Trade, product cycles, and inequality within
and between countries
Susan Chun Zhu
Department of Economics, Michigan State
University
Abstract. This paper incorporates Northern product innovation and product-cycledriven technology transfer into the continuum-of-goods Heckscher-Ohlin model. The
creation of very skill-intensive goods induces the North to transfer production of older,
less skill-intensive goods to the South. These relocated goods are the most skill intensive
by Southern standards. Hence, product cycles raise the relative demand for skilled
workers and thus wage inequality within both regions. This runs contrary to the
Stolper-Samuelson theorem, but accords well with the fact that wage inequality has
risen in both Northern and Southern countries. Moreover, product cycles increase
income inequality between countries. JEL classification: F1
Commerce international, cycles de produit, et ine´galite´ à l’inte´rieur des pays et entre
eux. Ce mémoire incorpore le processus d’innovation et de transfert de technologie
engendré par le cycle du produit dans le Nord dans le continuum de produits d’un
modèle Hecksher-Ohlin. La création de biens à forte intensité en habiletés amène le
Nord à transférer la production de biens à moins forte intensité en habiletés vers le Sud.
Ces biens relocalisés sont ceux qui sont les plus intensifs en habiletés dans le Sud. En
conséquence, les cycles de produit augmentent la demande de main d’œuvre qualifiée et
donc l’inégalité entre les régions. Voilà qui ne va pas dans le sens de ce que le théorème
de Stolper-Samuelson suggère, mais s’accorde bien avec le fait que les inégalités de
salaires augmentent dans le Nord et le Sud. De plus les cycles de produit augmentent
l’inégalité entre pays. Même si le transfert de technologie diminue l’écart de revenu entre
le Nord et le Sud, cet effet est plus que compensé par l’effet de l’innovation de produit.
Ce mémoire examine aussi les effets de bien-être des cycles de produit. Les cycles de
I am indebted to Dan Trefler for his encouragement and many helpful comments. I also thank
Tony Creane, Nancy Gallini, Wolfgang Keller, Angelo Melino, Diego Puga, Martin
Richardson, Aloysius Siow, Nadia Soboleva, and especially two anonymous referees for helpful
comments and suggestions. Financial support from the Social Sciences and Humanities
Research Council of Canada is gratefully acknowledged. Email: [email protected]
Canadian Journal of Economics / Revue canadienne d’Economique, Vol. 37, No. 4
November / novembre 2004. Printed in Canada / Imprimé au Canada
0008-4085 / 04 / 1042–1060 /
#
Canadian Economics Association
Trade, product cycles, and inequality
1043
produit engendrent des avantages pour le Nord et le Sud, et améliorent le sort des
travailleurs hautement qualifiés dans les deux régions.
1. Introduction
There is increasing evidence that in recent decades wage inequality between
skilled and unskilled workers has grown not only in many Northern countries,
but also in some Southern countries (Feenstra and Hanson 1996, 1997; Robbins
1995; Cragg and Epelbaum 1996; Hanson and Harrison 1999; Berman, Bound,
and Machin 1998). The pervasiveness of rising wage inequality leads people to
think international trade might be an important factor (e.g., Wood 1994;
Leamer 1996). However, the traditional Stolper-Samuelson theorem predicts
that when wage inequality increases in the North, it should decline in the
South. Thus, some authors claim that the traditional Heckscher-Ohlin model,
the backbone of the Stolper-Samuelson theorem, fails (e.g., Robbins 1995).
One purpose of this paper is to show that widening wage inequality in both
regions can be explained within a Heckscher-Ohlin framework. To this end, I
incorporate technical change into the continuum-of-goods Heckscher-Ohlin
model (Dornbusch, Fischer, and Samuelson 1980). I consider a world economy
driven by Northern product innovation. I further assume that new goods use
relatively more skilled labour than old goods. This assumption is consistent with
the experience of the past several decades, which have seen the rapid spread of
computers and other new technologies in workplaces. Since these new technologies favour skilled workers, technical change is considered by many economists
as a dominant factor contributing to rising inequality in developed countries
(e.g., Krueger 1993; Goldin and Katz 1998; Berman, Bound, and Griliches 1994;
Autor, Katz, and Krueger 1998). While R&D-induced or computer investmentinduced technical change is likely to be a major force raising the demand for
skills in developed countries, such factors would seem to be less relevant in
developing countries where innovative capacity is limited. If technical change
matters for these countries, the mechanism must be via trade or foreign direct
investment. In this paper I show that international trade serves as a channel
through which technical change originated in the North spreads to the South.
Specifically, the creation of new, skill-intensive goods can endogenously induce
developed countries to move less skill-intensive goods to developing countries.
In this paper I present a new theory of product cycles. Unlike Vernon’s
(1966) original product-cycle model, this new theory has nothing to do with the
ongoing process of standardizing new goods. Instead, in my model product
cycles are generated by rich general equilibrium interactions between international trade and labour markets. What is particularly interesting about this
new theory of product cycles is that it has important implications for the
domestic distribution of income. With the partial exception of Dinopoulos
1044
S. Chun Zhu
and Segerstrom (1999),1 domestic income distribution issues have not been
addressed by previous product-cycle models (e.g., Vernon 1966; Krugman
1979; Dollar 1986; Flam and Helpman 1987; Jensen and Thursby 1987;
Grossman and Helpman 1991).
The core result is that product innovation and technology transfer increase
inequality within both regions. In this model rising wage inequality is driven by
increased demand for skilled labour due to changes in the product mix. When
new, skill-intensive goods are introduced, the relative demand for Northern skilled
labour increases, thus raising Northern inequality. If the aggregate elasticity of
substitution between Northern skilled labour and unskilled labour is sufficiently
large, the introduction of new goods makes the North less competitive in low-end
goods. The result is technology transfer – the North moves production of its older,
less skill-intensive goods to the South. Such technology transfer reduces the
relative demand for Northern unskilled labour and aggravates the wage gap in
the North. At the same time, since the transferred Northern goods are more skill
intensive than the previously produced Southern goods, the relative demand for
Southern skilled labour increases. Thus inequality also rises in the South.
Product cycles increase inequality not only within countries, but also
between countries. Product innovation and endogenous technology transfer
have opposing effects on the North-South income gap. Unlike product innovation, technology transfer narrows the gap. However, the product innovation
effect, being more direct, dominates. This result differs sharply from Krugman
(1979). The difference arises from the way technology transfer is modelled: in
Krugman, technology transfer is exogenous. Krugman considers the case
where there is an increase in the rate of technology transfer while the rate of
product innovation is kept constant, and he concludes that the income gap can
be narrowed. In my model, however, technology transfer is induced by product
innovation and, in equilibrium, may not catch up with it.
The simplicity of the model allows me to derive a rich set of welfare
implications of product cycles. The terms of trade move in favour of the
North and against the South. The North further benefits from a wider range
of new products. Strikingly, the South also benefits from product cycles. This
is because the loss to the South from worsened terms of trade is entirely offset
by the gain from new goods. At the same time, since income is redistributed
from unskilled to skilled workers, skilled workers in both regions are better off.
It is worth pointing out that Feenstra and Hanson (1996) and Xu (2003)
also extend the continuum-of-goods Heckscher-Ohlin model in order to
explain rising inequality within both the North and the South. Like mine,
their explanation relies on changes in the product mix. However, there are
two major differences between my work and theirs. First, the source of
1 Dinopoulos and Sergerstrom (1999) present a dynamic general equilibrium model of NorthNorth trade that has implications for wage inequality in Northern countries. However, it does
not deal with Southern countries.
Trade, product cycles, and inequality
1045
product-mix changes is very different. In Feenstra and Hanson (1996), a higher
rate of return to capital investment in the South causes production relocation from
the North to the South. In Xu (2003), changes of the product mix are attributed to
tariff reductions in the South and the resulting change in the boundary between
traded and non-traded goods. In contrast, in my model Northern product innovation drives all the changes in production patterns. Second, in Feenstra and
Hanson (1996) and Xu (2003), widening inequality in the North is entirely caused
by production relocation from the North to the South. In contrast, in my model
the creation of new, skill-intensive goods is the dominant factor contributing to
inequality in the North. In particular, rising inequality can occur in the North
without the relocation of older, less skill-intensive goods to the South. This result
accords well with the empirical finding that the use of computers and other new
technologies is a dominant factor explaining rising wage gap in developed
countries (Krueger 1993; Goldin and Katz 1998; Berman, Bound, and Griliches
1994, Autor, Katz, and Krueger 1998).2
Beaulieu, Benarroch, and Gaisford (forthcoming) and Long, Riezman, and
Soubeyran (forthcoming) also examine the issue of rising inequality within
both the North and the South. However, the mechanism of inequality in
these two papers differs from that in my model. In Beaulieu, Benarroch, and
Gaisford (forthcoming), the growing wage gap is due to the Stolper-Samuelson
effects rather than product-mix changes. Specifically, a reduction in trade
barriers in the skill-intensive high-tech sector typically raises the relative prices
of skill-intensive goods, leading to rising wage gap in both regions. In Long,
Riezman, and Soubeyran (forthcoming), trade liberalization not only directly
affects product prices, but also indirectly influences human capital accumulation. Hence, in addition to the Stolper-Samuelson mechanism, their model
suggests a new channel through which trade liberalization affects the wage
gap between skilled and unskilled workers.
The paper is organized as follows. In section 2 I describe the basic model. In
section 3 I illustrate the effects of product cycles on labour markets and conclude
that inequality can rise within and between countries. In section 4 the welfare
implications of product cycles are examined. Conclusions are drawn in section 5.
2. The basic model
The set-up is based on Dornbusch, Fischer, and Samuelson (1980). There are
two regions (the North and the South), two factors (skilled and unskilled
2 Using a monopolistic competition model with non-homothetic production, Dinopoulos,
Syropoulos, and Xu (1999) show that a move from autarky to free intra-industry trade
increases wage inequality in Northern countries. The mechanism of inequality operates in
product markets characterized by monopolistic competition and relates the size of the firm to
the mix of factor inputs and factor prices. Sener (2001) develops a dynamic model of NorthNorth trade that has implications for rising inequality in Northern countries. In his model
inequality results from a Schumpeterian version of the Stolper-Samuelson effects.
1046
S. Chun Zhu
labour), and a continuum of goods indexed by z in the interval [0,n]. I make the
standard Heckscher-Ohlin assumptions. Production functions are quasi-concave and exhibit constant return to scale. Goods markets and labour markets
are perfectly competitive. Furthermore, there are no trade barriers in the
model. Trade is always balanced.
I focus on the complete specialization equilibrium where the North produces more skill-intensive goods and the South produces less skill-intensive
goods. To this end, I make two additional assumptions. First, the North is
relatively abundant in skilled labour and the South is relatively abundant in
unskilled labour. Further, the difference in labour endowment is so large that
the relative wage for skilled labour is lower in the North than in the South.
Second, there are no factor intensity reversals. This implies that goods can be
ranked uniquely by skill intensity independently of factor prices. I use a higher
z to index a more skill-intensive good. Then, it can be shown that the North
has a comparative advantage in skill-intensive goods (z,n] while the South has
a comparative advantage in unskilled-intensive goods [0,z). Good z is the
‘competitive margin’. It is the only good that is produced in both regions.
Under the assumption that there are no trade barriers, the value of z is
determined by
pN (z) ¼ pS (z),
(1)
where pi (z) is the price of good z in region i (¼N,S).
On the demand side, I assume that all individuals have identical preferences,
which are represented by the CES utility function
Z n
1
1
U¼
x(z) dz
( > 1),
(2)
0
where x(z) is the consumption of good z and is the elasticity of substitution
between goods.
Equilibrium is characterized by conditions of balanced trade and
labour market clearing. Let Yi be national income in region i. Let pi (z) be
1
hR
i1
Rn
z
the price of good z. Let P 0 pS (z)1 dz þ z pN (z)1 dz
be the aggregate price index. With identical CES preferences, the balance-of-trade
condition is
Z z
Z n
pS (z) 1
pN (z) 1
dz ¼ YS
dz:
(3)
YN
P
P
0
z
The left-hand side is the value of Northern imports and the right-hand side is
the value of Northern exports. Combining the balance-of-trade condition with
equation (1) yields
(
YN
B(z) ln
pN (
z)
Z z
0
pS (z)
pS (
z)
Trade, product cycles, and inequality
1047
(
)
1 )
Z n
YS
pN (z) 1
dz ln
dz ¼ 0:
pS (
z) z pN (
z)
(4)
Using good z as numeraire simplifies the following analysis.
Let Hi and Li be the supply of skilled and unskilled labour, respectively. Let
wHi and wLi be the wages of skilled and unskilled workers, respectively. Define
hi Hi/Li and wi wHi/wLi. I assume that dHi/dwi 0 and dLi/dwi 0, thereby
allowing for the possibility that unskilled labour may obtain skills when the
relative wage rises.3 Let Hid and Ldi be the aggregate demand for skilled and
unskilled labour, respectively. Let Hi (wi, z) and Li (wi,z) be the amount of
skilled and unskilled labour, respectively, required to produce one unit of good
z. Finally, define hi (wi, z) Hi (wi,z)/Li (wi, z). To simplify notation, in the
following I will drop wN and wS as arguments. However, this should not be
misconstrued as an assumption that substitution between the two types of
labourR is restricted. The aggregate demand for Northern skilled labour is
n
HNd ¼ z x(z)HN (z)dz. With CES preferences, world demand for Northern
good z is x(z) ¼ [pN (z)/P]1 (YN þ YS)/pN (z). With zero profits, pN (z) ¼
wHNHN (z) þ wLNLN (z). Plugging x(z) into HNd , the condition of Northern skilled
labour market clearing can be expressed as
Z n
pN (z) 1 (YN þ YS )HN (z)
d
dz:
(5)
HN ¼ HN ¼
P
wHN HN (z) þ wLN LN (z)
z
Similarly, the condition of Northern unskilled labour market clearing is
Z n
pN (z) 1
(YN þ YS )LN (z)
dz:
LN ¼ LdN ¼
P
w
HN HN (z) þ wLN LN (z)
z
(6)
Since I am interested in the wage gap between skilled and unskilled labour, I
combine equations (5) and (6) and express the labour market clearing conditions in terms of wN. To this end, define N(
z) HNd =HN LdN =LN . N(
z) is the
excess demand for skilled labour relative to unskilled labour in the North.
With some manipulation, N (
z) ¼ 0 can be written as4
3 Note that this assumption is made for simplicity. The model can be generalized easily to allow
an endogenous skill decision (see Dinopoulos and Segerstrom 1999; Sener 2001; Beaulieu,
Benarroch, and Gaisford, forthcoming).
4 The skilled labour market equilibrium condition (5) can be rewritten as
Z n
HNd
YN þ YS
hN (z)
dz ¼ 1:
(7)
¼
pN (z)1
1
1 þ wN hN (z)
HN wLN HN P
z
Similarly, the unskilled labour market equilibrium condition (6) yields
Z n
LdN
YN þ YS
hN
dz ¼ 1:
¼
pN (z)1
1
LN wLN HN P
1 þ wN hN (z)
z
Equation (7) minus equation (8) results in the labour market equilibrium condition (9).
(8)
1048
S. Chun Zhu
N(z) Z n
z
pN (z)
pN (
z)
1
½hN (z) hN dz ¼ 0:
1 þ wN hN (z)
(9)
Similarly, the corresponding Southern labour market clearing condition
SðzÞ ¼ HSd =HS LdS =LS can be written as
Z z
pS (z) 1 ½hS (z) hS dz ¼ 0:
(10)
S(z) 1 þ wS hS (z)
z)
0 pS (
The competitive margin z and relative wages (wN,wS) are determined simultaneously by equations (4), (9), and (10).5 In particular, the competitive margin
z serves as a link between the two labour markets. In this model prices of goods
and national income are also endogenized. The proof of existence and uniqueness of the equilibrium in Dornbusch, Fischer, and Samuelson (1980) can be
applied with only minor modifications.
3. Product cycles and inequality
While Dornbusch, Fischer, and Samuelson (1980) examine endowment
changes, I focus on the impact of technical change on labour markets and
trade patterns. In this paper technical change takes the form of product
innovation in the North.6 This is consistent with the fact that new goods are
mainly invented and first produced in a few industrial countries. In the 1980s
the United States, Japan, Germany, Great Britain, and France accounted for
91% of total R&D expenditures in the OECD area, and the United States
alone accounted for more than half of total R&D expenditures (calculated
using the OECD ANBERD Database 2000). Krugman (1979) and Grossman
and Helpman (1991) also make a similar assumption.
I make two additional assumptions about Northern product innovation.
First, since my goal is to examine the impacts of innovation rather than its
determinants, I assume that product innovation is exogenous. Second, in the
light of recent work on technology-skill complementarities,7 I assume that new
goods use relatively more skilled labour than old goods. Note that this
assumption is made for analytical convenience. It can be shown that all results
hold under a weaker assumption that on average new goods are more skill
intensive than existing Northern goods.
5 Both Yi/pi (
z) and pi (z)/pi (
z) (i ¼ S,N) can be expressed in terms of wi: Yi/pi (
z) ¼ [(wihi þ 1) Li]/
z) þ 1) Li (
z)], and pi (z)/pi (
z) ¼ [(wihi (z) þ 1) Li (z)]/[(wihi (
z) þ 1) Li (
z)].
[(wihi (
6 Process innovation is taken up in Zhu and Trefler (forthcoming).
7 Goldin and Katz (1998) document that technology-skill complementarities existed in
manufacturing early in this century. Krueger (1993) and Berman, Bound, and Griliches (1994)
report that use of computers raises the demand for skills. Bresnahan, Brynjolfsson, and Hitt
(2002) find that information technology and the corresponding change in firm organization also
increase the demand for skilled labour. The theoretical work on technology-skill
complementarities includes Galor and Tsiddon (1997).
Trade, product cycles, and inequality
1049
In this section I will provide a weak condition guaranteeing that as the
North produces more new goods, it loses competitiveness in less skill-intensive
goods. As a result, older less skill-intensive Northern goods migrate South.
Following Krugman (1979), I will use the term ‘technology transfer’ to refer to
this process of production relocation. I will also examine the implication of
product cycles for inequality within and between countries.
3.1. Outline
The creation of new goods has a direct impact on the trade balance. The utility
function in equation (2) implies that for given income and prices, consumers
would be better off if they have a wider range of goods. Thus, as new goods
become available, consumers allocate some of their budget to new goods and
spend less on all old goods. This leads to a shift in demand from Southern goods
to Northern goods. Ceteris paribus, the North develops a trade surplus. To
restore the trade balance, Northern national income must rise (see equation (3)).
The creation of new goods also directly affects the Northern labour market.
Since new goods are more skill intensive than all existing Northern goods, the
creation of new goods raises the relative demand for skilled labour. Thus, the
relative wage of skilled labour rises. This, together with the increase in national
income just discussed, implies that the wage of Northern skilled labour must
rise. At the same time, the creation of new goods leads to an excess supply of
Northern unskilled workers. Whether the wage of unskilled labour rises or falls
in equilibrium hinges on the degree of substitutability between Northern
skilled and unskilled labour. Unskilled labour can be substituted for skilled
labour in three ways. First, cheaper unskilled labour replaces skilled labour
within production of each good, that is, within-good substitution. Second, by
the Rybczynski effect, production of less skill-intensive goods expands, that is,
between-good reallocation. Third, in response to rising wage inequality some
unskilled labour upgrades and becomes skilled labour. When Northern skilled
and unskilled workers are sufficiently substitutable, the oversupplied unskilled
labour can be absorbed without lowering their wage. In this case, the North
loses its competitiveness in less skill-intensive Northern goods, so that these
goods move South. In the above I have sketched out a simple story about
product cycles. In the following section I will formalize this idea.
3.2. Product cycles
I introduce new goods as follows. Let t index the state of technology and let n
be the highest goods index given t. As technology evolves from t to t þ dt, new
goods are introduced over the range (n,n þ dn). I consider the impact of
changes in t and hence n on wS, wN, and z.
As discussed above, the conclusion that Northern innovation leads to
product cycles (i.e., raises z) hinges on the degree of substitutability between
skilled and unskilled labour in the Northern production. Let
"aN d ln (HNd =LdN )=d ln wN be the aggregate elasticity of substitution
1050
S. Chun Zhu
between Northern skilled and unskilled labour. Theorem 1 formalizes this
observation.8
1. There exists a constant " 2 (0,) such that "aN > " , d z=dt > 0. That
is, if and only if skilled and unskilled labour are sufficiently substitutable in the
production of Northern goods, Northern innovation sets up product cycles in which
new goods are initially produced in the North and then relocated to the South.
THEOREM
The critical degree of substitutability between Northern skilled and
unskilled labour (") depends on factor intensity differences across goods. If
the differences are large, the creation of very skill-intensive goods imposes
more pressure on the unskilled labour market. In order to absorb the oversupplied unskilled labour, a larger value of " is required.
Theorem 1 also implies that "aN > is a sufficient condition for product
cycles to occur. In particular, when approaches 1 (i.e., preferences are
represented by the Cobb-Douglas utility function), the sufficient condition
becomes "aN > 1. Empirically, this sufficient condition is likely to be satisfied.
Most estimates of the aggregate elasticity of substitution are between 1 and 2
(Johnson 1970; Freeman 1986; Katz and Murphy 1992; Heckman, Lochner,
and Taber 1998, and Krusell et al. 2000).
3.3. The role of the elasticity of substitution
I have discussed how product cycles rest on the substitutability between skilled
and unskilled workers. In this section I further develop this point and show
that care is needed in thinking about the aggregate elasticity of substitution.
The aggregate elasticity of substitution incorporates direct factor substitution
within goods as well as indirect factor substitution via changes of output mix
(i.e., the Rybczynski effect). The elasticity of substitution between skilled and
unskilled labour in the production of good z is defined as "N (z) d ln hN (z)/d
ln wN. (Recall that wN wHN/wLN is the relative wage of Northern skilled
labour and hN (z) hHN (z)/hLN (z) is the relative employment of skilled labour
in good z.) Using the labour demand equations in (5) and (6), "aN can be
expressed as a weighted average of within-good elasticities of substitution
between factors ("N ()) and the elasticity of substitution between goods ():
Rn
½pN (z)1 LN (z)HN (z)"N (z)dz
a
"N ¼ z
Rn
YLN YHN z ½pN (z)1 dz
"
#
Rn
1
½
p
(z)
(z)
(z)dz
N
LN
HN
,
(11)
þ 1 z
Rn
YLN YHN z ½pN (z)1 dz
8 Proofs are available upon request.
Trade, product cycles, and inequality
1051
where LN (z) wLNLN (z)/pN (z) is the cost share of Northern unskilled labour
in good z, HN (z) wHNHN (z)/pN (z) is the cost share of Northern skilled
labour, YLN wLNLN/YN is the national income share of unskilled labour,
and YHN wHNHN/YN is the national income share of skilled labour. Note
that the second term in equation (11) is always positive.9
Equation (11) is a continuum-of-goods version of the aggregate elasticity of
substitution discussed in Jones (1965). As "N () increase, "aN becomes larger.
When "N () ¼ 0 (i.e., no within-good substitution), labour market adjustment
depends on a Rybczynski-style reallocation of output between skill-intensive and
unskilled-intensive goods. This is captured by the second term in equation (11).
A bigger value of implies a stronger substitution effect via output reallocation.
This is because, with a bigger , consumers are more willing to substitute
cheaper goods for more expensive ones. Therefore, as the creation of new
goods raises the relative wage of Northern skilled workers and with it the
relative prices of skill-intensive goods,10 a larger value of facilitates output
reallocation from skill-intensive goods to less skill-intensive ones. This increases
the capacity to absorb oversupplied unskilled Northern workers. Equation (11)
thus helps one to understand what has been estimated by researchers such as
Katz and Murphy (1992). It also helps one to understand how the FeenstraHanson model equilibrates: even though they assume that there is no substitution between skilled and unskilled labour within goods production
("N () ¼ "S () ¼ 0), equilibration occurs via a Rybczynski-style reallocation.
Both "N () and affect not only the sign of d z=dt, but also its magnitude.
The more substitutable unskilled labour is for skilled labour, the bigger is the
rate of technology transfer. With small values of "N () and , oversupplied
unskilled Northern labour can be only partially absorbed by factor substitution within goods and output reallocation between existing goods. Most of the
absorption must come from expanding the production of the least skillintensive goods, that is, by reducing z. The higher "N () and are, the weaker
is the pressure to lower z and, hence, the more effective is the product-cycle
pressure to raise z. The elasticities of substitution in the South ("S () d ln
hS ()/d ln wS) affect d z=dt in a similar way. To formalize these observations,
write "i as a function of a shift variable i (i ¼ S,N). i shifts the entire "i (,i)
9 Using
hN (z) hN
HN (z) YHN YLN LN (z)
¼
¼
,
wN YLN
wN hN (z) þ 1
wN YLN
Rn
equation (9) can be rewritten as z ½pN (z)1 ½LN (z) YLN dz ¼ 0. Combining this with LN (z)2 ¼
Rn
Rn
1
2
2
½LN (z) YLN 2 þ2½LN (z) YLN YLN þ YLN
yields z ½pN (z)1 LN (z)2 dz > YLN
dz.
z ½pN (z)
Rn
R
R
n
n
1
1
1
It follows that z ½pN (z) LN (z)HN (z)dz ¼ z ½pN (z) LN (z)dz z ½pN (z) LN (z)2 dz <
Rn
YHN YLN z ½pN (z)1 dz.
10 Consider two Northern goods z1 and z2. The change in the relative good price is d ln [pN (z2)/
pN (z1)]/dt ¼ [HN (z2) HN (z1)]d ln wN/dt. This is positive when z2 > z1, i.e., z2 is more skill
intensive than z1.
1052
S. Chun Zhu
schedule up. That is, a large i makes the "i more elastic. The results are
summarized in theorem 2.
2. d z=dt is increasing in S, N, and . That is, an increase in either
region’s within-good elasticities of substitution between factors or the elasticity of
substitution between goods raises the rate of technology transfer.
THEOREM
3.4. Rising wage inequality within countries
In recent decades many developed countries and some developing countries
have experienced rising wage inequality. This poses a challenge to traditional
trade theory. The Stolper-Samuelson theorem appeals to shifting terms of
trade to predict that rising inequality in developed countries will go hand in
hand with falling inequality in developing countries. This contradiction has led
some authors to doubt the relevance of the Heckscher-Ohlin framework (e.g.,
Robbins 1995). Interestingly, the next theorem shows that this puzzle can be
resolved by embedding technical change into the continuum-of-goods
Heckscher-Ohlin model. Recall that wi ¼ wHi/wLi (i ¼ N,S) is the wage of
skilled relative to unskilled workers. It is the measure of within-country
inequality in my model.
3. (i) dwN/dt > 0. (ii) Assume "aN > ". Then dwS/dt > 0. That is, product cycles raise inequality in the North. If Northern skilled and unskilled labour
are sufficiently substitutable, then product cycles also raise inequality in the South.
THEOREM
The creation of new, skill-intensive goods raises the relative demand for
Northern skilled labour. Thus, the relative wage in the North rises. It is worth
noting that this result holds whether z rises or falls. Even if z falls, thereby
increasing the relative demand for Northern unskilled labour, this effect is entirely
offset by the effect of newly created goods. This is consistent with the empirical
finding that domestic skill-biased technical change is likely the main factor behind
rising inequality in developed countries (e.g., Berman, Bound, and Griliches 1994;
Autor, Katz, and Krueger 1998; Berman, Bound, and Machin 1998).
In contrast, technology transfer (rising z) is the only factor affecting the
relative labour demand in the South. The goods that migrate South may be the
least skill intensive from a Northern perspective, but they are the most skill
intensive from a Southern perspective. Technology transfer therefore raises the
relative demand for skilled labour in the South, leading to wage inequality
there.11 The condition "aN > " in theorem 3 ensures that z will rise.
11 Zhu (2003) examines empirically the extent to which increasing demand for skilled workers can
be explained by product cycles, that is, by U.S. innovation and the subsequent relocation of
production to U.S. trading partners. She finds strong evidence that product cycles are
significantly and positively correlated with rising demand for skilled workers in a large panel of
industries and countries.
Trade, product cycles, and inequality
1053
This basic insight of theorem 1 appears in Feenstra and Hanson’s (1996)
study on outsourcing and inequality in the United States and Mexico. However, my work also differs from theirs in several major aspects. First, the
driving force is different. In my two-factor model (skilled labour and unskilled
labour), all the changes in labour markets and trade patterns are driven by
Northern product innovation. In contrast, in Feenstra and Hanson’s threefactor model (capital, skilled labour and unskilled labour), a higher rate of
return to capital investment in the South causes production relocation from the
North to the South. Second, Feenstra and Hanson consider a partial equilibrium model. This is because they mainly examine the impact of foreign direct
investment on labour demand within a single industry. In contrast, since I am
interested in the general equilibrium interactions between international trade
and labour markets, I use a general equilibrium model of trade in final goods.
In particular, my model has richer general equilibrium feedbacks through the
trade balance. Third, in Feenstra and Hanson there is no substitutability
between skilled and unskilled labour. This is incompatible with the focus on
such elasticities that dominates the literature on wage inequality (e.g., Katz and
Murphy 1992). In contrast, in my model the substitutability between skilled
and unskilled workers plays a central role in generating product cycles. Finally,
in Feenstra and Hanson Northern inequality is entirely driven by production
relocation. In contrast, in my model Northern product innovation is the
dominant factor behind rising inequality in the North.
It is also worth noting that the wage gap between skilled and unskilled
workers is rising in some but not all less developed countries. One explanation
for falling inequality in some Southern countries is that these countries may
experience a rapid growth in the relative supply of skilled workers, which
largely results from expansion of public education. This explanation is supported by Lam and Levison (1992) on Brazil, and Kim and Topel (1995) on
South Korea. In both empirical studies strong evidence is found that declining
education differentials are closely associated with relative labour supply shifts.
To formalize this idea, I can extend the model by incorporating a shift in the
skill composition of Southern labour force.12 It can be shown that when the
shift in the relative supply of skilled labour is greater than the shift in the
relative demand for skilled labour (due to production relocation), the wage gap
between skilled and unskilled labour can fall.
3.5. Rising inequality between countries
Product cycles increase inequality not only within countries, but also between
countries. Northern product innovation and endogenous technology transfer
12 Here, the change in the relative labour supply means a shift of the labour supply curve rather
than a movement along an upward-sloping labour supply curve. This is because an expansion
of public education reduces the cost of education and thus induces more workers to get
education for any given wage rate.
1054
S. Chun Zhu
have opposing effects on the North-South income gap. Unlike product innovation, technology transfer narrows the North-South gap. This raises the concern
about whether technology transfer will help the South to catch up with the
North. The next theorem shows that this concern is unwarranted. Since the
effect of product innovation is more direct, it offsets the negative effect of
technology transfer on Northern income. Thus, product cycles widen the
North-South income gap.13
THEOREM 4. d(YN/YS)/dt > 0. That is, product cycles widen the North-South
income gap.
Theorem 4 further implies that when the elasticity of substitution between
goods () is close to unity, the rate of technology transfer (d ln z=dt) can
never exceed the rate of product innovation (d ln n/dt).14
Theorem 4 stands in sharp contrast to Krugman (1979). The difference
mainly arises from the way technology transfer is modelled. In Krugman,
technology transfer is exogenous. Krugman considers the case where there is
an increase in the rate of technology transfer while the rate of Northern
innovation is kept constant, and he concludes that the North-South gap can
be narrowed. In my model, however, technology transfer is endogenous. Since
the rate of technology transfer lags behind the rate of innovation, the effect of
technology transfer on the income gap is of a second order compared with the
effect of product innovation. This completes the discussion of the implications
of product cycles for inequality within and between countries. I now turn to
welfare analysis.
4. Welfare analysis
The simplicity of this model allows me to derive a rich set of welfare implications of product cycles. In this section I will first examine a change in the terms
of trade. This is the basis for further analysis of national welfare and labour
welfare.
4.1. Terms of trade
In a model with a continuum of goods, it is natural to define terms of trade as a
price index using initial net exports as the weights. By this definition, an
increase in the terms of trade implies that the initial consumption bundle is
13 An extension of the model by including the increasing supply of Southern skilled labour can
help one explain the income catch-up by some newly industrialized countries in recent decades.
14 When approaches 1, the balance-of-trade condition in equation (3) implies
d ln (YN =YS ) d ln (n z) d ln z
¼
:
dt
dt
dt
By theorem 4, d ln (YN/YS)/dt > 0. Thus, d ln n=dt > d ln z=dt.
Trade, product cycles, and inequality
1055
cheaper at the new prices than at the old ones. This further implies that
improved terms of trade always benefit consumers. (See Dixit and Norman
1980, 132.)
Using the above definition, the change in Northern terms of trade may be
Rn
R z
written as dPN =dt ¼ YS z ½pN (z)=P1 ½d ln pN (z)=dtdz YN 0 ½pS (z)=P1
1
hR
i1
Rn
z
½d ln pS (z)=dtdz. (Recall that P 0 pS (z)1 dz þ z pN (z)1 dz
is the
aggregate price index.) The change in Southern terms of trade is dPS/dt ¼
dPN/dt. Theorem 5 states that product cycles improve the terms of trade in
the North while worsening the terms of trade in the South.
Assume "aN > ".Then dPN/dt > 0 and dPS/dt < 0. That is, the terms of
trade rise in the North and fall in the South.
THEOREM 5.
It is worth noting that product innovation improves the terms of trade in
the North. This is in contrast to the conventional result that technical progress
in the export sector generally worsens the terms of trade. When product cycles
raise the relative wages of skilled labour in both regions, the goods that use
relatively more skilled labour become more expensive within each region (see
fn. 10.) Note that good z is the least skill intensive from a Northern perspective
while it is the most skill intensive from a Southern perspective. Thus, in terms
of good z, the relative price of any Northern good increases and the relative
price of any Southern good decreases, implying that the terms of trade must
rise in the North and fall in the South.
4.2. National welfare
Since each region has two types of labour, care is needed in measuring national
welfare. If the government can do a lump-sum transfer within a region, or can
redistribute domestic income optimally through a complete set of indirect
taxes, then a higher indirect utility, which is derived using national income,
will imply that all types of labour in the region can be made better off (see
Dixit and Norman 1980, 20).
When all types of labour have the same CES preferences, it is straightforward to derive the Northern indirect utility as UN ¼ YN/P. Then the change
in Northern welfare can be further derived as
d ln UN
1
pN (n) 1 dn
1 dPN
þ
¼
:
(12)
1
P
dt YN dt
dt
The first term reflects the gain from consuming new goods. The second term
captures the effect of terms of trade. Since the terms of trade improve in the
North (see theorem 5), equation (12) suggests that the North will always
benefit from product cycles.
1056
S. Chun Zhu
This differs markedly from Krugman (1979), who finds that technology
transfer must make the North worse off. The difference arises from the
different impact of technical change on the terms of trade. In Krugman,
when the rate of technology transfer catches up with the rate of product
innovation, the terms of trade in the North will fall.15 In contrast, in my
model, although technology transfer shifts income from the North to the
South, it is a second-order effect compared with the effect of product innovation. It can be shown that product cycles improve the terms of trade in the
North.16 Thus, even when technology transfer reduces Northern income, the
North is still better off.
Likewise, the change in Southern welfare (US) can be written as
d ln US
1
pN (n) 1 dn
1 dPS
þ
¼
:
(13)
1
P
dt YS dt
dt
Equation (13) suggests that new goods benefit the South to the same extent as
the North. It can be shown that the gain from new goods always outweighs the
loss to the South from worsened terms of trade. Therefore, the South is also
better off from product cycles. Theorem 6 summarizes these results.
6. Assume "aN > ". Then dUN/dt > 0 and dUS/dt > 0. That is, product
cycles improve welfare in both the North and the South.
THEOREM
4.3. Labour welfare
It is worth pointing out that previous product-cycle models largely consider
one type of labour and thus cannot have any welfare implications for different
types of labour. In this paper labour welfare is measured by the indirect utility of
each type of labour. Let UHN and UHS denote the indirect utility of skilled labour
in the North and the South, respectively. Note that UHi ¼ wHi/P(i ¼ S,N).
Then the change in welfare of skilled labour may be written as
d ln UHi
1
pN (n) 1 dn 1 dPi
d ln wi
þ
¼
þ YLi
, i ¼ S,N:
(14)
1
P
dt Yi dt
dt
dt
The first term indicates that new goods benefit skilled labour in both regions to
the same extent. The second term reflects the welfare effects of terms of trade.
Specifically, improved terms of trade in the North (dPN/dt > 0) make Northern
15 Similar to Krugman (1979), Dollar (1986) considers the case where there is an increase in the
rate of technology transfer while the rate of product innovation is kept constant. In Dollar’s
model technology transfer also worsens the terms of trade in the North.
16 Jensen and Thursby (1987) develop a product-cycle model with endogenous innovation but
exogenous technology transfer. Since an increase in the rate of technology transfer raises the
rate of innovation, the Northern terms of trade may not deteriorate with an increased transfer
rate.
Trade, product cycles, and inequality
1057
skilled labour better off, while worsened terms of trade in the South (dPS/
dt < 0) make Southern skilled labour worse off. However, for Southern skilled
labour, the loss from worsened terms of trade is fully offset by the gain from
new goods (see equation (13) and theorem 6). Further, as suggested by the
third term in equation (14), when product cycles shift domestic income from
unskilled to skilled labour, welfare of skilled labour is further improved in both
regions. Therefore, skilled labour in both regions must be better off.
Let ULN and ULS denote the indirect utility of unskilled labour in the North
and the South, respectively. The change in welfare of unskilled labour can be
derived as
d ln ULi
1
pN (n) 1 dn 1 dPi
d ln wi
þ
¼
YHi
, i ¼ S,N:
(15)
1
P
dt Yi dt
dt
dt
A comparison of equations (14) and (15) reveals that the divergence in welfare
between skilled and unskilled labour within each region is entirely caused by
domestic income redistribution. In particular, as implied by the third term in
equation (15), rising domestic inequality lowers welfare of unskilled labour in
both regions. This negative welfare effect offsets the gains from product cycles
(e.g., the creation of new goods). Thus, it is less certain whether unskilled
labour would be better or worse off. If the negative effect of increasing wage
gap dominates, unskilled labour in both regions can be worse off. These results
are summarized in theorem 7.
7. Assume "aN > ". Then (i) dUHN/dt > 0 and dUHS/dt > 0. That is,
product cycles improve welfare of skilled labour in both the North and the South.
(ii) dUHN/dt 0 0 and dUHS/dt 0 0. That is, unskilled labour in both regions may
gain or lose from product cycles.
THEOREM
5. Conclusions
Previous work on the product cycle neglects its implications for domestic
income distribution. However, in recent decades, inequality has risen in both
developed countries and some developing countries. Since this contradicts the
Stolper-Samuelson theorem, it poses a challenge to traditional trade theory.
This paper incorporates product innovation and technology transfer into
the continuum-of-goods Heckscher-Ohlin model. It shows that inequality can
rise in both regions. The intuition is simple. The creation of new, highly skillintensive goods in the North raises the relative demand for Northern skilled
labour and hence raises inequality. When the aggregate elasticity of substitution between skilled and unskilled labour is sufficiently large in the North, the
creation of new goods causes the North to lose competitiveness in older goods.
These older Northern goods thus migrate South. Since these older goods are
the least skill intensive of the goods produced in the North and the most skill
1058
S. Chun Zhu
intensive of the goods produced in the South, technology transfer reduces the
relative demand for Northern unskilled labour and increases the relative
demand for Southern skilled labour. This aggravates inequality in the North
and also creates inequality in the South.
Product cycles increase inequality not only within countries, but also
between countries. Product innovation widens the North-South income gap
while technology transfer narrows the gap. Since the effect of technology
transfer is entirely offset by the effect of product innovation, product cycles
increase the North-South gap.
This simple model also has rich welfare implications of product cycles.
Product cycles benefit both the North and the South. At the same time, since
income is redistributed from unskilled to skilled workers, skilled workers in
both regions are better off from product cycles.
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