Real Exchange Rate and Economic Growth
-- A Theoretical Re-examination of the Balassa Hypothesis
Yunfa Zhu*
Adian A. McFarlane†
Abstract
We formulate a model with three sectors and two countries linked by international
trade in a general equilibrium framework to re-examine the theoretical foundations
of the Balassa Hypothesis. The three sectors consist of two tradable and one
nontradable. Prices and exchange rates are determined by the interaction of demand
and supply across the two countries. The model allows for differential technological
change across countries and sectors. Our model examines under what conditions the
Balassa Hypothesis holds. We find that the Balassa Hypothesis may not hold in the
case of productivity changes in the tradable sector but may hold in the reverse
direction in when there are productivity changes in the nontradable sector.
Keywords: general equilibrium, international trade, real exchange rate
JEL Classification: D58, F1, F31
*Department of Economics, University of Manitoba umzhuy@cc.umanitoba.ca
†
Department of Economics, University of Manitoba mcfarlaa@cc.umanitoba.ca
We thank. Ryan Compton, Hickmet. Gunay, John Serieux, Wayne Simpson, and Lindsay Tedds for helpful
comments. All remaining errors are our own.
Real Exchange Rate and Economic Growth
1. Introduction
The well known Harrod-Balassa-Samuelson Hypothesis, (Harrod, 1973; Balassa, 1964;
Samuelson, 1964) or simply the Balassa Hypothesis, sets out a channel through which real
variables, in particular productivity changes, can affect the real exchange rate. The Balassahypothesis postulates that as the process of economic growth unfolds the effect of relatively
higher productivity growth in the tradable sector raises the relative price of the nontradable to
tradable sector within a country. This in turn has implications for the real exchange rate across
countries.
Balassa’s argument can be summarized as follows. In the original formulation of the Balassa
hypothesis there are two sectors, tradable and nontradable sector (Balassa, 1964). Economic
growth is primarily driven by productivity improvements in the tradable sector and there is little
or no difference in the productivities of non-tradable sectors between rich and poor countries. In
addition, for the tradable sector, the law of one price applies to rich and poor countries and under
a competitive labour market the same wage applies to nontradable and tradable sectors within
countries. Thus, the relative price of the non-tradable sector will be higher in rich countries than
in poor countries. This implies that the price of any given basket of goods will be higher in a
rich country than in a poor country. The Balassa Hypothesis postulates that if economic growth
is driven by productivity improvements in the tradable sector, then higher productivity growth
will lead to secular real exchange appreciation.
The Balassa Hypothesis is intuitively appealing and theoretical proofs have been
proposed (Gandolfo, 2002), but the empirical support has been mixed (Froot and Rogoff, 1994;
Bahmani-Oskooee and Niroomand, 1996 ). Notwithstanding this; authors tend to attribute the
mixed empirical results to the assumptions made about the underlying forces generating
economic growth itself and its impact on the real exchange rate. For example, economic growth
may sometimes be driven by productivity improvement in the tradable sector and at other times
by productivity improvements in the non-tradable sector. In addition, the real exchange rate may
be influenced by capital flows (Harberger, 2003). The theoretical foundation of the hypothesis is
rarely questioned itself as in Harberger (2003)
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Real Exchange Rate and Economic Growth
“I have no hesitancy in recognizing that what I now call the Balassa effect follows directly, if
indeed productivity tends to be significantly more stagnant in the nontradable area and more
dynamic in the tradables sectors.”
“In my view, nearly everybody agrees that, ceteris paribus, productivity advance in tradables1
leads to currency appreciation and productivity advance in nontradables to currency depreciation”
In this paper, we depart from the existing literature by questioning the theoretical part of
the Balassa Hypothesis theoretically. We maintain all the assumptions in the Balassa Hypothesis
except, within a general equilibrium framework; we divide the tradable sector into exporting and
importing sectors and explicitly take the external balance into consideration. The model also
includes a nontradable sector. Our findings are that the Balassa hypothesis generally does not
hold under the assumptions of our model. The rest of the paper is organized as follows. Section 2
presents the general equilibrium model. Section 3 assesses the Balassa Hypothesis and its
implications for the real exchange rate. Section 4 concludes.
2. Model
Consider a model which consists of two countries and three sectors (unlike the original
formulation in Balassa (1964)). Sectors 1 and 2 are the tradable sectors and sector 3 is the
nontradable sector. We assume perfectly competitive product and labour markets with balanced
trade (excess demand is equal to zero) and no transaction costs. Country 1 is endowed with L1
units of labour and country 2 with L2 units. Money incomes are given by m1 and m2 for country 1
and country 2 respectively. Technological progress is treated as exogenous. In addition, there are
no barriers to inter-sector labour mobility.
To get explicit solutions it is necessary to make the following simplifying assumption. In
particular, we shall assume that country 1 has the comparative advantage in the production of
good 1 and country 2 has the comparative advantage in the production of good 2. Thus country 1
specializes in good 1 and country 2 specializes in good 2.
1
In the original text, “nontradables” is in place of “tradables” in quote. We believe this was a typo error.
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Real Exchange Rate and Economic Growth
2.1 Production
The production functions for the three sectors are of the form:
Yij = Aij Lij
(1)
where index i = 1,2 represents countries, index j = 1,2,3 represents sectors, and Aij is a
productivity parameter. Given specialization according to comparative advantage mentioned
earlier, L12 = 0 , L21 = 0 and thus Y12 = 0 and Y21 = 0 so we can write
Country 1:
Y11 = A11 L11 ,
Y13 = A13 L13
and L1 = L11 + L13
Country 2:
Y22 = A22 L22 , Y23 = A23 L23
and L2 = L22 + L23
2.2 Wages, Prices, and Exchange rates
Let wi be the wage rate for workers in country i , mi the money income for country i , Pij
domestic prices and r the nominal exchange rate (the value of one unit of money in country 2
denominated in terms of country 1’s money). From the foregoing we can write:
w1 = A11 P11 = A13 P13
(2)
w2 = A22 P22 = A23 P23
(3)
P2 j =
1
P1 j
r
j = 1,2
(4)
The following relations hold for countries 1 and 2 respectively:
For country 1,
Since m1 = w1 L1 and thus w1 = m1 / L1 , then from (2) we can write,
P11 =
w1
m1
=
A11 A11 L1
(5)
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Real Exchange Rate and Economic Growth
and
P13 =
w1
m1
=
A13 A13 L1
(6)
Similarly in country 2, from equation (3),
P22 =
w2
m2
=
A22 A22 L2
(7)
w2
m2
=
A23 A23 L2
(8)
and
P23 =
For the tradable sector purchasing power parity holds, therefore:
P12 = rP22 =
m2 r
A22 L2
(9)
and
P21 =
m1
1
P11 =
r
A11 L1 r
(10)
2.3 Preferences
For country i the preferences of a representative household are represented by Cobb-Douglas(CD) utility functions of the form:
U i = X ia1i1 X ia2i 2 X i13−ai1 −ai 2
(11)
Where, X ij is the consumption of good j from sector j in country i and aij ' s
( i = 1,2 , j = 1,2,3 ) are constants such that, 0 < aij < 1 2. The demand functions are:
2
The C-D utility function necessarily imposes a fixed expenditure share on each good and may limit the generality
of the results.
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Real Exchange Rate and Economic Growth
Country 1
X 11 =
a11 m1
a11 m1
=
= a11 A11 L1
P11
m1 ( A11 L1 ) −1
X 12 =
a12 m1
a12 m1
a A Lm
=
= 12 22 2 1
−1
P12
m2 r
m2 r ( A22 L2 )
X 13 =
(1 − a11 − a12 )m1 (1 − a11 − a12 )m1
=
= (1 − a11 − a12 ) A13 L1
P13
m1 ( A13 L1 ) −1
Country 2
X 21 =
a 21 m 2
a 21 m 2
a A L rm
=
= 21 11 1 2
−1
P21
m1
m1 ( A11 L1 r )
X 22 =
a 22 m2
a 22 m2
=
= a 22 A22 L2
P22
m2 ( A22 L2 ) −1
X 23 =
(1 − a 21 − a 22 )m2 (1 − a22 − a23 )m2
= (1 − a21 − a23 ) A23 L2
=
P23
m2 ( A23 L1 ) −1
2.4 Equilibrium
In equilibrium demand equals supply and thus we can write for country i , ( i = 1,2 ), for
the non-tradable sector:
Yi 3 = X i 3 = Ai 3 Li 3 = (1 − ai1 − ai 2 ) Ai 3 Li
i = 1,2
Which implies ,
Li 3 = (1 − ai1 − ai 2 ) Li , i = 1,2
3
Since Li = ∑ Lij i = 1,2
j =1
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Real Exchange Rate and Economic Growth
Recalling that L12 = 0 and L21 = 0 then following relations follow
Country 1: L13 = (1 − a11 − a12 ) L1
and L11 = (a11 + a12 ) L1
Country 2: L23 = (1 − a 21 − a 22 ) L2
and L22 = (a 21 + a 22 ) L2
For the tradable sectors, equilibrium implies:
Y11 = X 11 + X 21 ⇒ A11 (a11 + a12 ) L1 = a11 A11 L1 +
a 21 A11 L1 rm2
m1
or
Y22 = X 12 + X 22 ⇒ A22 (a 21 + a 22 ) L2 =
a12 A22 L2 rm1
+ a 22 A22 L2
m2 r
Finally we can obtain an expression for the nominal exchange rate, r , by solving any one of the
two equations above,
r=
a12 m1
a 21 m2
(12)
Having obtained the equilibrium exchange rate, we can substitute it into (9) and (10), to get:
a12 m1
a 21 A22 L2
(9′)
a m
1
P11 = 21 2
r
a12 A11 L1
(10′)
P12 = rP22 =
P21 =
Equations (5)-(8), (9′), (10′) and (12) constitute the solution to the general equilibrium system.
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Real Exchange Rate and Economic Growth
3 The Balassa Hypothesis and the Real Exchange Rate
3.1 The Balassa Samuelson Hypothesis
Having laid out the model above we now investigate if the effect implied by the Balassa
Hypothesis holds. Now if the hypothesis holds then, ceteris paribus, when labour productivity
improves in country 1, the price of a fixed basket of goods will be relatively higher in country 1
than in country 2. In the model the relative price in the nontradable sectors across countries is
given by:
P13
A23 L 2 m1
a A L
=
= 21 23 2
rP23 a12 m1
a12 A13 L1
A1 3 L1 m 2
a 21 m 2
(13)
From equation (13), the relative price in the nontradable sector between the two countries does
not depend on the productivities in the tradable sector, but depends instead on the labour force,
consumer preference and labour productivities in the nontradable sector in the two countries.
Thus the Balassa Hypothesis may not hold in the case of labour productivity improvement in the
tradable sector but is valid in reverse in the case of labour productivity improvement in the
nontradable sector.
Why is there a difference? The Balassa Hypothesis does not take into consideration the
effect of international trade on the relative price across countries. Specifically, the Hypothesis
asserts that when labour productivity improvement takes place in a country, the price in the
nontradable sector relative to the tradable sector will increase in that country but remain
unchanged in the other country. Thus, the relative price of a fixed basket of goods will increase
in the country with labour productivity improvement. Our model takes the effect of international
trade into account. Let us consider the price of sector 3 relative to sector 1 in each country as an
example. From (5) and (6), the price in the nontradable sector relative to tradable sector 1 in
country 1 is:
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Real Exchange Rate and Economic Growth
m1
A L
A
P13
= 13 1 = 11
m1
A13
P11
A11 L1
(14)
From (8) and (10′), the price of the nontradable sector relative to tradable sector 1 in country 2 is
m2
a A L
A23 L2
P23
=
= 12 11 1
a
m
a 21 A23 L2
P21
21 2
a12 A11 L1
(15)
Now, when labour productivity A11 increases, not only does the price in sector 3 increase relative
to sector 1 in country 1, but the relative price of sector 3 to sector 1 in country 2 increases
proportionally. Hence, the productivity improvement in the tradable sectors may have no effect
on the relative price of a fixed basket goods between the two countries. However, when labour
productivity A13 increases, the price of sector 3 relative to sector 1 in country 1 decreases, but the
relative price of sector 3 to sector 1 in country 2 remains unchanged. In this case the productivity
improvement in the nontradable sector will decrease the relative price of a fixed basket goods in
the country in which the improvement occurs, ceteris paribus.
3.2 Real Exchange Rate
Let r R denote the real exchange rate given by
rR = r
P*
P
(16)
where P and P * denotes the aggregate domestic and foreign price levels respectively. We can
define the real exchange rate with respect to the consumer price index or the terms of trade.
I. Consumer Price index
Let country 1 be the domestic country and country 2 be the foreign country in what follows.
Given the utility function we can write the domestic and foreign price levels as the sum of the
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Real Exchange Rate and Economic Growth
price level in each sector weighted by the share of income spent in that sector. For the domestic
price level we have:
P = a11 P11 + a12 P12 + a13 P13 =
a m
a11 m2
a2 m
+ 12 2 + 13 1
A11 L1 a 21 A22 L2 A13 L1
and the foreign price level is given by:
2
a m
a 21
m2
a m
P* = a 21 P21 + a 22 P22 + a 23 P23 =
+ 22 2 + 23 2
a12 A11 L1 A22 L2 A23 L2
and the real exchange rate is thus
2
a 21
a a
+ a12 a 22
+ 23 12
A11 L1
A22 L2
A23 L2
P*
r =r
= 2
P
a a
a12
+ 21 13
+ a11 a 21
A22 L2
A13 L1
A11 L1
R
(17)
From (17), productivity change in the tradable sectors, such as a change in A11 or A22, has an
ambiguous effect on the real exchange rate. However, productivity change in the nontradable
sector, such as a change in A13 or A23, has an unambiguous effect on the real exchange rate. An
increase in A13 will lead to increase in r R : that is, the real exchange rate will depreciate. On the
other hand an increase in A23 will lead to the decrease in r R , or an appreciation of the real
exchange rate.
II. Terms of Trade
Prices of exports and imports for country 1 are respectively given by:
P* = P22 =
m2
m1
and P = P11 =
A11 L1
A22 L2
and the real exchange rate using is thus:
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Real Exchange Rate and Economic Growth
P * a12 m1 m2 ( A22 L2 ) −1 a12 A11 L1
=
=
r =r
P
a21m2 m1 ( A11 L1 ) −1 a21 A22 L2
R
(18)
Obviously, from equation (18) the advance of productivity in the tradable sector for country 1
will lead to an improvement in the terms of trade for country 2 (deterioration of the terms of
trade for country 1).
4. Conclusion
The Balassa Hypothesis describes one channel through which productivity changes affect the
real exchange rate. The theoretical foundation of the hypothesis has rarely been called into
question even though it has not enjoyed full empirical support. We formulate a model with three
sectors and two countries linked by international trade. Our model does not support the
theoretical predictions of the Balassa Hypothesis. We find that the theoretical shortcoming of the
Balassa Hypothesis lies in its failure to take into account the effect of international trade on the
relative price across countries. According to the Balassa Hypothesis the effect of productivity
improvements in one country is not transmitted to other countries. In our model such spill over
effects are taken into account through international trade linkages. So if there is a productivity
improvement in the tradable sector in
country 1 this leads to relative price changes between
tradable and nontradable sectors, not only in country 1 but also in country 2 because of trade
linkages.
From the foregoing the Balassa hypothesis may not hold if labour productivity
improvement takes place in the tradable sector. In particular, under our assumptions, productivity
improvements in the tradable sector may have no effect on the relative price of a fixed basket of
goods across countries. If a variation in the prediction of the hypothesis is accepted, then it may
be valid in the case of productivity improvements in the nontradable sector. In this case,
productivity improvements in the nontradable sector will decrease the relative price of a fixed
basket of goods in the country in which the improvement occurred. If economic growth is driven
primarily by productivity improvement in the tradable sector, then higher growth may not lead to
secular real exchange rate appreciation. Furthermore, if economic growth is driven primarily by
productivity improvement in the nontradable sector, higher growth may be lead to secular real
exchange rate depreciation.
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Real Exchange Rate and Economic Growth
References
Balassa B. (1964). The purchasing power parity doctrine: A Reappraisal, Journal of Political
Economy, 72, 584-596.
Bahmani-Oskooee, M and Niroomand F (1996). A Reexamination of Balassa's Productivity
Bias Hypothesis Economic Development and Cultural Change, 45(1), 195-204.
Froot, K. and Rogoff, K. (1994). Perspectives on PPP and Long Run Real Exchange Rates,
National Bureau of Economic Research Working Paper No. 4950.
Gandolfo, G. (2002). International Finance and Open Economy Macro-economics. Springer
Verglag. Appendix Chapter 15.
Harberger, A. (2003). Economic Growth and The Real Exchange Rate: Revisiting the BalassaSamuelson Effect. Paper prepared for a Conference organized by
Economics,
Moscow
April
2003.
The Higher School of
http://www.econ.ucla.edu/harberger/ah-
ecgrowth.pdf#search='real%20exchange%20rate%20and%20economic%20growth'
Harrod, R. (1973). International economics. 2nd ed. Cambridge: Cambridge University Press.
Samuelson, P. (1964). Theoretical Notes on Trade problems, Review of Economics and Statistics,
56, 145-164.
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