2.3. The government
The government taxes the tradable sector as explained above. The revenues are
completely spent on non tradable goods. Those non tradable goods are however
not given back to the individual2. In that case the government budget constraint
is:
PxtτxYxt + Pmtτm(cmt + bmt)=PntGnt (5)
Where Gnt is government consumption of non tradable goods at time t and
Yxt =F(Kxt,Lxt).
2.4. The determinants of real exchange rate
It is possible to characterize the evolution of relative prices that determines con-
sumption in this economy. We require ﬁrst, the conditions that clear the markets.
The market clearing condition of the non tradable goods is:
Ynt = H(Knt,L nt)=Cnt + Int + Gnt (6)
Where Ynt is the total output on the non tradable sector. We can also obtain
a condition for the tradable sector also. In fact, using our using the national
account identity, we have3:
2We may think on them as consume by governement bureaucrats.
3The condition can be obtained by using the budget constraint of the individuals’ problem,
replacing the government budget constraint, the ﬁrms’ ﬁrst order condition and using the fact
that the production functions are constant returns to scale.
4TBt = −CAt = PxtYxt − PmtCmt = GNPt − (PCt + PntInt + PntGnt)( 7 )
Where GNPt is nominal GNP at time t while TBt,C A t and PCt are trade
balance, current account balance and nominal private consumption at time t4.
The characterization of the determinants of the RER is next. Using equations
(2), (6) and (7), plus some steps of algebra and the fact that Ln(1+x)≈ x, we
ﬁnally get:
ln(
g Pmt
Pnt
)=β0 − β1 ln(
Pxt
Pmt
) − β1 ln(
Yxt
Ynt
) − β2t(
CAt
GNPt
) − β3t(
Pnt(Gnt + Int)
GNPt
) (8)
Where β0 =l n (
1 − α
α
),β1 =( ρ +1 ) ,β2t =[
(ρ +1 )
(PxtYxt
GNPt )
] and β3t =[
(ρ +1 )
(PntYnt
GNPt )
]
Equation 8 presents some interesting results about the evolution of the relative
prices (RER). First, there are four main variables that have inﬂuence on RER.
The ﬁrst one is terms of trade - Pxt
Pmt− which has as elasticity the inverse of the
elasticity of substitution. Larger terms of trade produce a positive income eﬀect
over the individual’s budget constraint that increase demand both for traded
and non traded goods. Since the individual faces the prices of the traded goods
but prices of non tradable goods are endogenous to the system, there is a direct
negative eﬀect over RER. The same argument follows for the variable Yxt
Ynt. This
variable is similar to the ”Harrod-Balassa-Samuelson” eﬀect on the international
trade theory. Larger output on the tradable sector, holding constant non tradable
output, produces a positive income eﬀect. Notice that elasticity of substitution
matters. In fact larger elasticity of substitution is associated with smaller eﬀects
on real exchange rate as facing larger non tradable prices, due to increases on
demand, the individual substitutes away from non tradable goods.
The third variable inﬂuencing RER - CAt
GNPt− is the traditional ”Salter” eﬀect
w h i c hi nt h i sc a s ei sw r i t t e na saf u n c t i o no fc a p i t a lﬂows. Notice that the eﬀect
of larger capital ﬂows aﬀects negatively the RER but the eﬀect depends on the
elasticity of substitution and on the size of the exportable sector. The larger
is the tradable sector, the smaller will be the non tradable sector and hence
larger changes on Pnt will be required to accommodate increases on demand.
Hence, the eﬀect of capital ﬂows relates to the composition of production between
4There are two additional markets that must clear, namely the capital and the la-
bor market. Those conditions are used when solving the ﬁrms’ problem and they are
kt+bt=kxt+knt+bxt+bnt=K
d
xt+K
d
nt and L=Lxt+Lnt=L
d
xt+L
d
nt.
5sectors. The fourth variable -
Pnt(Gnt+Int)
GNPt − relates to the additional eﬀect of
government expenditure and investement on RER. A similar case was stressed
before by Rodriguez (1989). This variable has a diﬀerent and additional eﬀect
to the ”Salter” eﬀect, since this type of expenditure is relatively more intensive
on non tradable goods. Notice that the elasticity depends on the elasticity of
substitution as usual but also on the size of the non tradable sector. In fact,
given some increase on the level of expenditure on the non tradable sector, the
larger is the non tradable sector, the smaller should be the eﬀect of the increase
on demand. Hence, this last eﬀect relates to the eﬀect of expenditure within the
non tradable sector.
Finally, notice that taxes on the tradable sector do not appear on our above
equation. However, there is an eﬀect. From the ﬁrms’ problem we may deter-
mine some implicit demand functions for capital and labor. In the case of the ex-
portable sector, they are Kd
xt =Kd
xt(Pxt,w xt,r xt,τx)a n dL d
xt =Ld
xt(Pxt,w xt,r xt,τx).
Simply comparative statics shows that
∂Kd
xt
∂τx ,
∂Ld
xt
∂τx ≤ 05. Hence, larger tradable
taxes decrease the size of the tradable sector. This last result shows that coun-
tries with more restrictions on the tradable sector must have larger ﬂuctuation of
their RER due to capital ﬂows.
3. Conclusion
This paper develops a simple competitive equilibrium model that summarizes the
eﬀects of diﬀerent theories of RER determination. The main ﬁnding of the model
is that highly protected countries will face large variations on their RER for a
given level of capital ﬂows.
4. References
Balassa, B. (1964) ”The Purchasing Power Parity Doctrine: A Reappraisal”,
Journal of Political Economy, Vol. 72, pp. 584-596.
Frenkel, J. (1983) ”Remarks on the Southern Cone”, IMF Staﬀ Papers, Vol.
30; pp. 164-173
McKinnon, R. (1982) ”The order of Economic Liberalization: Lessons from
Chile and Argentina” in Economic Policy in a World of Change, Karl Brunner
and Allan Metzler (eds.), Carnegie-Rochester Conferences Series on Public Policy,
Vol. 17
5 ∂Kxt
∂τx =
P2
x(1−τx)[FkFLL−FLFKL]
FKKFLL−(FLK)2 < 0,
∂Lxt
∂τx =
P2
x(1−τx)[FLFKK−FKFLK]
FKKFLL−(FLK)2 < 0
6Rodriguez, C. (1989) ”Macroeconomic Policies for Structural Adjustments”
PRE Working Papers 247, The World Bank.
Salter, W. (1959) ”Internal and External Balance: The Role of Price and
Expenditure Eﬀects” Economic Record, Vol. 35, No 71, pp. 226-238.
Sjaastad, L. (1991) ”Debts, Deﬁcits and Foreign Trade”, Economic Letters,
V o l .1 0 ,N o3 ;S e p t e m b e r .
7

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