Kyoto University,
Graduate School of Economics
Research Project Center Discussion Paper Series

Export of Deindustrialization and Anti-Balassa-Samuelson Effect: The
Consequences of Productivity Growth Differential

Hiroaki Sasaki

Discussion Paper No. E-10-015

Research Project Center
Graduate School of Economics
Kyoto University
Yoshida-Hommachi, Sakyo-ku
Kyoto City, 606-8501, Japan

March 2011

Export of Deindustrialization andAnti-Balassa-Samuelson Effect: The Consequencesof Productivity Growth Differential
Hiroaki SASAKI∗
Graduate School of Economics, Kyoto University

Abstract
This paper focuses on productivity growth differentials between manufacturing and services, deindustrialization, and changes in the real exchange rate. Using a Ricardian
trade model with a continuum of goods that introduces nontraded services, the paper
investigates these interrelationships. The main results are as follows: (i) if deindustrialization proceeds in both home and foreign countries, then the ratio of home manufacturing employment share to foreign manufacturing employment share and the real exchange rate move in the same direction; (ii) even if the productivity growth differential
in the home country is greater than that in the foreign county, the extent of deindustrialization in the home country is not necessarily larger than that in the foreing country. On
the contrary, it is possible that the foreign deindustrialization exceeds the home deindustrialization; and (iii) even if the productivity growth differential in the home country
is greater than that in the foreign county, the real exchange rate of the home country candepreciate contrary to the expectaion of the Balassa-Samuelson effect.
Keywords: Productivity growth differentials; Deindustrialization; Real exchange rate;
Shift in specialization patterns
JEL Classification: F10; F31; O14∗

Address for correspondence: Hiroaki, SASAKI. Graduate School of Economics, Kyoto University.
Yoshida-Honmachi, Sakyo-ku, Kyoto 606-8501, Japan. E-mail: sasaki@econ.kyoto-u.ac.jp1

1

Introduction

The purpose of this paper is to theoretically investigate the relationship among productivity
growth differentials between manufacturing and services, deindustrialization, and changes
in the real exchange rate.1
Here, deindustrialization is defined as a decline in the share of employment in industry or manufacturing. Since the employment share of agriculture in developed countries isvery small, deindustrialization suggests a rise in the share of employment in services. As
many data and empirical studies show, the share of service employment consistently rises
while that of industrial employment declines in all developed countries without exception.
Deindustrialization in this sense is first analyzed theoretically by Baumol (1967). He proposes a two-sector model that consists of manufacturing and services, and shows that deindustrialization is caused by interaction between productivity growth differentials (between
manufacturing and services) and inelastic demand. On the basis of Baumol (1967), many
theoretical models have been produced.2
However, those are models of closed economy and there are few models that consider
deindustrialization in open economy. A noteworthy exception is Spilimbergo (1998). He
presents a model that extends the standard Ricardian trade model with a continuum of goods(Dornbusch, Fischer, and Samuelson, 1977; DFS hereafter) to introduce nontraded goods,that is, services. He shows that compared with autarky, free trade spurs deindustrialization and decreases the rate of economic growth. Spilimbergo’s model is based on two key
assumptions, productivity growth differential3 and inelastic demand.4
In this paper, using Spilimbergo’s (1998) model, we attempt to a comparison between
two trading countries rather than a comparison between autarky and free trade as in Spilimbergo (1998). In particular, we investigate how a change in a parameter of one country
affects the deindustrialization of the other country, which is not investigated in Spilimbergo(1998). As will be shown later, it is possible that even if the productivity growth differential
in the home country is greater than that in the foreign country, the extent of the deindustri1

Obstfeld and Rogoff (1996, ch. 4) also consider these three concepts simultaneously.
For the endogenization of productivity growth, see Pugno (2006) and De Vincenti (2007). Fixler andSiegel (1999), Oulton (2001), and Sasaki (2007) discuss the importance of services as intermediate inputs.
Bonatti and Felice (2008) considers capital accumulation in both manufacturing and services.
3
For empirical evidence as to the existence of productivity growth differentials, see Rowthorn andWells (1987), Rowthorn and Ramaswamy (1997), Kendrick (1985), Bernard and Jones (1996), and Fixler
and Siegel (1999).
4
According to Fuchs (1968), the income elasticity of demand for services is 1.12 in the US 1929–1965.
Summers (1985) reports that the income elasticity of demand for services is 0.977 and the price elasticity isvery low in a cross-sectional analysis for 34 countries. Following the method of Summers (1985), Falvey andGemmell (1996) update the data and show that the income elasticity of services is about unity and the priceelasticity is 0.32.
22

alization in the home country is less than that of the foreign country owing to the effect of ashift in trade specialization.
Moreover, using our model, we also analyze the real exchange rate.5 In the field ofinternational economics, the Balassa-Samuelson (BS) effect is well known as a fundamental
factor in determining the movement of the real exchange rate (Balassa, 1964 and Samuelson,
1964). According to the BS effect, a country will experience an appreciation in the realexchange rate if its productivity growth differential between the traded and nontraded goods
sectors is greater than the productivity growth differential of its trading partner. However,according to our analysis, it is possible that even if the productivity growth differential in thehome country is greater than that in the foreign country, the real exchange rate depreciates,
and not appreciates, owing to the effect of a shift in trade specialization.
The remainder of the paper is organized as follows. Section 2 presents our model andthen explains the mechanism of deindustrialization. The equilibrium of the model is summarized by two variables: the factorial terms of trade and the index of borderline good.
Accordingly, Section 3 conducts a comparative statics analysis with regard to these variables. Section 4 derives the equilibrium real exchange rate and investigates the relationshipbetween deindustrialization and changes in the real exchange rate. Section 5 investigates theeffect of productivity growth differential on deindustrialization and the real exchange rate.
Section 6 concludes the paper.

2

The Model

Our model is based mainly on the work of Spilimbergo (1998), which is modified for our
purpose in some respects.

2.1 Production side
Each sector uses only labor as input and operates with fixed coefficient technology.
S = as Ls,

m(z) = am (z)Lm (z),5z ∈ [0, 1],(1)

Recent studies on changes in the real exchange rate derive the equilibrium real exchange rate by using
an intra-industry trade theory due to product differentiation. Moreover, these studies emphasize other factors
besides the traditional BS effect in determining changes in the real exchange rate. See, for instance, Unayama (2003) and Bergin, Glick, and Taylor (2006). The present paper, in contrast, derives the equilibrium
real exchange rate by using the traditional inter-industry trade theory. It is true that intra-industry trade arisingfrom product differentiation captures reality to some extent, but inter-industry trade arising from differencesin productivity still has significance even among developed countries. For instance, Golub (1994), Golub andHsieh (2000), and Kasuya and Okada (2007) empirically show the validity of the traditional Ricardian trade
theory.

3where S and L s denote the output and the employment of services, respectively, and m(z)and Lm (z) the output and the employment of each manufacturing sector, respectively. a s
and am (z) represent the levels of labor productivity of services and the manufacturing sector,
respectively. Each manufacturing sector is indexed by a real number z on the closed interval[0, 1].
Given the perfect mobility of domestic labor across sectors, wages are equalized within
the country. Competition equalizes the price of each good with its unit labor cost.
ps =

w
,
as

pm (z) =w,
am (z)(2)

where p s denotes the price of services, pm (z) the price of each manufacturing good, and w
the money wage in terms of the domestic currency.

2.2 Demand side
Suppose that the social welfare in a country is given by the following CES utility function.
hiσ
σ−1 σ−1σ−1,
U = αM σ + (1 − α)S σ

σ > 0, σ , 1, 0 < α < 1,(3)

where M denotes the aggregate consumption of manufacturing goods, S the consumption ofservices, and σ the elasticity of substitution between M and S . α is the utility weight of the
manufacturing consumption. Suppose that M takes the following Cobb-Douglas form.
"Z 1#

M = exp

log m(z) dz .

(4)0

The budget constraint is given by pm M + p s S = Y. Assuming full employment, we canR1write nominal national income Y as Y = w(Lm + L s ) = wL̄, where Lm ≡ 0 Lm (z) dz.
The price index for M is given by"Z 1
pm = exp#
log pm (z) dz ,(5)0which is the minimum expenditure for buying one unit of M. Moreover, the price index
corresponding to the utility function (3) is given byhi 1
σ 1−σ 1−σ.
P = ασ p1−σ
+
(1
−
α)
p
m
s

(6)

Maximizing (3) subject to the budget constraint, we obtain the following demand func4

tions.
σ

M=α p −σ  Y 
m

P

P

,

σ

S = (1 − α)

 p −σ  Y 
s

P

P

,

(7)

where Y/P is the real national income. Since the preference is homothetic, the income elasticity of demand is unity. The elasticity of substitution σ also represents the price elasticity
of demand.

2.3 Employment share
The manufacturing employment Lm is given by subtracting L s from L̄. To begin with, let us
turn to L s . From the market clearing condition for service, we obtainσ

a s L s = (1 − α)

 p −σ  Y 
s

P

P

.

(8)

Substituting Y = wL̄ into equation (8) and rearranging it, we have the following employment
share of services.
Ls
1
.
=
 σ
α
L̄
(pm /p s )1−σ
1+

(9)

1−α

Using equation (9), we obtain the employment share of manufacturing.
 σα(pm /p s )1−σ
Lm
1−α
=
.
 σ
L̄
1 + α (pm /p s )1−σ

(10)

1−α

Each employment share depends on the relative price pm /p s . If the elasticity of substitution is smaller than unity, then the manufacturing employment share is increasing in pm /p s .
Therefore, when the relative price falls, the manufacturing employment share also falls,
which is nothing less than deindustrialization. The elasticity of substitution here, as has
been stated above, corresponds to the price elasticity of demand. The elasticity of substitution below unity means inelastic demand.

2.4 Free trade
Let us introduce a foreign country to consider trade between the two countries. Suppose thatthe two countries differ in their labor endowments and production functions in each sector.
Suppose also that the manufacturing goods are tradable while services are nontradable, andthat there exist no international transportation costs and no trade barriers. We assume that
5that the social utility function of the foreign country is given byσh
σ−1
σ−1 i σ−1
U ∗ = α∗ (M ∗ ) σ + (1 − α∗ )(S ∗ ) σ,

0 < α∗ < 1.

(11)

The parameter α∗ in the foreign country is different from that in the home country, but σ iscommon to the two countries. In what follows, foreign variables are marked with an asterisk“∗”.
To consider international trade based on the principle of comparative advantage, we
define the relative labor productivity as
A(z) ≡a∗m (z),am (z)A0 (·) > 0.

(12)

The sign of the derivative implies that the manufacturing goods are ordered in accordancewith diminishing home country comparative advantage.
The home country has a cost advantage over the foreign country in producing z if thefollowing condition holds:
w
ew∗
< ∗ ,
am (z) am (z)(13)

where w∗ is the foreign money wages expressed in terms of its own currency and e is thenominal exchange rate in terms of home currency.
Now let us define z̄ such thatew∗
= A(z̄).
w(14)

Given the relative wage ew∗ /w, the home country has a cost advantage in the range z ∈ [0, z̄),while the foreign country has a cost advantage in the range z ∈ (z̄, 1]. Thus, the home(foreign) country exports (imports) the manufacturing goods z ∈ [0, z̄) and imports (exports)
the goods z ∈ (z̄, 1].
We will derive a condition for balanced trade. The home country spends a part of its
national income Y, Em ≡ pm M, on the manufacturing goods, and the fraction 1 − z̄ of Em
is spent on the imported goods. In a similar way, the foreign country spends a part of its
national income Y ∗ , Em∗ ≡ p∗m M ∗ , on the manufacturing goods, and the fraction z̄ of Em∗
is spent on the imported goods. From these, the value of imports of the home country is(1 − z̄)Em in terms of the home currency while that of the foreign country is z̄Em∗ in terms of6the foreign currency. Thus, the balanced trade condition is given by(1 − z̄)Em = ez̄Em∗ .

(15)

Note that z̄Em∗ is multiplied by e.
Let us return to Em and Em∗ . There is just one factor of production and there are no profits
in the model, so that the expenditure spent on the manufacturing goods has to be equal to thevalue of total production in the manufacturing, which is consequently equal to the income
earned by the employees in the manufacturing sector. Thus, we have
Z z̄Em = w

Em∗ = w∗

Lm (z) dz,
0

Z 1
z̄

Lm∗ (z) dz.

(16)

R z̄
R1
R1
We define Lm = 0 Lm (z) dz and Lm∗ = z̄ Lm∗ (z) dz. Note that Lm = 0 Lm (z) dz under autarky.
Substituting equation (16) into equation (15), we can rewrite the balanced trade condition as
ew∗
where ω ≡.
w

Lm 1 − z̄,ω= ∗ ·Lmz̄

(17)

The relative wage ω also means the inverse of the factorial terms of trade. What is importantin equation (16) is Lm /Lm∗ . In the usual DFS model Lm /Lm∗ is replaced by L̄/L̄∗ , whichis constant and exogenously given. In our model, on the other hand, there appears the
manufacturing employment ratio between the two countries, which is a function of pm /p s ,not constant (see equation (10)).
The prices of the manufacturing goods after trade in terms of the home currency are
given by
 w





 am (z)pm (z) = 
ew∗




 a∗ (z)mz ∈ [0, z̄],z ∈ [z̄, 1].

(18)

Using these prices, we obtain the price index for the manufacturing goods in each country:
#
Z 1
ew∗
w
dz +
log ∗
dz ,
pm = explog
am (z)am (z)
z̄
0
"Z z̄
#
Z 1
w
w∗
∗
pm = exp
log
dz +
log ∗
dz .
eam (z)am (z)
0
z̄
"Z z̄

(19)
(20)

Note that pm = ep∗m because the law of one price holds for the traded goods and bothcountries are identical in the index for the aggregate consumption of manufacturing goods.
7Therefore, purchasing power parity (PPP hereafter) for traded goods holds in our model.
The relative prices between manufacturing and services are given by" Z z̄
#
Z 1
pm
1−z̄
∗
= a s ω exp −log am (z) dz −log am (z) dz ,ps0z̄" Z z̄
#
Z 1
p∗m
∗ −z̄
∗
= a s ω exp −log am (z) dz −log am (z) dz .
p∗s
0
z̄

(21)
(22)

For analytical tractability, we specify the production functions as follows:am (z) = exp(T m + 1 − z),a∗m (z) = exp(T m∗ + z),

a s = exp(T s ),a∗s = exp(T s∗ ),

(23)
(24)

where T m (T m∗ ) and T s (T s∗ ) capture the overall level of technology in the manufacturing andservices, respectively, which are given exogenously.6 Under these specifications, the relativelabor productivity in manufacturing is rewritten as follows:
A(z) = exp[T m∗ − T m + 2z − 1],(25)

which implies that ∂A(·)/∂z = 2 exp[T m∗ − T m + 2z − 1] > 0

2.5 Equilibrium of the model
The equilibrium values of z̄ and ω are given by the intersection of the curve given by equation(14) and the curve given by equation (17), which are restated as follows:
AA : ω = A(z̄),
Lm (ω, z̄) 1 − z̄
BB : ω = ∗.
Lm (ω, z̄) z̄

(26)
(27)

The AA curve determines z̄ with ω given, while the BB curve determines ω with z̄ given.
Since Lm and Lm∗ depend on the relative prices, which in turn depend on ω and z̄, we canwrite Lm and Lm∗ as Lm (ω, z̄) and Lm∗ (ω, z̄), respectively. The AA curve is upward-slopingin (z̄, ω) space because A0 (·) > 0. The shape of the BB curve is not evident at this stage
because Lm (·)/Lm∗ (·) is not constant. However, if the BB curve were upward-sloping, theequilibrium could be unstable, so that comparative static analysis below might be meaningless. Following Spilimbergo (1998), we assume that the BB curve is downward-sloping in
6

Such functional forms follow Obstfeld and Rogoff (1996, ch. 4).

8our analysis below.7 Figure 1 shows the AA and BB curves, the intersection of which gives
the equilibrium values of z̄ and ω.
[Figure 1 to be inserted here]

3

Comparative statics analysis

This section conducts a comparative statics analysis with regard to ω, z̄, and the commodity
terms of trade.
We define the commodity terms of trade as follows:
pT ≡

pm,EX
,
ep∗m,EX(28)

where pm,EX denotes the price of home export goods and p∗m,EX the price of foreign export
goods. These prices are respectively specified as follows:" Z z̄
#1
pm,EX = exp
log pm (z) dz ,z̄ 0"p∗m,EX = exp

1
1 − z̄

Z 1z̄

#log p∗m (z) dz

.

(29)

Substituting (29) into (28), we obtain
pT =

i
h
1
exp T m∗ − T m + z̄ − 12 .
ω

(30)

Since we have ω = A(z̄) at the equilibrium, we can rewrite equation (30) ashipT = exp −z̄ + 21 .

(31)

Note that z̄ in equation (31) is the equilibrium value of z̄. From (31), we can see that a risein z̄, that is, the expansion of the range of manufacturing goods produced at home leads to a
deterioration in the home commodity terms of trade.
7

Under our specifications, the relative prices of the domestic and foreign countries are given byihpm= ω1−z̄ exp T s − z̄T m − (1 − z̄)T m∗ + z̄2 − z̄ − 12 ,
ps
h
i
p∗m
= ω−z̄ exp T s∗ − z̄T m − (1 − z̄)T m∗ + z̄2 − z̄ − 12 .
∗ps

Substituting these prices in equation (27) yields an implicit function for the BB curve, in which z̄ and ω are
the endogenous variables while L̄, L̄∗ , T m , T s , T m∗ , T s∗ , α, α∗ , and σ are the parameters. Appendix presents
conditions for the downward-sloping BB curve.

9In what follows, we consider cases where σ is smaller than unity. When the elasticity
of substitution is not unity, Lm /Lm∗ in the BB curve depends on the relative prices between
manufacturing and services, so that the BB curve depends on the labor productivity both inmanufacturing and in services.8
 Changes in relative labor endowments
Suppose that L̄/L̄∗ increases: the labor endowment in the home country increases relative
to that in the foreign country. While the AA curve does not shift, the BB curve rotatesclockwise around (1, 0). As a result, both ω and z̄ rise. That is, the equilibrium factorial
terms of trade deteriorates and the range of manufacturing goods produced at home expands.
Moreover, the home commodity terms of trade deteriorate.
[Figure 2 to be inserted here] Changes in the home manufacturing productivity
Suppose that the manufacturing labor productivity in the home country increases. To
begin with, the AA curve shifts downward. In addition, the BB curve rotates on a certain
point as shown in Figure 3. Figure 3 describes a case where both countries are symmetricconcerning all the parameters and labor endowments before T m rises. In this case, the BB
curve rotates around the initial equilibrium point as in Figure 3. Note that the BB curve
does not generally rotate around the equilibrium point.9 In any case, however, the AA curve
shifts more largely than the BB curve, so that ω declines and z̄ increases, which leads to a
deterioration in the home commodity terms of trade.
[Figure 3 to be inserted here] Changes in the home services productivity
Suppose that the productivity of services sector in the home country T s increases. While
the AA curve does not shift, the BB curve rotates clockwise around (1, 0). This results in therise of ω and the expansion of the range of manufacturing goods produced at home, which
deteriorates the home commodity terms of trade.
[Figure 4 to be inserted here]

8∗
When σ = 1, Lm /Lmremains constant. Thus, the AA and BB curves shift separately, not simultaneously.
Moreover, labor productivity in services does not appear in the BB curve.
9
For this, see Appendix.

10 Changes in the utility weight of manufacturing consumption
A rise in α means a demand shift toward manufacturing goods in the home country.10
The parameter α appears in the BB curve. Then the rise of α rotates the BB curve clockwisearound (1, 0), which is similar to the case of a rise in L̄/L̄∗ . A fall in α, in contrast, meansa demand shift toward services in the home country. In this case, both ω and z̄ fall, thereby
improving the home commodity terms of trade.
Table 1 summarizes the results above. From the table we see that a rise in productivity
both in manufacturing and in services deteriorates the home commodity terms of trade.
[Table 1 to be inserted here]

4

Real exchange rate

The real exchange rate, ε, can be defined as ε ≡ eP∗ /P. A fall in ε means that the homecountry experiences appreciation in the real exchange rate relative to the foreign country.
Substituting P and P∗ into the above definition yields
σ


 1
 α∗ !σ 1 + 1−α∗ ∗ (p∗m /p∗s )σ−1  1−σα ,ε = 
·
 σ

1−α
σ−1
α
1+
(pm /p s )

(32)

α

where the relative prices are given byhipm= exp −(T m − T s ) − (z̄ − 1)2 − 12 ,
ps
i
h
p∗m
∗
∗
2
1
.
=
exp
−(T
−
T
)
−
z̄
−
m
s
2
p∗s

(33)
(34)

Note that z̄ is evaluated at the equilibrium.
As has been shown above, the equilibrium value of z̄ depends on each parameter, so that
we can express it as z̄ = z̄(T m , T m∗ , T s , T s∗ , α, α∗ , L̄, L̄∗ ). From equations (33) and (34) together
with (32), we can state that changes in the real exchange rate depend both on the direct
effect of productivity growth and on the indirect effect of a shift in specialization patterns
via the productivity growth. Besides the usual BS effect, the effect of a shift in specialization
patterns affects the real exchange rate.
In our model, both deindustrialization and changes in the real exchange rate are consequences, so that there is no causal relationship between them. However, we can interrelate
10With pm /p s being constant, a rise in α increases M/S irrespective of the size of σ.

11them because both the manufacturing employment share and the real exchange rate dependon the relative price. This is what we are turning to in what follows.
Let us consider the ratio of manufacturing employment share in the home and foreigncountries. Which country experiences more rapid deindustrialization depends on the decreasing rates of the relative prices pm /p s and p∗m /p∗s . In a similar way, whether the realexchange rate appreciates or depreciates depends on the rates of changes in the relative
prices. Accordingly, we can investigate the relationship between the real exchange and theratio of manufacturing employment share.
Let lm ≡ Lm /L̄ and lm∗ ≡ Lm∗ /L̄∗ be the manufacturing employment share in the homeand foreign countries, respectively. Then, the ratio of the manufacturing employment share,φ ≡ lm /lm∗ , is given by ∗ σ(p∗m /p∗s )σ−1
1 + 1−α
α∗
.
φ=
 σ
σ−1
1 + 1−α
(p
/p
)
m
s
α

(35)

Suppose that both lm and lm∗ decline for any reason. If α and α∗ are constant, then a fall in
φ means that home deindustrialization is more rapid than foreign deindustrialization. Fromequations (32) and (35), we obtain the following relationship between φ and ε:φ= α σα∗ε1−σ .

(36)

When σ < 1, both φ and ε move in the same direction given that α and α∗ are constant.
Result 1. Suppose that the elasticity of substitution between the aggregate consumption of
manufacturing goods and the consumption of services is smaller unity and that the utility
weight of manufacturing consumption in both countries is constant. Then, an economy inwhich deindustrialization is more rapid than its trading partner experiences an appreciationof the real exchange rate. Moreover, changes in φ is smaller than changes in ε, that is, theratio of manufacturing share in the home and foreign countries changes less than the realexchange rate.

5

Numerical analysis

Section 3 reveals how equilibrium values of ω and z̄ change with a change in each parameter. This subsection analyzes changes in variables such as ε and φ by using numerical12

simulations.11
Let us derive indirect utility functions because we are interested in changes in welfare.
1

 σ−1
!
 σ pm 1−σ
V = a s α+ (1 − α)σ  ,
ps

1

 σ−1
!
∗ 1−σ


p


V ∗ = a∗s (α∗ )σ m∗+ (1 − α∗ )σ  ,
ps

(37)

where V and V ∗ are per capita utility, which are not directly dependent on population.
To start with, we set the initial parameters so that both countries will be symmetric.
T m = 0, T m∗ = 0, T s = 0, T s∗ = 0, α = 1/2, α∗ = 1/2, L̄ = 1, L̄∗ = 1, σ = 2/3.

(38)

In this benchmark case, each endogenous variable is determined as listed in Table 2 (see thecolumn “Benchmark”).
[Table 2 to be inserted here]
Next, we change each parameter to analyze how the endogenous variables change. Since
the home and foreign countries are symmetric in their structures, we focus on the parametersof the home country only. Compared with the benchmark case, each parameter is set as
follows:
L̄ = 2, T m = 1, T s = 1, α = 1/3.

(39)

Table 2 summarizes the results of these parameters.
Some results are worth commenting. When T m rises, the real exchange rate appreciates
and the ratio of manufacturing employment share declines. In addition, both lm and lm∗
decline. This result suggests that a rise in the home manufacturing productivity can cause
deindustrialization in the foreign country. We can consider this case to be a case where theproductivity growth differential between manufacturing and services in the home country
is greater than that in the foreign country because T m rises whereas T s , T m∗ , and T s∗ remain
constant. Therefore, we are able to compare this case with the usual BS case. In the usual BS
11This numerical analysis is conducted as follows. To begin with, eliminating ω from equations (26) and(27), we derive an equation for z̄:noih ∗ σexp (1 − σ) (T m∗ − T s∗ ) + z̄2 + 21
1 + 1−α∗L̄
1 − z̄
αexp[T m∗ − T m + 2z̄ − 1] = ∗ ·
.
n
oi ·
h
 σ
3
1−α
z̄
L̄ 1 +
exp (1 − σ) (T m − T s ) + z̄2 − 2z̄ +α

2Next, substituting numerical values into the parameters of the equation above, we can solve it for z̄. Using
the numerical value of z̄, we can obtain other endogenous variables. To solve the equation of z̄, we use the“FindRoot” command, a built-in function of Mathematica.

13

case, the real exchange rate appreciates, and in this case, the real exchange rate appreciates
as well.
When T s rises, the manufacturing employment share of the home country increases whilethat of the foreign country decreases. The relative price of the home country rises, but thelevel of utility increases. The home utility is decreasing in the relative price and increasingin the level of productivity in services. When T s rises, the latter positive effect dominates theformer negative effect, and consequently the utility of the home country rises. Moreover, therise of T s in the home country leads to a decline in the relative price of the foreign country,
thereby increasing the foreign utility.
[Table 3 to be inserted here]
In contrast to the case above, we will change some of the parameters simultaneously. In
this case, we will obtain interesting results. Let us set the productivity parameters to T m = 1,
T s = 1/2, T m∗ = 1/2, and T s∗ = 0. This means that the productivity growth differential
between manufacturing and services in the home country is greater than that in the foreigncountry.12
From Table 3, we obtain the following result with regard to deindustrialization.
Result 2. Suppose that the growth rate of productivity in manufacturing is greater than thatin services. Suppose also that this sectoral difference in productivity growth is larger in thehome country than that in the foreign country. Then, depending on the size of the effect ofa shift in trade specialization, it is possible that the extent of the deindustrialization in theforeign country is greater than that of the home country.
According to Baumol’s (1967) closed economy model, other things being equal, a country whose productivity growth differential is large shows the large extent of deindustrialization. However, with condideration for international trade, it is possible that the extent ofdeindustrialization of a country is smaller than that of the trading partner even though the
productivity growth differential is large. Obstfeld and Rogoff (1996, p. 225) point out thatthe extent of deindustrialization in Japan is small though the productivity growth differential
is large. Then, they conclude that it is difficult to explain the decline in manufacturing share
12

We must note the following. Let us write benchmark parameters and parameters after the change as T m,0 ,T s,0 and T m,1 , T s,1 , respectively. Then, (T m,1 − T m,0 ) − (T s,1 − T s,0 ) does not represent the productivity growthdifferential. Recall that the levels of the productivity are am (z) = exp(T m + 1 − z) and a s = exp(T s ). Thus,
the productivity growth differential is given by exp(T m,1 − T m,0 ) − exp(T s,1 − T s,0 ). When T m = 1, T s = 1/2,
T m∗ = 1/2, and T s∗ = 0, the home productivity growth differential, compared with the benchmark case, will beexp(1) − exp(1/2) ≈ 1.07 and the foreign productivity growth differential will be exp(1/2) − exp(0) ≈ 0.65,
so that the former is certainly larger than the latter. That is, the productivity growth differential between
manufacturing and services in the home country is greater than that in the foreign country.

14

by the productivity growth differential. However, as our analysis shows, when the productivity growth differential in the home country is large, the extent of deindustrialization in
the trading partner can be greater than that in the home: we might call this phenomenon theexport of deindustrialization.
From Table 3, we obtain the following result with regard to the real exchange rate.
Result 3. Suppose that the growth rate of productivity in manufacturing is greater than thatin services. Suppose also that this sectoral difference in productivity growth is larger in thehome country than that in the foreign country. Then, depending on the size of the effect of ashift in trade specialization, it is possible that the real exchange rate depreciates in contrast
to what the usual BS effect expects.
According to the usual BS effect, the real exchange rate in this case should appreciate because the productivity growth differential between manufacturing and services in the homecountry is greater than that in the foreign country. However, we observe an depreciationin the real exchange rate. With the effect of a shift in specialization patterns, it is possiblethat the real exchange rate depreciates, which is opposite to what the BS effect expects (theanti-BS effect).
Recent empirical studies challenge the goodness of fit of the BS effect as an explanation
for the long-term movement of the real exchange rate (Lee and Tang, 2007 and literaturecited therein). These studies emphasize that PPP does not hold even for traded goods (e.g.,
Engel, 1999). In the intra-industry trade theory mentioned in footnote 5, PPP for traded
goods does not hold. However, we show that it is possible that the real exchange rate moves
in the direction opposite to the expectation of the BS effect even though PPP for traded
goods holds.
Why does it happen? When the elasticity of substitution is smaller than unity, the realexchange rate is increasing in pm /p s whereas it is decreasing in p∗m /p∗s . Each relative pricewill fall when the growth rate of productivity in manufacturing exceeds that in services ineach country. A fall in pm /p s has an effect of decreasing ε (i.e., appreciation), and on theother hand a fall in p∗m /p∗s has an effect of increasing ε (i.e., depreciation). This means thatthe real exchange rate appreciates (depreciates) if the decreasing rate of the home relative
price is larger (smaller) than the decreasing rate of the foreign relative price. These relative
prices are given by equations (33) and (34). As has been stated above, changes in the relative
prices depend both on the direct effect of productivity growth differentials and on the indirect
effect of a shift in z̄. In benchmark case, we have z̄ = 1/2. When z̄ becomes larger than 1/2,
the indirect effect in (33), that is, (−(z̄ − 1)2 − 21 ) is increasing in z̄ while the indirect effect in(34), that is, (−z̄2 − 21 ) is decreasing in z̄. This suggests that whereas a shift in specialization
has an effect of diminishing the decreasing rate of pm /p s in the home country, the shift in15

specialization has an effect of enhancing the decreasing rate of p∗m /p∗s in the foreign country.
From this it follows that the real exchange rate can depreciate even though the productivity
growth differential between manufacturing and services in the home country is greater thanthat in the foreign country.
Note that the same mechanism works behind Results 2 and 3 because from Result 1, φand ε move in the same direction as long as 0 < σ < 1

6Concluding remarks

We have analyzed deindustrialization and changes in the real exchange rate by using a Ricardian trade model with a continuum of goods that introduces nontraded services. The
main results are summarized as follows: (i) if deindustrialization proceeds in both countries,
then the ratio of manufacturing employment share and the real exchange rate move in thesame direction; (ii) even if the productivity growth differential in the home country is greaterthan that in the foreign county, the extent of deindustrialization in the home country is notnecessarily larger than that in the foreing country. On the contrary, it is possible that theforeign deindustrialization exceeds the home deindustrialization; and (iii) even if the productivity growth differential in the home country is greater than that in the foreign county,
the real exchange rate of the home country can depreciate contrary to the expectaion of theBalassa-Samuelson effect.
A shift in specialization patterns in the model corresponds to structural change in manufacturing sectors. Thus, we can conclude that when investigating the manufacturing employment shift and the movement of the long-term real exchange rate, we should consider
structural change as well as productivity growth differentials.
Comparative statics analysis in this paper assumes that trade is balanced before and after
changes in the parameters because our model is a static one. If, however, we introduce dynamic optimization into the model, then the effect of a change in a parameter in the dynamic
model might differ with that in the static model because trade need not be balanced at eachpoint in time. Moreover, the correlation between the ratio of the manufacturing employment
share and the real exchange rate should be empirically analyzed. These issues will be left to
future research.

16

References
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Political Economy, 72 (6), pp. 584–596.
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Bonatti, L. and G. Felice (2008) “Endogenous Growth and Changing Sectoral Composition
in Advanced Economies,” Structural Change and Economic Dynamics 19 (2), pp.
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Engel, C. (1999) “Accounting for U.S. Real Exchange Rate Changes,” Journal of Political
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Fixler, D. J. and D. Siegel (1999) “Outsourcing and Productivity Growth in Services,” Structural Change and Economic Dynamics, 10, pp. 177–194.
Fuchs, V. R. (1968) The Service Economy, New York: Columbia University Press.
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Kasuya, M. and T. Okada (2007) “The Effects of Technology Changes on Sectoral Trade
Patterns,” Review of International Economics, 15 (1), pp. 112–125.

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Kendrick, J. W. (1985) “Measurement of Output and Productivity in the Service Sector,” in
R. Inman (ed), Managing the Service Economy: Prospects and Problems, Cambridge:
Cambridge University Press.
Lee, J. and M.-K. Tang (2007) “Does Productivity Growth Appreciate the Real Exchange
Rate?” Review of International Economics, 15 (1), pp. 164–187.
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18

ω

BB

ω

AA

BB

ω

AA

AA

BB

ω̄

O

1 z

z̄

Figure 1: Equilibrium

ω

BB

O

1 z

Figure 2: A rise in L̄/L̄∗

ω

AA

O

1 z

Figure 3: A rise in T m

ω

ω0

ω0
O

1 z

Figure 4: A rise in T s

O

1 z

Figure 5: A large ω0

19

O

1 z

Figure 6: A small ω0Table 1: Results of comparative statics analysis of z̄, ω, and pTz̄
L̄/L̄ ↑ ↑
Tm ↑
↑
Ts ↑
↑
α↓
↓
∗

ω
↑
↓
↑
↓

pT
↓
↓
↓
↑

Table 2: Results of numerical analysis

z̄
ω̄
pT
ε
φ
lm
lm∗
pm /p sp∗m /p∗s
V
V∗

Benchmark
0.5
1
1
1
1
0.438
0.438
0.472
0.472
0.711
0.711

L̄ ↑
0.621
1.275
0.886
1.147
1.047
0.447
0.427
0.526
0.412
0.678
0.754

Tm ↑
0.640
0.487
0.869
0.647
0.865
0.367
0.425
0.196
0.403
1.012
0.761

Ts ↑
0.531
1.063
0.970
1.738
1.202
0.523
0.435
1.323
0.458
1.178
0.721

α↓
0.449
0.903
1.052
0.897
0.736
0.325
0.442
0.448
0.496
0.691
0.696

Table 3: Simultaneous change in parameters

z̄
ω̄
pT
ε
φ
lm
lm∗
pm /p sp∗m /p∗s
V
V∗

Benchmark After the change
0.5
0.589
1
0.724
1
0.915
1
1.113
1
1.036
0.438
0.404
0.438
0.390
0.472
0.311
0.472
0.260
0.711
1.398
0.711
0.910

20

A Appendix
 The slope of the BB curve
The BB curve is given as follows:ω=

Lm (ω, z̄) 1 − z̄.
Lm∗ (ω, z̄) z̄

(A-1)

Note that z̄ in the equation above is not a value obtained by the intersection with the AA
curve but a value on the BB curve.
Applying the implicit function theorem to (A-1), we can totally differentiate it as follows:#"∂Lm∗ Lm
1 − z̄ ∂Lm 1
dω
dω =
−
z̄
∂ω Lm∗∂ω (Lm∗ )2"#
1 Lm 1 − z̄ Lm
1 − z̄ ∂Lm 1
1 − z̄ ∂Lm∗ Lm+−−− 2 ∗ dz̄.
(A-2)
z̄ ∂z̄ Lm∗z̄ ∂z̄ (Lm∗ )2 z̄ Lm∗z̄ Lm
Here, we introduce the following elasticities:
η=∂Lm z̄
,∂z̄ Lmη∗ =∂Lm∗ z̄,∂z̄ Lm∗

θ=

∂Lm ω
,
∂ω Lm

θ∗ =

∂Lm∗ ω
.
∂ω Lm∗

Substituting these into equation (A-2) and rearranging it, we havedω ω η − η∗ − 1=.
dz̄z̄ 1 − θ + θ∗

(A-3)

From this, the BB curve is downward-sloping if the following condition holds.
η − η∗ − 1< 0.
1 − θ + θ∗

(A-4)

Now we derive the elasticities. Considering the fact that Lm depends on pm /p s , which inturn depends on z̄ and ω, we obtain the following relations:
Ls
,
L̄
L∗
η∗ = z̄D(1 − σ) ∗s ,L̄η = z̄D(1 − σ)

θ = (1 − z̄)(1 − σ)L∗θ∗ = −z̄(1 − σ) ∗s ,
L̄

21

(A-5)
(A-6)
Ls
,
L̄

(A-7)
(A-8)

where D ≡ − log ω + (T m∗ − T m + 2z̄ − 1). First, from these relations we obtain
"
#
L∗s
Ls
∗
1 − θ + θ = 1 − (1 − σ) (1 − z̄) + z̄ ∗ .
L̄
L̄

(A-9)

Since 0 < σ < 1 by supposition and the employment share in services is smaller than orequal to unity, 1 − θ + θ∗ > 0 holds. Therefore, the denominator of the left-hand side of (A-4)
is always positive. Second, we obtain!
L s L∗s∗−− 1.
(A-10)
η − η − 1 = z̄D(1 − σ)L̄ L̄∗
Since 1 − θ + θ∗ > 0 holds, (A-10) needs to be negative so that the BB curve will be
downward-sloping. Analysis in the text assumes η − η∗ − 1 < 0.
 A shift in the BB curve with a rise in T m
How the BB curve shifts with a rise in T m depends on the sign of the following derivative:dω.
dT m z̄=const.

(A-11)

Applying the implicit function theorem to the BB curve, we can totally differentiating it asfollows:!
dωωz̄(1 − σ) L s L∗s−=−.
(A-12)
dT m z̄=const.
1 − θ + θ∗ L̄ L̄∗
Since 1 − θ + θ∗ > 0 from the analysis above, the sign of (A-12) depends on which is larger,
L s /L̄ s or L∗s /L̄∗s . If L s /L̄ > L∗s /L̄∗ , then the sign of (A-12) is negative. Consequently, the BB
curve shifts downward with a rise in T m .
Let us analyze the size of the employment share in services. The inequality L s /L̄ > L∗s /L̄∗is identical with
1
1
>
.
σ
 ∗ σαα1 + 1−α(pm /p s )1−σ 1 + 1−α(p∗m /p∗s )1−σ∗(A-13)

Substituting the relative prices into (A-13) and computing it further, we finally obtain thefollowing relation:
a∗
ω< s
as

"

!
#σ
α∗   α  1−σ≡ ω0 .
1 − α∗1−α(A-14)

From this it follows that if ω < ω0 , then L s /L̄ > L∗s /L̄∗ . This means that the part of the BB
curve such that ω < ω0 shifts downward with a rise in T m . On the other hand, the part of theBB curve such that ω > ω0 shifts upward with a rise in T m . The point of the BB curve suchthat ω = ω0 does not shift with a rise in T m . Summarizing these results, we can conclude
that the BB curve rotates on the point of ω = ω0 as shown in Figures 3, 5, and 6.
22

In the benchmark case, ω0 = 1 and the intersection of the AA and BB curves is ω = 1,
so that the BB curve happens to rotate on the initial equilibrium point.
 A shift in the BB curve with a rise in T s
How the BB curve shifts with a rise in T s depends on the sign of the following derivative:dz̄ω(1 − σ) L s=· .
dT s ω=const. 1 − θ + θ∗ L̄

(A-15)

When σ < 1, the sign of (A-15) is positive. Therefore, the BB curve shifts upward with arise in T s .
 A shift in the BB curve with a rise in α
How the BB curve shifts with a rise in α depends on the sign of the following derivative:
dz̄
ωσ
Ls
· .
=
∗
dα ω=const. α(1 − α)(1 − θ + θ ) L̄

(A-16)The sign of (A-16) is always positive. Therefore, the BB curve shifts upward with a rise inα.

23