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28
SEPTIEMBRE DE 2012Documentos CEDE
C E D E
Centro de Estudios sobre Desarrollo EconómicoHernando Zuleta
Luiza Pogorelova
Trade, Technology, Income Distribution
and Growth
Serie Documentos Cede, 2012-28 ISSN 1657-7191 Edición electrónica
Septiembre de 2012
© 2012, Universidad de los Andes–Facultad de Economía–CEDE Calle 19A No. 1 – 37 Este, Bloque W.
Bogotá, D. C., Colombia
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1
C E D E
Centro de Estudios sobre Desarrollo Económico0
Trade, Technology, Income Distribution and Growth
Hernando Zuleta*
Luiza Pogorelova
Abstract
We modify the standard trade model introducing the possibility of biased technological changes. This model help to explain the falling labor shares as well as the mixed changes in skill premium in developing countries after trade liberalization takes place.
Key words: skill premium, biased technological change, international trade, Heckscher-Ohlin model, factor income shares
JEL Codes: F10, D33, J31, O33
* Corresponding author. Economics Department, Universidad de los Andes. Email: [email protected]
Department of Economics, Louisiana State University. Email: [email protected]
0
Trade, Technology, Income Distribution and Growth
Hernando Zuleta*
Luiza Pogorelova
Abstract
We modify the standard trade model introducing the possibility of biased technological changes. This model help to explain the falling labor shares as well as the mixed changes in skill premium in developing countries after trade liberalization takes place.
Key words: skill premium, biased technological change, international trade, Heckscher-Ohlin model, factor income shares
JEL Codes: F10, D33, J31, O33
* Corresponding author. Economics Department, Universidad de los Andes. Email:
Department of Economics, Louisiana State University. Email: [email protected]
2
1
Comercio Exterior, Tecnología, Distribución del Ingreso y
Crecimiento
Hernando Zuleta*
Luiza Pogorelova
Resumen
En este artículo se modifica el modelo convencional de comercio exterior introduciendo la posibilidad de cambio tecnológico sesgado. El modelo ayuda a explicar la caída en la participación del trabajo así como el aumento en la prima de educación observada en los países en vías de desarrollo después de la liberalización del comercio exterior.
Palabras Clave: prima de educación, cambio tecnológico sesgado, comercio exterior, modelo Heckscher-Ohlin, participación del trabajo en el ingreso
Códigos JEL: F10, D33, J31, O33
* Corresponding author. Economics Department, Universidad de los Andes. Email:
Department of Economics, Louisiana State University. Email: [email protected]
1
Comercio Exterior, Tecnología, Distribución del Ingreso y
Crecimiento
Hernando Zuleta*
Luiza Pogorelova
Resumen
En este artículo se modifica el modelo convencional de comercio exterior introduciendo la posibilidad de cambio tecnológico sesgado. El modelo ayuda a explicar la caída en la participación del trabajo así como el aumento en la prima de educación observada en los países en vías de desarrollo después de la liberalización del comercio exterior.
Palabras Clave: prima de educación, cambio tecnológico sesgado, comercio exterior, modelo Heckscher-Ohlin, participación del trabajo en el ingreso
Códigos JEL: F10, D33, J31, O33
* Corresponding author. Economics Department, Universidad de los Andes. Email:
Department of Economics, Louisiana State University. Email: [email protected]
3 2
1.
Introduction
All across the world labor shares have been going down for the last decades.1 Additionally, in developing countries the skill premium has grown after trade liberalization.2 These results contrast with the predictions of the Heckscher-Ohlin theory.
Theoretical technology-related explanations have been offered for these facts. For example, Zuleta (2008) and Peretto and Seater (2010) model the change in factor shares as being induced by raw lactor saving technological progress.3
Other authors provide theoretical explanations of the issue of increased skill premium in developing countries after trade liberalization.4 In particular, explanations based on skill-biased technological changes have been offered by Acemoglu (2003) and Zeira (2007). Acemoglu considers a CES production function which combines skilled and unskilled labor and proves that trade liberalization can induce skill-biased technological change with the resulting increase in wage inequality. He provides the conditions under which trade liberalization increases wage inequality in a less developed country. Zeira (2007), assuming a production function of fixed coefficients, develops a model with the endogenous adoption of skill-biased technologies and replacement of unskilled workers by more skilled ones. He assumes that technological progress and trade liberalization are independent and finds that trade liberalization increases the demand for unskilled workers and thus reduces wage inequality in less developed countries.
Similar to Acemoglu and Zeira we relate relative supplies of factors, technology and trade. However, we use a different setting. In particular, we consider a general production function and we refer to reproducible factors in general and not only to skilled labor. In this setting, we explain why trade may increase the income share of scarce factors and connect the behavior of capital shares to economic growth. In contrast with Zeira, we show that trade liberalization in a developing economy can cause a technological change,
1 See Blanchard (1997); Jones (2003); Glyn (2007); Bental and Demougin (2010) and Zuleta (2012) for OECD countries and Bai and Qian (2010) and Harrison (2002) for developing countries.
2 See Wood (1997), Freeman and Oostendrop (2001) and Zhu and Trefler (2005).
3 See also Seater (2005).
4
3
which, in its turn, increases the return to reproducible factors and fosters economic growth.
We consider an economy with two goods, A and B, two factors of production, one reproducible and one not reproducible, and two technologies for the production of good
A, αandβ, α being more capital intensive. For ease of presentation we denote the factors by K (capital) and L (labor) respectively. The production of good B is relatively labor intensive. The choice of technology is costless and depends on the capital-labor ratio of the country. We assume that in the state of autarky the economy is relatively capital-scarce and chooses technology β. In these circumstances, trade opening increases the capital-labor ratio of sector A up to a point where it induces a switch in production technology from β to α. In this case, contrary to the original Heckscher-Ohlin model, the return to the scarce factor (capital) may increase after trade liberalization. Finally, the increase in the capital share may be accompanied by economic growth because it augments the return to capital as well as the incentives to invest.
We conclude that the effects of international trade depend on the capital abundance of the economy and the international price of the exported good. Given the international prices of final goods, for very labor abundant economies international trade does not induce technological changes and, for this reason, the standard results of the H-O model hold. However, in relatively labor abundant economies where the capital-labor ratio is close to one, international trade induces technological changes. For this group of economies, the labor income share may go down and the return to capital may increase.
The rest of the paper is organized as follows. In section II we present the general model and the main results, in section III we present an example using Cobb-Douglas production functions and a logarithmic utility function and, finally, we present the conclusions in section IV.
2. The model
2.1 Production
The production function of good B is:
) , ( B B
B H K L
5
4
For the production of good A firms can choose either technology α or β (α>β):
) , (
, A A
A F K L
Y (2.2)
) , (
, A A
A G K L
Y (2.3)
The functions H(KB,LB), F(KA,LA) and G(KA,LA)exhibit all the usual assumptions. Technology F(KA,LA)is more capital intensive than technology G(KA,LA):
) , (
) , ( )
, (
) , (
A A L
A A K
A A L
A A K
L K F
L K F L K G
L K G
A A A
A (2.4)
) , ( )
,
( A A KK A A
KK K L G K L
F (2.5)
) , ( )
,
( A A LL A A
LL K L G K L
F (2.6)
Producers of good A choose the technology which maximizes output given KA and LA:
If F(KA,LA)G(KA,LA)then producers chooseF(KA,LA), otherwise they choose )
, (KA LA
G .
We assume constant returns to scale so this condition can be rewritten as follows:
If FKA(KA,LA)KAFLA(KA,LA)LA GKA(KA,LA)KAGLA(KA,LA)LA, then firms
choose F(KA,LA), otherwise they chose G(KA,LA). Rearranging, the condition can be written as follows:
) , ( )
, (
) , ( ) , (
A A K A A K
A A L A A L
A F K L G K L
L K F L K G k
A A
A A
where
A A A KL k .
Equations 2.5 and 2.6 imply that the right hand side of the condition above is a decreasing function of kA. Result 1 is a direct implication of these assumptions.
Result 1: There exists a critical level k~A such that if KA/LA k~A then producers of good A choose
the technology and if KA/LA k~A then producers of good A choose the technology.
In other words, firms choose technologies and βfor high and low levels of the sector A
6 5 2.2 Factor Markets
Assuming perfect competition, factor mobility and normalizing , we find factor prices:
) , ( )
,
( B B B L A A
L K L P G K L
H
w B A (2.7)
) , ( )
,
( B B B K A A
K K L P G K L
H
r B A (2.8)
So,
) , (
) , ( )
, (
) , (
A A K
A A L
B B K
B B L
L K G
L K G L K H
L K H r w
A A B
B
(2.9)
Result 2: In equilibrium kB can be expressed as a function of kA, kB (kA)where 1
) ('
0 kA and
A
k(kA)
lim .
Given that the production of good A is more capital intensive, result 2 also implies that output per worker in sector B can be expressed as a function of output per worker in sector
A, yB (yA) where 0 ('yA)1.
From equations 2.7 and 2.8 the price of good B can be written as
) , (
) , ( )
, (
) , (
B B K
A A K
B B L
A A L
B H K L
L K G L K H
L K G P
B A
B
A
(2.10)
Result 3 follows directly from equation 10.
Result 3:In equilibrium, kA can be expressed as a function ofPB, kA(PB) where 0
) ('PB
and
B
P(PB) lim
From results 2 and 3 it follows that kB can be expressed as a function ofPB, kB (PB)
where ('PB)0 and
B
P(PB)
lim .
7 6
2.3 Consumption
In a dynamic setting consumers maximize their life time utility subject to the budget
constraint: Max
0 ) , ( t t B A C C
U s. t. at1 at
1rt
wt CAPBCB,Where a is the amount of assets owned by the representative consumer, r is the interest rate, w the wage and η the discount factor. From the first order conditions we find
) , ( ) , ( , , , , , t B t A C t B t A C t
B U C C
C C U P A B
(2.11)
) 1 ( ) , ( ) , ( 1 1 , 1 , , , t t B t A C t B t A C r C C U C C U B
A (2.12)
We assume that the economy is in steady state so
1
r .
Without depreciation, CA YA and CB YBso,
) , ( ) , ( )) , ( (' )) , ( (' B B L A A L A A B B
B H K L
L K G L K G U L K H U P B A (2.13)
Result 4 follows directly from equation 2.13:
Result 4: In the autarkic equilibrium the ratio of outputs
B A Y
Y can be expressed as a function of the price
level of sector B, ( B) B
A P
Y
Y where(' )0 B
P .
From result 4 it follows that ( B)
A A B A P L L L y
y
. Therefore,
8
7
Equation 2.14 together with result 2 implies result that, in the autarkic equilibrium, the ratio of labor allocated to sector A can be expressed as a function of the capital labor ratio of
sector A:
) ( A
A k
L L
.
Proposition 2.1: There is a critical capital-labor ratio k~such that if K/Lk~ then producers of good A choose the technology .
Proof:
Claim 1: Under autarky, in equilibrium kA can be expressed as a function of the capital-labor ratio of the
economy: kA,AUTARKY (k) where ('k)0.
Capital and labor are allocated between the two sectors so,
kA(kA)
(kA)(kA)k (2.15)Define (kA)
kA(kA)
(kA)(kA) 0) (' 0 )
('kA kA
(2.16)
Suppose that ('kA)0and consider that kA grows. Then kB grows but (kA)decreases soLBand KBgrow. But then YB must be growing, YA decreasing, and PB decreasing implying that
A
k and kB are decreasing which contradicts the initial assumption. The analogous argument can be done for the case where kA decreases. Therefore, ('kA)0 and ('kA)0.
Finally we can define (k) 1(k).
Claim 1 follows form equation 16 together with results 2 and 4.
Claim 2:
( ) lim k
k
It follows directly from result 2 and equation 2.15.
9
8
Assumption 1: In the autarkic steady state the capital-labor ratio of the domestic economy is such that
technology β is used so the production function of good A is YA, G(KA,LA), namely, K/Lk~ .
As usual in equilibrium the amount of assets per capita is equal to the capital labor ratio of the economy a=k. Therefore proposition 2.1 implies that there is a critical level a~such that if aa~ then producers of good A choose the technology .
2.3 Trade
Given that the economy is labor abundant, opening the economy leads to an exogenous increase on and the economy exports good B.
) , (
) , ( )) ,
( ('
)) ,
( ('
, ,
, ,
, ,
, , ,
Trade B Trade B L
Trade A Trade A L
Trade A Trade A
Trade B Trade B Trade
B H K L
L K G L
K G U
L K H U P
B A
where PB,TRADE PB
However, if the increase in is big enough then international trade may generate a change of technology. We formalize this result in proposition 2.
Proposition 2.2: There exists a critical price level ~p such that, if PB,Trade ~p then after the domestic
economy starts trading with the foreign economy the domestic economy switches to technology in the production of good A.
Proof: From result 1 it follows that there exists a critical capital-labor ratio k~A such that, if
A Trade A Trade
A L k
K , / , ~ then after the domestic economy starts trading the economy switches to technology in the production of good A.
From result 3 it follows that there exists a price level p~ such thatk~A(~p). Q.E.D.
Proposition 2.3: Holding relative prices constant, if the economy switches to technology in the production of good A then kA0and kB 0.
Proof: From equations 2.2 to 2.5 it follows that, givenkA 1, the adoption of the
10
9
If the capital-labor ratio of the domestic economy is close to the critical level k~then with a small increase in the economy switches to technology α. If the distance between
technologies α and β is big then the effect of the technological change may be stronger than the effect of the increase in the relative price of good B.
Proposition 2.4: If the capital-labor ratio of the economy is high enough then there exists a critical price level P such that, if PPB,Trade p~
, then after the domestic economy starts trading with the foreign economy the wage-interest rate ratio decreases.
Proof:
Claim 1: Given the technologies F(.) and G(.) there exists a critical capital-labor ratio k such that if
k kATRADE
, then AUTARKY TRADE r w r w
From equation 4 it follows that
) , ( ) , ( ) , ( ) , ( , , , , , , , AUTARKY A AUTARKY A K AUTARKY A AUTARKY A L AUTARKY A AUTARKY A K AUTARKY A L L K G L K G L K F L K F .
The two sides of the inequality are increasing ink. Therefore, there exists a capital-labor ratio k such that , k kA,AUTARKY
and ) , ( ) , ( ) , ( ) , ( , , , , , , , , AUTARKY A AUTARKY A K AUTARKY A AUTARKY A L TRADE A TRADE A K TRADE A TRADE A L L K G L K G L K F L K F
for any kATRADE k
, .
Claim 2: There exists a critical price level P such that, if PBTrade P
, , then after trade opening the
capita- labor ratio in the production of good A, kA, is such that kA k
.
Result 3 implies that kA (PB) where (PB) is continuous and monotonically
increasing. Therefore, there exists a critical price level P such that, if PPB,Trade
then
) (
)
(P PB,TRADE
Claim 3: If the capital- labor ratio of the economykis high enough then(P)1.
Proposition 1 implies kA,AUTARKY (k) where ('k)0.
11
10
Therefore, we can define the function M(PB,k)(PB,)(k), where MPB(PB,k)0,
0 ) , (P k
Mk B and M(PB,AUTARKY,k)0.
Now, choose an arbitrary small number ε and choose P is such a way that M(P,k)
(P)1(k)1 . Therefore, (P)1k 1(1).
From claims 1, 2 and 3 it follows that if k1(1)then there exists a critical price level P such that, if PPB,Trade p~
, then after the domestic economy starts trading with
the foreign economy decreases. Q.E.D.
Proposition 2.5: If the capital-labor ratio of the economy is high enough then there exists a critical price level P such that, if PPB,Trade p~
, then after the domestic economy starts trading with the foreign economy the interest rate increases.
Proof:
Claim 1: Given the technologies F(.) and G(.) there exists a critical capital-labor ratio k such that if
k kATRADE
, then rTRADE rAUTARKY .
From equation 4 it follows that GK(KA,AUTARKY,LA,AUTARKY)FK(KA,AUTARKY,LA,AUTARKY).
The two sides of the inequality are decreasing ink. Therefore, there exists a capital-labor ratio k such that , k kA,AUTARKY
and
) ,
( ) ,
( A,AUTARKY A,AUTARKY K A,TRADE A,TRADE
K K L F K L
G for any kATRADE k
, .
Claim 2: There exists a critical price level P such that, if PBTrade P
, then after the domestic economy
starts trading with the foreign economy the capital-labor ratio in the production of good A, kA, is such that
k kA
.
Given kA (PB), there exists a critical price level P
such that, if PPB,Trade
, then
) (
)
(P PB,TRADE
12 11
Claim 3: If the capital-labor ratio of the economykis high enough then(P)1.
The proof is identical to the one of proposition 1.4.
From claims 1, 2 and 3 it follows that if k1(1)then there exists a critical price level P such that, if PPB,Trade p~ then after the domestic economy starts trading with the foreign economy increases. Q.E.D.
Corollary 2.1: If the capital-labor ratio of the economy is high enough then there exists a critical price level P such that, if PPB,Trade p~
then after the domestic economy starts trading with the foreign economy the rate of growth of economic increases.
From equation 2.12, when the interest rate increases the growth rate of consumption grows and the savings rate has to increase as well, leading to faster capital accumulation and economic growth. This result also holds outside the steady state as long as consumption depends positively on output.
3. The Cobb-Douglas example
The production function of good B for country Home is:
1
B B B K L
Y (3.1)
For the production of good A firms can choose either technology or ( ):
1
, A A
A K L
Y (3.2)
1
, A A
A K L
Y (3.3)
Consequently, if kA 1 , then firms choose technology α.
Assuming perfect competition and normalizing , we find the wage being equal to the marginal productivity of labor in production of both goods A and B:
B B
A k P
k
w(1) (1) and
B B
A k P
k
r 1 1 . Therefore,
B
A k
k r
w
) (1 )
1
(
13
12
This gives the price of good B:
B A
B kk
P ) 1 ( ) 1 ( (3.5)
Combining, equations 3.4 and 3.5,
A B k P 1 1
1 (3.6)
Equation 3.6 together with assumption 1 implies that
1 1 1 B
P (3.7)
We assume a logarithmic utility function so
B A B CC P .
Again, in steady state, assuming no depreciation, CA YA and CB YBso,
B A B A B A L L k k k k ) 1 ( ) 1
( (3.8)
and B A L L ) 1 ( ) 1 ( (3.9)
Setting we get
L LB )) 1 ( 1 ( ) 1 (
and LA L
)) 1 ( 1 ( ) 1 ( (3.10)
Combining with equation 2.5, KAKB so
K
14 13 k
kB
1
2 and k k
A
1 2 (3.12)
These equations together with assumption 1 imply that
2 1
k (3.13)
Now, under autarky the interest rate is given by 1 A
k
r but, from equation 3.6 it follows that 1 1 2 k
rAutarky (3.14)
and k
wAutarky (1 ) 21 (3.15)
Trade leads to the exogenous determination of . In the open economy, from equation 3.6 it follows that the capital labor ratio in the production of good A is given by
1 1 ,,Trade BTRADE 11
A P
k (3.16)
Given that under trade 1 ,
TRADE A k
r , equation 3.16 implies
) 1 )( 1 ( ) 1 ( 1,TRADE 11
B Trade P r (3.17) and
) 1 (, 11
) 1
( BTRADE
Trade P
15 14 Proposition 3.1: If
1
,TRADE 11 B
P then under trade technology beta is not
an equilibrium.
Proof: Suppose firms choose technology . In this case,
1 1 ,,Trade BTRADE 11
A P k . Therefore, if 1
,TRADE 11 B
P then kA 1. Q.E.D.
Proposition 3.2: If
1
,TRADE 11 B
P then under trade technology alpha is an
equilibrium.
Proof: If firms choose technology alpha then the capital labor ratio is given by equation
2.14. Therefore, if
1
,TRADE 11 B
P then kA,Trade1. Q.E.D.
Corollary 3.1: If
1 1
1 then
1
,TRADE 11 B
P is a sufficient
condition for the new technology to be adopted.
Proof: If 1 1
1 then
1 1
1 1 1 1 . Therefore, 1
,TRADE 11 B
P implies
1
,TRADE 11 B
P Q.E.D.
Proposition 3.3: If the technology α is adopted and the international price of good B is low enough,
kPBTRADE 11 2 1 ((11 ))
1
, , then
1r w r w
16
15
Proof:
From equations 2.14, 2.15, 2.17 and 2.18 it follows that
k
P r w r w TRADE B
TRADE
1 , 1 2 1 1 1 ) 1 ( ) )( 1 ( Therefore if k
PBTRADE 11 (1 (1)( ) ) 21
1
, then
1r w r w
TRADE Q.E.D.
Proposition 3.3 implies that given the capital labor ratio of the economy and the parameters of the available technologies, there exists a critical price level for good B such that if the international price is above this critical price then International Trade redistributes income in favor of the abundant factor (labor) and if the international price is below this critical level then International Trade redistributes income in favor of the scarce factor (capital). But it also implies that given the technologies and the international price, there exists a critical level for the capital labor ratio such that if the capital labor ratio of the economy is above this critical level then International Trade redistributes income in favor of the scarce factor (capital) and if the capital labor ratio of the economy is below this critical level then International Trade redistributes income in favor of the abundant factor (labor).
Note however, that for the wage interest rate ratio to go down the technology alpha should be adopted and the technological change would not occur unless
TRADE B
P, 1
1
1
.
From propositions 3.2 and 3.3, the condition for the adoption of the new technology and the decrease in the wage interest rate ratio is the following:
P k
TRADE
B 11 2 1 ((11 ))
1
1 1
17
16
A necessary condition for this result to be possible is
k ) 1 ( ) 1 ( 1 2
1 or
k ) 1 ( ) 1 ( 2 1
We began assuming that
2 1
k . Therefore, the parameters must be such
that 1 ) 1 ( ) 1 ( .
But note that this condition holds whenever . Therefore, the necessary condition always holds.
Proposition 3.4:
If the technology α is adopted and the international price of good B is low enough, then 1
Autarky Trade
r r
.
Proof: From equations 3.14 and 3.17 it follows that
1 ) 1 )( 1 ( ) 1 ( 1 , 1 2 1 1 k P rr BTRADE
Autarky Trade Therefore, if 1 1 ) 1 ( 1
, 11 21 k
PBTRADE then 1
Autarky Trade
r
r .
18 17
When the interest rate increases and labor abundant sector grows after the trade liberalization, the growth rate of consumption is increased and the savings rate has to increase as well, leading to faster economic growth.
IV. Conclusion
19
18
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