Patterns of skill premia

by "Review of Economic Studies, The" (Jun 15, 01:55 AM)

But an increase in the supply of skills over time also induces a
change in technology, increasing the demand for skills. The most
important result of the paper is that increased international trade
induces skill-biased technical change. As a result, trade opening can
cause a rise in inequality both in the U.S. and the less developed
countries, and thanks to the induced skill-biased technical change,
this can happen without a rise in the relative prices of
skill-intensive goods in the U.S., which is the usual intervening
mechanism in the standard trade models.

(Proquest Information and Learning: ... denotes formula omitted.)

1. INTRODUCTION

This paper develops a tractable model linking skill premia (returns to
skills) to relative supplies, technology, and trade. The main
innovation of the model is to treat the degree of skill bias of
technology, and hence the demand for skills, as endogenous, and relate
it to the supply of skills and to international trade. I show that
this framework is broadly consistent with the time-series evidence on
the evolution of the relative supplies and the skill premium in the
U.S., and cross-country differences in skill premia. It also suggests
that increased international trade could be a major cause of the
increase in wage inequality because it induces skill- biased technical
change.

The literature on wage inequality is now vast. Figure 1 shows, a
number of U.S. facts pertinent to this literature (see Appendix A for
details). Starting in 1979, the college premium-the wages of college
graduates relative to the wages of high school graduates- increased
rapidly to a level unprecedented in the post-war period. Moreover,
this happened while the supply of college skills was rising rapidly.
The implication is that the demand for skills must have expanded even
more sharply during this time period. The literature has drawn a sharp
distinction between two possible causes for the increase in the demand
for skills: skill-biased technical change and increased international
trade.1

The trade explanation suggests that the U.S. skill premium increased
because trade with skill-scarce less developed countries (LDCs) raised
the demand for skilled Americans. In fact, between the early 1970's
and mid-1990's the share of imports from LDCs in the U.S. GDP
increased by over fourfold. Although the trade explanation is
theoretically plausible, most economists discount the role of
international trade for a variety of reasons.

First, international trade should increase the relative price of
skill-intensive goods and raise the "derived" demand for skills via
this channel. However, most evidence points to a declining or constant
relative price of skill-intensive goods over this period (see, for
example, Lawrence and Slaughter (1993), Sachs and Shatz (1994),
Desjounqueres, Machin and Van Reenen (1999)). Second, as Figure 1
shows the skill premium rose despite steadily increasing relative
supply of skills for the whole post-war period. This pattern suggests
that there has been secular skill-biased technical change, increasing
the demand for skills for most of this period. Many economists then
find it more plausible that skill-biased technical change is also
responsible for the more rapid increase in the demand for skills over
the recent decades (e.g. Autor, Katz and Krueger, 1998). The fact that
all sectors, even those producing less skilled goods, increased their
demands for more educated workers over this time period also suggests
that skill-biased technical change played a more important role than
trade. Third, if trade were the cause of the increase in inequality in
the U.S., inequality should have fallen in the LDCs that have started
trading with the more skill-abundant U.S. economy. The evidence,
however, suggests that more of the LDCs experienced rising inequality
after opening to international trade (see the discussion presented in
Section 2). Finally, a number of economists have pointed out that the
U.S. trade with the LDCs is not important enough to have a major
impact on the U.S. product market prices and consequently on wages.2

FIGURE 1

The behaviour of the (log) college premium and relative supply of
college skills (weeks worked by college equivalents divided by weeks
worked by noncollege equivalents) in the U.S. between 1939 and 1996

The most important hypothesis in this paper is that increased
international trade may have been more important than generally
believed because it induces skill-biased technical change. Therefore,
this paper argues that the two competing explanations for the increase
in the demand for skills, trade and technology, may be related. The
basic reason why trade induces skill-biased technical change is that
it creates a tendency for the U.S. relative price of skill-intensive
goods to increase. This change in relative prices increases the demand
for technologies used in the production of these goods, makes these
technologies more profitable to develop, and encourages further
technical change directed at them.

The theory proposed in this paper avoids the main criticisms levelled
against explanations that view trade as the major cause of the recent
rise in U.S. wage inequality. Because trade induces skill- biased
technical change, the explanation offered here is consistent with the
importance of skill-biased technical change documented by other
studies and points out that standard calculations underestimate the
impact of trade on wage inequality. Furthermore, with sufficiently
pronounced skill-biased change, the demand for skills and inequality
can increase in the LDCs also. Finally, although it is the increase in
the relative price of skill- intensive goods that encourages
skill-biased technical change, the increased productivity of skilled
workers both in the U.S. and in other countries may eventually return
the relative price of skill- intensive goods to its original
(pre-trade) level in the U.S. So existing evidence on the changes in
the U.S. relative price of skill- intensive goods does not refute
trade-based explanations of the increase in U.S. wage inequality.

The related literature includes models of the increase in inequality
in the U.S., such as Galor and Tsiddon (1997), Greenwood and Yorukoglu
(1997), Acemoglu (1999a), Caselli (1999), Aghion, Howitt and Violante
(2000), Krusell, Ohanian, Rios-Rull and Violante (2000) and Galor and
Maov (2000). Acemoglu (1998) is most closely related. In that paper, I
constructed a similar model of directed technical change to show that
the increase in the number of college graduates during the 1960's and
1970's in the U.S. can explain both the decline in the college premium
during the 1970's and its sharp rise during the 1980's. Here, I extend
that model in a number of directions. First, in Acemoglu (1998), I
considered a closed economy model, while here I analyse a multicountry
set-up, where the equilibrium skill bias of technology is determined
at the world level. This analysis highlights how the relationship in
the time series and the cross section between the supply of skills and
skill premia is shaped by different factors. Second and most
important, I incorporate the analysis of international trade into this
framework, and show that trade opening induces skill-biased technical
change.

Previous studies, including among others Kennedy (1964), Drandakis and
Phelps (1965), Samuelson (1965), Ahmad (1966), Hayami and Ruttan
(1970) and David (1975), discuss the concept of induced innovations,
which is closely related to directed technical change, but these
papers do not have a micro-founded model of technological change, and
do not focus on the determinants of skill premia. The analysis here
also obviously borrows from the endogenous growth literature (for
example, Romer (1990), Grossman and Helpman (1991a,b), Aghion and
Howitt (1992, 1998)), but technical change here is not only
endogenous, but also directed, in the sense that the degree of skill
bias of new technologies responds to profit incentives.

Finally, previous contributions that emphasize the importance of trade
on inequality include Learner (1992, 1994), Wood (1994), Baldwin
(1995), Borjas and Ramey (1995) and Baldwin and Cain (1997) and the
papers in Bhagwati and Kosters (1994). The potential impact of trade
on technology was first raised by Wood (1994) who argued that trade
with the LDCs will lead to defensive skill-biased innovations. Wood,
however, did not develop the mechanism through which such defensive
innovations could occur.3

The plan of the paper is as follows. In the next section, I analyse
the effect of international trade on skill premia with exogenous
technology. In Section 3, I introduce a model of endogenous (directed)
technical change where skill- and labour- complementary technologies
can be developed at different rates, and show that this model is
consistent with a number of salient features of time-series and
cross-country evi\dence on skill premia. In Section 4, I develop the
argument that trade opening can cause skill- biased technical change
in the U.S., and show that the increase in international trade could
be the driving force of the rise in inequality over the past several
decades. Section 5 concludes with some future directions and
extensions. In particular, I analyse the effect of trade on
technologies chosen by another set of technological leaders, such as
the European economies, and show how trade may lead to skill-biased
technical change in the U.S., but labour-biased technical change in
Europe. I also analyse how international trade may affect technology
adoption in LDCs.

2. TRADE AND SKILL PREMIA

I begin with a simple model that illustrates the effect of
international trade on skill premia in the standard (Heckscher- Ohlin)
trade model. I will then use this framework to endogenize technology,
and investigate the effect of relative supplies on technology and the
interaction between trade and technology.

Consider a world economy consisting of J + 1 countries, the U.S., and
J LDCs. H denotes skilled workers and L denotes unskilled workers. I
assume that the U.S. has a higher fraction of skilled workers than the
LDCs, that is, H^sup U^/L^sup U^ > H^sup j^/L^sup j^ for j = 1 , . . .
, J, where U denotes the U.S. and j denotes the j-th LDC. I will
sometimes denote the U.S. with j = 0 to simplify the notation. For
now, I take the relative supplies of skills as given. In the Appendix,
I show that all the results in the paper generalize when these
supplies are endogenized.

All consumers in all countries have identical preferences:

This equation highlights the main forces affecting skill premia in a
closed economy. For given skill bias of technology, as captured by
A^sup j^^sub h^/ A^sup j^^sub l^, the relative demand curve for skill
is downward sloping with elasticity [epsilon], as shown by the curve
denoted CT in Figure 2. An increase in H^sup j^ / L^sup j^ creates a
substitution of skilled workers for unskilled workers (or of the
skilled good for the unskilled good), and reduces the relative
earnings of skilled workers. The effect of a change in A^sup j^^sub
h^/ A^sup j^^sub l^ is more complex, and depends on the elasticity of
substitution. If the elasticity of substitution, [epsilon], is greater
than 1, then ...,, and improvements in the skill-complementary
technology increase the skill premium. The converse is obtained when
[epsilon] < 1 : an improvement in the productivity of skilled workers,
A^sup j^^sub h^, relative to the productivity of unskilled workers,
A^sup j^^sub l^, reduces the skill premium. The conventional wisdom is
that the skill premium increases when skilled workers become
relatively more-not relatively less-productive, which is consistent
with [epsilon] < 1. Almost all estimates show an elasticity of
substitution between skilled and unskilled workers greater than 1
(see, for example, Freeman, 1986). So in the rest of the paper I take
[epsilon] to be greater than 1.

Suppose that all countries start trading internationally without any
trading costs or thick borders. Free trade implies that there will be
a unique world relative price of skill-intensive goods, p , and given
this price, all consumers will choose the same consumption ratio of
skill intensive goods to labour-intensive goods, C^sup j^^sub h^/
C^sup j^^sub l^. Therefore, the world equilibrium relative price is
given by

FIGURE 2

Relative demand for skills

where the fact that the world skill premium, [omega] , is greater than
the pre-trade U.S. skill premium, [omega]^sup U^, is a direct
consequence of (11). Therefore, trade between the skill-abundant U.S.
and skill-scarce LDCs increases the demand for, and the price of,
skill-intensive goods produced in the U.S. Via this channel, trade
increases the (derived) demand for the services of American skilled
workers, raising the U.S. skill premium.

Although this analysis shows that increased international trade could
be responsible for the rise in skill premia and inequality in the
U.S., most economists discount the role of trade for the reasons
discussed briefly in the introduction. First, as equation (13) shows,
the effect of international trade works through a unique intervening
mechanism: free trade with the LDCs increases the relative price of
skill-intensive goods, [rho], and affects the skill premium via this
channel. Perhaps the most damaging piece of evidence for the trade
hypothesis is that most studies suggest the relative price of
skill-intensive goods did not increase over the period of increasing
inequality. Lawrence and Slaughter (1993) found that during the 1980's
the relative price of skill-intensive goods actually fell. Sachs and
Shatz (1994) found no major change or a slight decline, while a more
recent paper by Krueger (1997) found an increase in the relative price
of skill-intensive goods, but only for the 1989-1995 period. More
recent work by Desjounqueres et al. (1999) presents evidence showing
no increase or even a decline in the relative price of skill-intensive
goods in the U.K., Germany, Japan, Denmark and Sweden, and a small
increase in the U.S. between 1974 and 1989, while Haskel and Slaughter
(1999) show an increase using U.K. data.

Second, a variety of evidence suggests that skill-biased technical
change has been important in the changes in the wage structure. For
example, Figure 1 shows that there has been steady skill-biased
technical change throughout the past 60 years, and Berman et al.
(1994), Autor et al. (1998), Berman, Bound and Machin (1998) and
Machin and Van Reenen (1998) document that skill-biased technical
change may have been faster during the past 25 years. Moreover, these
authors show that all sectors, even those producing less skill-tensive
goods, increased their demands for more educated workers. This pattern
is consistent with the importance of skill- biased technical change,
but not with an increase in the demand for skills driven mainly by
increased international trade.

Third, a direct implication of the trade view is that, while demand
for skills and inequality increase in the U.S., the converse should
happen in the LDCs that have started trading with the more
skill-abundant U.S. economy. The evidence, however, suggests that more
of the LDCs experienced rising inequality after opening to
international trade. Although the increase in inequality in a number
of cases may have been due to concurrent political and economic
reforms, the preponderance of evidence is not favourable to this basic
implication of the trade hypothesis.6

Finally, a number of economists have pointed out that U.S. trade with
the LDCs is not important enough to have a major impact on the U.S.
product market prices and consequently on wages. Krugman (1995)
illustrates this point by undertaking a calibration of a simple
North-South model. Katz and Murphy (1992), Herman et al. (1994) and
Borjas et al. (1997) emphasize the same point by showing that the
content of unskilled labour embedded in U.S. imports is small relative
to the changes in the supply of skills taking place during this
period.

Although many of the assumptions that go into these factor- content
calculations can be questioned, it is useful to briefly consider the
relevant magnitudes to compare them later to the implications of the
theory developed here. The simple model in this section suggests that
to estimate the percentage (log point) change in the skill premium, we
only need to know the percentage (log point) difference between H^sup
U^/L^sup U^ and H^sup W^/L^sup W^. In particular, equations (11) and
(13) immediately imply that

In practice, there exist trade barriers even after trade opening, so
H^sup W/L^sup W^ does not correspond to the actual ratio of skilled to
unskilled workers in the world economy. The literature has attempted
to deal with this problem by estimating the factor content of trade
with the LDCs. Even though, as pointed out by Learner (1994, 1996),
there may be conceptual problems with such factor content studies,
they are theoretically correct within the context of the simple model
considered here, so I will make use of these calculations to quantify
the possible impact of trade.7

Borjas et al. (1997) present a number of alternative estimates of the
increase in the unskilled labour content of trade with LDCs between
1980 and 1995. The most appealing of these is what they refer to as
the "high" estimate. This estimate assumes that in the absence of the
increase in imports from the LDCs, domestic production would have
replaced these imports, using average industry skill shares and labour
productivity from 1970 (i.e. before the growth of manufacturing
imports from the LDCs). This counterfactual is plausible, in part,
because imports typically dislocate the less efficient and more
labour-intensive establishments. The numbers that Borjas et al. (1997)
report using this assumption, and taking 1980 as the pre-trade and
1995 as the post-trade period, imply that ln(H^sup W^/L^sup W^) -
ln(H^sup U/L^sup U^) [approximate] 0[middot]04. To translate this into
a change in skill premium, we also need an estimate of [varepsilon].
The typical elasticity used in this literature is [varepsilon] =
1[middot]4 which is estimated from time-series variation. The only
estimate using a quasi- exogenous variation comes from Angrist (1995),
who exploits the increase in the supply of college graduates in the
West Bank and Gaza Strip during the 1980's. The elasticity implied by
Angrist's (1995) estimates is over [varepsilon] = 2, which is also
consistent with the results of Card and Lemieux (2001). When
[varepsilon] = 1[middot]4, these numbers imply that international
trade will have led to an approximately 3% increase in the skill
premium (0[middot]04/1[middot]4 [approximate] 0[middot]03), while
[varepsilon] = 2 puts the same number at 2% (0[middot]04/2
[approximate] 0[middot]02).8 Over this ti\me period, the actual change
in the college premium was just under 20%, so international trade is
unlikely to account for more than 10-15% of the actual change (2-3% of
the 20% actual increase). Although this is a nontrivial amount, it
leaves the bulk of the increase unexplained, and underlies the
conclusion of many studies that international trade has played a
relatively minor role in the increase in inequality.

While the above arguments suggest that increased international trade
with the LDCs is not the major cause of the changes in the wage
structure by itself, they do not rule out a powerful effect of
international trade when it interacts with technical change: in a
world with endogenous technical change, increased international trade
could affect technology choice, and have a large effect through this
channel. This is the issue I turn to next.

3. ENDOGENOUS TECHNOLOGY

3.1. Endogenous technology without international trade

In this section, I introduce the baseline endogenous (directed)
technical change model, which draws on my previous work, Acemoglu
(1998). I start with the case in which there is no international trade
in commodities.

An equilibrium requires that firms choose the profit-maximizing
technology and rent the profit-maximizing amounts of all inputs;
innovators follow the profit-maximizing pricing policy; product,
intermediate good and labour markets clear; and there is no
opportunity for any research firm to enter (or exit) and increase its
profits. Equations (15), (18)-(21) ensure these conditions.

To highlight the forces that shape the skill bias of technology most
clearly, I start with the case in which [mu] = 0, so there is no
intellectual property rights enforcement in the LDCs. Although LDC
technology monopolists copy and sell U.S. technologies, they do not
pay patent fees or royalties to U.S. firms.

I start with the balanced growth path (BGP) along which V = 0.
Imposing this condition, equations (20) and (21) imply that in BGP

Since [mu] = 0, i.e. since there are no intellectual property rights
in the LDCs, we have [pi]^sub l^([lambda]q^sub l^(i)) = [beta](1 -
[beta])[lambda](p^sup U^^sub l^)^sup 1/[beta]^L^sup U^q^sub l^(i) and
[pi]^sub h^([lambda]q^sub h^(i)) = [beta](1 - [beta])[lambda](p^sup
U^^sub h^)1/[beta] H^sup U^ q^sub h^(i). First, note that these
profits are linear in q^sub s^(i), so the BGP condition (22) implies
that research effort devoted to a machine is independent of its
quality, q^sub s^(i). So the same research effort, say z^sub h^, will
be devoted to the discovery of all skill- complementary technologies,
and the same research effort, z^sub l^, will be devoted to the
discovery of all labour-complementary technologies. We therefore only
have to determine two variables, z^sub l^ and z^sub h^. Moreover,
because of the absence of international intellectual property rights,
the profitabilities of new innovations, and therefore of research
effort, depend only U.S. supplies and prices.

Using the free-entry and BGP equilibrium conditions, (21) and (22),
for s = l and h, we obtain

As a result, the direction of technical change is determined by two
factors: (1) The price effect: technologies producing more expensive
goods will be upgraded faster. Because goods using the scarce factor
will command a higher price (see (18) above), this effect implies that
there will be more innovation directed at the scarce factor. (2) The
market size effect: a larger clientele for the technology leads to
more innovation. Since the clientele for a technology is effectively
the workers who use it, the market size efeect encourages innovation
for the more abundant factor. Equilibrium bias in technical change is
determined by these two opposing forces. A greater supply of skilled
workers, via the price effect, induces the development of more
labour-complementary technologies. When there are more skilled
workers, the size of the market for skill-complementary technologies
is also larger, and this encourages further skill-based technical
change.

More formally, for BGP, we need V ^sub s^ = 0, which implies that
Q^sub h^/Q^sub l^ has to remain constant, so z^sub l^ = z^sub h^.
Equation (22) then implies that along the BGP there is a technology
equilibrium condition given by

Q^sub h^/Q^sub l^, the average quality of skill-complementary machines
relative to labour-complementary machines, is the measure of
equilibrium skill bias. Equation (24) implies that equilibrium skill
bias is determined by the relative supply of skills in the U.S., and
the parameter [beta]([epsilon] - 1) captures the strength, and the
sign, of this directed technology effect.14

Because [epsilon] > 1, i.e. because skill- and labour-intensive goods
are relatively close substitutes, of the two influences on the
direction of technical change, the market size effect is more
powerful.15 Since profits to innovation are proportional to market
size, they are proportional to the number of workers using the
technology. Therefore, when H^sup U^/L^sup U^ increases, innovation
and R&D in the skill-intensive sector become more profitable, inducing
Q^sub h^/Q^sub l^ to increase. This provides an attractive explanation
for the patterns shown in Figure 1, whereby the steady increase in the
relative supply of skilled workers in the U.S. over the post-war
period is the underlying cause of the secular increase in the demand
for skilled workers (this increase itself can be a response to the
rise in the skill premium, see Appendix C).

The first important result is that the degree of skill bias, Q^sub
h^/Q^sub l^, is endogenous and depends on the U.S. relative supply of
skills. A larger relative supply translates into a greater skill bias
of technology. Moreover, in the unique BGP there is a monotonie
relationship between the relative supply of skilled workers in the
U.S. and their relative wage. However, because of the endogeneity of
skill bias, this relationship can be either increasing or decreasing.
If technology were exogenous in this economy in the sense that Q^sub
h^/ Q^sub l^ were constant or changing exogenously, the skill premium
would be a decreasing function of H^sup U^/L^sup U^ as in section 2.
Instead, when technology is endogenous, a greater H^sup U^/L^sup U^
encourages more R&D activity towards the skill-complementary
technologies. As a result, the long-run relative demand curve for
skills will be flatter than the constant-technology demand curve, CT,
for example like ET^sub 1^ in Figure 2. Furthermore, if the directed
technology effect, [beta]([epsilon] - 1) from (24), is large enough,
[eta] will be positive, and the long-run relative demand curve for
skills will be upward sloping as ET^sub 2^ in Figure 2. In this case,
the higher supply of skilled workers in the U.S. may lead to higher
returns to skills, in line with the recent developments in the U.S.
labour market.16

FIGURE 3

Cross-country and time-series variation in skill premia when [eta] > 0

Equation (27), on the other hand, shows that the cross-country
relationship between the supply of skills and skill premia will be
decreasing. In particular, a higher H^sup j^/L^sup j^ leads to a lower
skill premium, because among the LDCs, changes in the supply of skills
move a country along the constant technology demand curve for skills,
CT, in Figure 2.

It is also noteworthy that an increase in the U.S. supply of skills,
H^sup U^/L^sup U^, leads to an increase in the skill premium in the
LDCs. Therefore, both the time-series and the cross-country patterns
implied by this model can be summarized in Figure 3.17 All countries
are along a downward sloping relative demand curve, but this relative
demand curve shifts out over time in response to changes in the supply
of skilled workers in the U.S. In particular, when [eta] > 0, these
shifts trace out an upward sloping long-run U.S. relative demand curve
for skills.

Finally, it is useful to observe that with [eta] positive, a possible
explanation for the large increase in the demand for skills during the
1980's is the substantial increase in the supply of skilled workers in
the U.S. during the 1960's and 1970's. As argued in Acemoglu (1998),
this increase in the supply of skills could have caused rapid
skill-biased technical change, raising wage inequality in the U.S. and
in countries using U.S. technology. In the next section, I propose a
complementary mechanism for the increase in wage inequality in both
the U.S. and the LDCs: increased international trade between these
countries.

The next proposition summarizes the transitional dynamics and is
proved in Appendix B.

Proposition 2. If [phi]' ([middot]) < 0, then the system is locally
saddlepath stable. In particular, if Q^sub h^/Q^sub l^ < ((1 -
[gamma])/[gamma])[varepsilon] (H^sup U^/L^sup U^)^sup 1+[eta]^, then
z^sub h^ > z^sub l^, and if Q^sub h^/Q^sub l^ > ((1 - [gamma])/
[gamma])[varepsilon] (H^sup U^/L^sup U^)^sup 1+[eta]^, then z^sub h^ <
z^sub l^.

If [phi]' ([middot]) = 0, then the economy immediately jumps to the BGP.

An implication of this proposition is that, as long as [phi]'
([middot]) < 0, Q^sub h^/Q^sub l^ does not immediately react to an
imperfectly anticipated increase in H^sup U^/L^sup U^: the economy
first moves along a downward sloping relative demand for skills as CT
in Figure 2. This will be followed by a period of rapid skill- biased
technical change with Z^sub h^ > z^sub l^. This is interesting in part
because this pattern might provide an explanation for why the U.S.
skill premium fell during the 1970's in the face of the rapid increase
in the supply of skilled workers, and then increased sharply during
the 1980's.

The above discussion has provided an explanation for the cross-
country and time-series patterns of skill premia over the past 60
years, relying on the notion that [eta] > 0. Is [eta] > 0 empirically
plausible? There are two ways to tackle this question. First, in this
simple setup, [eta] = [eta]([varepsilon] - 1) - 1, soone can
investigate whether for plausible values of [beta] and [varepsilon],
[eta] can be positive. The elasticity of substitution between skilled
and unskilled workers is now [sigma] = 1+ [beta]([varepsilon]- 1) = 2
+ [eta] (from equation (19), [partial differential][omega]^sup
j^/[partial differential](H^sup j^/L^sup j^) |Q^sub h^/Q^sub l^= -
1/(1+[beta]([varepsilon]- 1))). Taking the value of 1[middot]4 for
this elasticity implies [eta] = - 0[middot]6, while a value for the
elasticity greater than 2 implies that [eta] > 0. So for [eta] to be
positive, we need an elasticity of substitution greater than 2, which
is on the higher side of the estimates, but still plausible, and
consistent with a number of studies (e.g. Angrist (1995), Card and
Lemieux (2001)). Moreover, the model here does not feature any
state-dependence in the R&D process-that is, greater Q^sub h^ does not
make future skill- complementary innovations easier relative to
labour-complementary innovations. Acemoglu (2002) shows that when
there is such state- dependence, an upward-sloping relative demand
curve requires an elasticity of substitution less than 2.18

Second, equation (26) gives the long-run relationship between skill
premia and the relative supply of skills as 1n [omega]^sup U^ = [eta]
1n (H^sup U^/L^sup U^). The data shown in Figure 1 can be used to run
a regression of this form. This regression leads to an estimate of
[eta] equal to 0[middot]13 with standard error 0[middot]02, which is
consistent with a positive value for [eta], though of course the skill
premium and the relative supply of skills might have increased
simultaneously, for different reasons over this time period.

3.3. Intellectual property rights in the LDCs

The analysis so far assumed no enforcement of intellectual property
rights in the LDCs. In practice U.S. firms do receive some royalties
and patent fees from companies in the LDCs. I now show that the
qualitative results highlighted above are not affected in this case.
To do this suppose that [mu] > 0, that is, R&D firms in the U.S.
capture some of the revenues generated by machine sales in the LDCs.
Equation (20) still determines the value of innovation, and equation
(21) is the free-entry condition. The only difference is that total
profits now include profits from machine sales in the LDCs. Balanced
growth again requires the same research effort, z, to be allocated to
all types of machines. In particular, in BGP we need

FIGURE 4

The determination of the skill bias of technology with intellectual
property rights enforcement in the LDCs

where, as before, the quality levels of individual machines, ql(i) or
qh(i), cancel out from both sides. Then, we can see that the BGP
requires

Comparative statics follow immediately from this figure. As long as
[epsilon] > 1, an increase in H^sup U^ (or a reduction in L^sup U^)
shifts out of this curve, increases Q^sub h^/Q^sub l^, and causes
skill-biased technical change, exactly as in the case without property
rights. An increase in the degree of intellectual property rights
enforcement, [mu], shifts the curve to the left, and reduces Q^sub
h^/Q^sub l^. The reason for this is clear: the LDCs are more
skill-scarce than the U.S., and a greater enforcement of intellectual
property rights creates a market size effect favouring unskilled
workers. The following proposition, proved in Appendix B, states these
results:

Proposition 3. Consider the case in which there is some degree of
intellectual property rights enforcement in the LDCs, i.e. [mu] > 0.
Then, there exists a unique BGP skill bias Q^sub h^/Q^sub l^ such that
[Delta][Pi](Q^sub h^/Q^sub l^) = 0. An increase in the relative supply
of skills in the U.S., H^sup U^/L^sup U^, increases Q^sub h^/ Q^sub l^
and an increase in [mu] reduces Q^sub h^/Q^sub l^.

Therefore, as in the case without property rights in the LDCs, the
skill bias of technology responds to the market size effect. In
particular, an increase in the number of skilled workers in the U.S.
causes skill-biased technical change. In addition, now an increase in
the number of skilled workers in the LDCs, H^sup j^, also causes
skill-biased technical change. The important implication is that
irrespective of the degree of intellectual property rights enforcement
in the LDCs, the framework here predicts that technology should have
become more skill biased over the past 60 years because the relative
supply of skilled workers has increased substantially both in the U.S.
and in the rest of the world.

The analysis so far has treated the supply of skills as exogenous. The
skill premium in a country is likely to affect the willingness of
individuals to undertake investments in human capital, and this will
have a number of implications for the interpretation of cross-country
and time-series patterns of the post- war period. Appendix C
generalizes this set-up to endogenize the supply of skills. There are
three main implications from this extension. First, with the supply of
skills endogenized, there can be multiple equilibria. Second, the
framework now offers an explanation for the joint behaviour of the
supply of skills and technology for the post-war period: it suggests
that along the transition path, we can have both the supply of skills
increasing and technology becoming more skill biased. Third, the
framework suggests that greater supply of skills in the U.S., through
its effect on technology and skill premia, encourages further
investment in skills in the LDCs.

4. TRADE OPENING AND CHANGES IN SKILL PREMIA

I now consider the impact of an increase in the volume of trade on
patterns of skill premia. To simplify the discussion, I compare the
two extreme cases of no international trade and free international
trade. I also assume that there is no change in the enforcement of
intellectual property rights in the LDCs as a result of trade opening,
so I focus on the case where only international trade patterns change.
From the results reported above, the implications of a greater degree
of intellectual property rights enforcement follow readily. Finally,
it is useful to observe at this point that despite the emphasis on the
case with [eta] > 0 in the previous section, the results in this
section do not depend on the sign of [eta].

4.1. Trade and skill-biased technical change

Suppose that there is free trade in Y^sub h^ and Y^sub t^. This will
affect innovation incentives through its effect on product prices. In
particular, in the presence of free trade, all product prices will be
equalized across countries, rather than being determined by domestic
supplies as in equation (5). The world relative price of
skill-intensive goods will be given by the world relative supply
through an equation similar to (8). More specifically, similar
arguments to before imply that

Therefore, trade increases the skill bias of technology from Q^sub
h^/Q^sub l^ to Q^sub h^/Q^sub l^, that is, trade induces skill- biased
technical change. This result follows from the price effect on the
direction of technical change emphasized above: international trade
increases the relative price of skill-intensive goods, and the higher
relative price of skill-intensive goods encourages further
skill-biased technical change.19

There is an additional and striking implication: trade does not affect
the long-run relative prices of skill-intensive goods in the U.S.
Before trade this relative price was given by p^sup u^ = (H^sup
u^/L^sup U^)^sup -[beta] (from equation (23) above), and now the world
relative price is p = (H^sup u^ / L^sup u^)-[beta] (from equation
(32)). Therefore, because of trade's effect on technical change, the
BGP relative price of skill-intensive goods faced by U.S. consumers
remains unchanged: the induced skill-biased technical change ensures
that the world relative supply of skill-intensive goods increases
sufficiently to reduce the world relative price to the pre-trade U.S.
level.

This result may, at first, appear somewhat paradoxical, since the
reason why technical change becomes more skill-biased is the price
effect-i.e. the fact that trade increases the relative price of
skill-intensive goods in the U.S. But it is quite intuitive, and
simply reflects the strength of the directed technology effect. To see
the intuition, note that the relative price of skill-intensive goods
plays two roles in this model. The first is to clear the market for
goods (i.e. equation (11)), and the second is to ensure equilibrium in
the technology market (i.e. equation (23)). Since the technology
equilibrium condition relates the relative price of skill- intensive
goods to the relative supplies in the U.S. market, which do not
change, the long-run equilibrium price of skill-intensive goods cannot
change either. So there has to be a sufficient amount of skill-biased
technical change to increase the supply of skill- intensive goods to
achieve the same relative price after trade opening. We will see below
that with transitional dynamics, the relative price of skill-intensive
goods in the U.S. first increases and then returns to its pre-trade
level.

Next, recall that the skill premium is still given by equation (17),
and Q ^sup j^^sub h^/Q ^sup j^^sub h^ is the same in all countries.
Also, international trade implies that the relative price of
skill-intensive goods is the same in all countries. Therefore, skill
premia in all countries are now equalized. Notice, however, that this
observation does not guarantee factor price equalization, since U.S.
technologies are typically less productive when used in the LDCs (i.e.
[theta]^sup j^< or = 1), making U.S. workers earn higher wages than
LDC workers. To calculate the post-trade world skill premium, [omega]
, I use equation (17) together with (31) and (33)

Clearly this is satisfied for j = U, since H^sup w^/L^sup w^ < H^sup
u^/L^sup u^, reiterating that [omega] > [omega]^sup u^. More
importantly, LDCs for which condition (37) holds will experience an
incr\ease in inequality, while the rest will experience a decline.
Condition (37) is more likely to be satisfied for LDCs that are
relatively skill-abundant, while LDCs that are most skill-scarce
should experience a decline in inequality as in the standard trade
models. This implication is consistent with the evidence discussed in
footnote 6 that, over the 1980's, wage inequality increased in a
number of LDCs, while declining in others. It can also be empirically
investigated in more detail using microdata from LDCs, and relating
wage inequality changes to trade opening and relative supply of
skills.

It is also straightforward to characterize the transitional dynamics
of the world economy. Suppose the opening to trade is unanticipated.
Then immediately after trade opening, Q^sub h^/Q^sub l^ is less than
its BGP level, so we will have z^sub h^ > z^sub l^, and the skill bias
of technology will gradually increase. Over this process, as shown in
Figure 5, the world skill premium, [omega] increases and the world
relative price of skill-intensive goods, p , falls. We thus have (the
proof is in the Appendix):

Proposition 4. Assume that [mu] = 0 and [straight phi] '([middot]) <
0. Suppose that the world economy opens to international trade, and
this change is unanticipated. After trade opening we have z^sub h^ gt;
z^sub l^. The BGP value of z^sub h^ = z^sub l^ = z is given by (25),
and hence the growth rate of the world economy is unchanged, ([lambda]
- 1)z[straight phi](z) with z given by (25). The skill bias of
technology increases from Q^sub h^/ Q^sub l^ given by (24) to Q ^sub
h^/ Q ^sub l^ given by (33). The skill premium in the U.S. immediately
increases from [omega]^sub u^ as given by (26) to [omega] as given by
(36), and then gradually rises to [omega] > [omega]^sub u^ as given by
(35).

FIGURE 5

Dynamics of the U.S. relative price of skill-intensive goods, U.S.
skill premium and equilibrium skill bias after trade opening

The skill premium in country j > 0 is higher in BGP if (37) is
satisfied, and lower otherwise. The relative price of skill- intensive
goods in the U.S. immediately increases from p^sup u^ = (H^sup u^
/L^sup u^)^sup -[beta]^ to p as given by (31) evaluated with Q^sub
h^/Q^sub l^ given by (24). This world relative price of
skill-intensive goods then declines asymptotically to its BGP value p
= p^sup u^ = (H^sup u^ /L^sup u^)-[beta].

If instead [straight phi]'([middot]) = 0, then the economy immediately
jumps to the new BGP after trade opening, and there is no change in
the relative price of skill-intensive goods in the U.S.

Overall, there are a number of conclusions significantly different
from the standard trade models. First, endogenous (directed) technical
change implies that trade with the LDCs induces skill-biased technical
change. The impact of trade on the U.S. labour market may therefore be
much larger than predicted by standard trade models. Second, because
trade induces skill-biased technical change, the productivity of
skilled workers increases. Third, there is a force counteracting the
decline in inequality in the LDCs implied by trade: these economies
use U.S. technologies, which are becoming more skill-biased.

Finally, trade first increases the relative price of skill- intensive
goods in the U.S., but then eventually this relative price returns to
its pre-trade U.S. level. This result is important because changes in
relative prices are the usual intervening mechanism in trade models.
So in evaluating the impact of trade on labour markets, previous work
has looked for evidence of an increase in the relative prices of
skill-intensive goods (e.g. Lawrence and Slaughter, 1993). In this
model, however, induced skill-biased technical change in the U.S.
implies that trade may increase the price of skill-intensive goods by
only a limited amount, or not at all, but may still have a major
effect on the U.S. labour market. The inconclusive or paradoxical
evidence reported in these papers on the behaviour of the relative
prices of skill-intensive goods does not imply that trade is not a
major driving force of the recent rise in inequality.

How large is the effect of trade opening on the skill premium for
plausible parameter values? To answer this question, consider the
estimate by Borjas et al. (1997) of ln(H^sup w^/L^sup w^) ln(H^sup
u^/L^sup u^) [approximate] 0-04 between 1980 and 1995 used in Section
2. Now equations (26) and (35) imply that In [omega] -In [omega]^sup
u^ = -[ln(H^sup w^/L^sup w^) - ln(H^sup u^/L^sup u^)], so we expect
trade opening to increase the skill premium by approximately 4%
between 1980 and 1995, which accounts for 20% of the actual increase
(4/20 [asymptotically =] 20%), or makes trade twice as important as in
models with exogenous technology. Given that some of the increase
between 1980 and 1995 is likely to have been due to the slowdown in
the supply of college graduates during the 1980's, this analysis
implies that international trade could be an important component of
the explanation for the increase in U.S. wage inequality.

4.2. Intellectual property rights enforcement in the LDCs

The previous subsection discussed the effect of international trade in
a world without intellectual property rights enforcement in the LDCs.
The next proposition generalizes this result to the case in which
there is intellectual property rights enforcement, and is proved in
the Appendix B:

Proposition 5. Suppose that the world economy opens to international
trade, and this change is unanticipated. Suppose moreover that [mu] >
0 and [straight phi]([middot]) < 0.

(1) There exists [mu]* > 0, such that if [mu] < [mu]*, then after
trade opening we have Z^sub h^ > Z^sub l^. The skill bias of
technology, Q^sub h^/Q^sub l^, unambiguously increases. The skill
premium in the U.S. immediately jumps up after trade opening, then
gradually increases further. The relative price of skill-intensive
goods in the U.S. immediately increases, and then gradually declines.

(2) Suppose also that [eta] < 0, than the above results hold for all [mu].

Therefore, most of the results are similar to those in Proposition
4.20 But now international trade might affect the world growth rate,
and the implications for the post-trade relative price of
skill-intensive goods in the U.S. is ambiguous-that is, we could have
p less than or greater than p^sup u^.

5. CONCLUDING REMARKS AND FUTURE DIRECTIONS

This paper has constructed a simple model to analyse the patterns of
skill premia we observe across countries and over time. Skill premia
are determined by the relative supply of skills, the degree of skill
bias in technology, and international trade. The major innovation of
this framework is that skill bias of technology is endogenous,
determined by the relative profitability of developing different types
of technologies. An increase in the number of skilled workers expands
the market size for skill-complementary technologies, and induces
skill-biased technical change. This increase in the demand for skills
implies that the long-run relative demand for skills can be upward
sloping: skill premia may increase in response to a rise in the supply
of skilled workers. The relationship between the relative supplies and
skill premia across countries is quite different in nature, however:
among countries with access to the same technology frontier, there
will be a negative relationship between the relative supply of skills
and the skill premium.

The most important results of the paper concern the effect of
increased international trade on the U.S. labour market. I show that
trade opening will cause skill-biased technical change in the U.S. In
contrast with the standard models, this induced technology effect also
implies that trade opening may increase skill premia in the LDCs,
increase the demand for skills more significantly and more broadly
than predicted by the standard calculations, and could have these
implications without affecting the long-run relative price of
skill-intensive goods.

One of the advantages of the framework presented here is its relative
simplicity, enabling a number of extensions, with a variety of
empirical implications. I conclude the paper with a brief discussion
of some of these extensions.

5.1. Trade and labour-biased technical change in Europe

The analysis so far focused on a model in which there is one
technological leader, the U.S. In reality, not only the U.S., but also
a number of other advanced economies, such as European countries,
develop frontier technologies. A natural conjecture may be that
increased trade with the LDCs will also cause skill-biased technical
change in Europe. However, in contrast to the U.S. experience, there
has been little increase in inequality in continental Europe, and
although the demand for skills has certainly increased in Europe over
the past several decades, this increase appears to be somewhat less
than in the U.S. (see Berman et al, 1998). The framework presented
here enables an analysis of this issue with some speculative and
surprising results that can be empirically investigated in future
work.

Suppose that "Europe" is relatively technologically advanced, in
particular q^sup u^^sub s^(i) > q^sup E^sub s^(i) >[theta] Q^sup
u^^sub s^ (i) for s = l, h and all i, where E denotes Europe. This
implies that European firms will prefer to use technologies designed
for their own needs rather than the U.S. ones, and there will be R&D
in Europe, improving European technologies. Since the U.S. is more
advanced than Europe, the LDCs continue to use U.S. technologies. Also
assume that H^sup u^ /L^sup u^ > H^sup E^ /L^sup E^ > H^sup j^/ L^sup
J^ or all j = 1,..., J.21 Finally, to simplify the analysis I assume
that Europe is small relative to the rest of the world economy.

The equations that describe technology choice in the U.S., in
particular the equivalent of (24), now hold for Europe, so Q^sup
E^^sub h^/Q^sup E^^sub h^ = ((1- [gamma])/ [\gamma])[varepsilon](H^sup
E^/L^sup E^)[beta]([varepsilon]-1). Differences in the relative supply
of skills between the U.S. and Europe will imply different degrees of
equilibrium skill bias in the two economies. In particular, since
H^sup u^/L^sup u^ > H^sup E^/ L^sup E^, the U.S. will develop more
skill-biased technologies than Europe. Also similarly, the skill
premium in Europe will be [omega]^sup E^ = ((1 -
[gamma])/[gamma])[varepsilon](H^sup E^/L^sup E^)[eta], where recall
that [eta] = [beta]([varepsilon] - 1) - 1. If the induced technology
effect is strong enough, that is, if [eta] is positive, the U.S. may
have higher returns to skills despite its greater supply of skills.22
This contrasts with the negative relationship between the supply of
skills and skill premia among the set of countries with access to the
same technology frontier (cf. Proposition 1). This result reflects the
fact that differences in the relative supply of skills between the
U.S. and Europe translate into differences in the technology frontiers
of these economies.

Now suppose the world economy opens to trade, and hypothetically hold
technologies fixed. Before trade, we have p^sup u^ < p^sup E^ < p^sup
j^ for j [not =] U, E, so the relative price of skill- intensive goods
is highest in the LDCs, next in Europe, and then in the U.S. Trade
would lead to a new, common, relative price p^sup t^.23 It is clear
that p^sup j^ > p^sup j^ > p^sup u^, so the relative price of
skill-intensive goods would increase in the U.S. and would fall in the
LDCs. The effect on Europe is ambiguous. It depends on the relative
sizes of the U.S. and the LDCs, and the distance between Europe and
these other countries. Let me assume that p^sup t^ > p^sup E^, which
is the reasonable case in practice. Therefore, in the absence of an
induced change in technology, the impact of trade would be to increase
the demand for skills in Europe.

Now consider trade opening in the world economy with endogenous
technology. We know from Section 4 that the long-run equilibrium
relative price of skill-intensive goods, denoted by p , will have to
adjust to satisfy the technology equilibrium condition (23) in the
U.S. (this follows from the fact that LDCs still use U.S. technologies
and Europe is relatively small). This implies that the technology
equilibrium condition in Europe, which would have required p = (H^sup
E^/L^sup E^)^sup-[beta], will not be satisfied. In fact, we have

p = p^sup u^ = (H^sup u^/L^sup u^)^sup -[beta]^ < (H^sup E^/ L^sup
E^)^sup -[beta]^ = p^sup E^.

In other words, given the number of skilled workers in Europe, the
world relative price of skillintensive goods is too low for skilled
innovations to be profitable there. European firms will therefore
develop only labour-complementary technologies, and European
skill-complementary technologies will stagnate. As a result, trade
will induce labour-biased technical change in Europe, while causing
skill-biased technical change in the U.S.24 As U.S.
skill-complementary technologies advance, it will eventually be
profitable for European firms to begin using U.S. technologies in the
skill-intensive sector, and skill-biased technical change will
progress at the same rate in the two economies.

Therefore, this analysis provides an alternative explanation for why
inequality did not increase in Europe. Implications of this analysis
are testable with detailed product price data from Europe and the U.S.
According to this approach, skill-intensive good prices should fall in
Europe after trade opening, while they increase and then fall (or not
change much) in the U.S. Interestingly, this is consistent with the
results reported in Desjounqueres et al. (1999), which show a small
increase in the relative price of skill- intensive goods in the U.S.
and a decline in a number of European countries between 1974 and 1989.

5.2. Trade and technology adoption

The framework here predicts that opening to trade with the U.S. can
increase skill premia and wage inequality in the LDCs. This follows
from the effect of trade with the LDCs on U.S. product prices. If
different LDCs were to open to U.S. trade at different times, the
prediction of the framework would be more similar to the standard
trade theory: to the extent that each individual LDC is small, its
addition to the world trade system has a negligible effect on product
prices in the U.S., and therefore a negligible effect on technology.
So when an LDC opens for trade, holding trading patterns of other LDCs
as given, it should experience a decline in wage inequality.25 The
available evidence, discussed for example in footnote 6, suggests that
trade opening does not lead to a decline in inequality, though this
may result from other market reforms taking place concurrently.

An interesting implication of this expression is that now each
country's relative supply of skills will affect its own technology,
and countries with greater supply of skills will adopt more
skillbiased technologies and may have greater skill premia-as in the
U.S.-Europe comparison in Section 5.1. But in addition, as in the
basic model of Section 3, the U.S. skill bias will also affect LDC
technology choices.

This model might shed some light on the patterns of diffusion of
skill-biased technology. For example, Berman and Machin (2000) show
that there has been rapid skill-upgrading in many middle income
countries, but there is much less evidence of rapid skill-upgrading in
the poorest economies. This may reflect differences in these
countries' choices of whether to adopt the new skill-biased
technologies developed in the U.S., which are in turn determined by
the relative supply of skilled workers in these countries. More
generally, a more detailed theoretical and empirical analysis of the
interaction between technical change in the U.S. and technology
adoption in LDCs, and its implications for the distribution of wages,
appears to be a fruitful area for future research.

Review of Economic Studies (2003) 70, 199-230

(C) 2003 The Review of Economic Studies Limited

0034-6527/03/00080199$02.00

1. Throughout I use the term skill-biased technical change to mean any
change in technology that increases the aggregate demand for skills.
Accordingly, an increase in the overall productivity of a sector that
uses skilled workers more intensively may correspond to skill-biased
technical change depending on the elasticities of substitution.

2. See, for example, Katz and Murphy (1992), Berman, Bound and
Griliches (1994), Krugman (1995) and Borjas, Freeman and Katz (1997),
but also the critique by Learner (1994, 1996).

3. Haskel and Slaughter (1999) investigate whether trade led to faster
technological progress and affected the wage structure through this
channel in the U.K. More recent works by Epifani and Ganica (2002) and
Thoenig and Verdier (2002) provide additional mechanisms for
international trade to affect the skill bias of world technology,
while Xu (2001) extends the analysis in my paper to an economy where
both sectors employ both factors. Zeira (2001) also discusses the
implications of trade and technology on inequality in a unified
framework, but does not model the impact of trade on technology.

4. Xu (2001) generalizes the results in this paper to the case where
both goods employ both factors. His results are relevant for the
debate on whether the sector or factor bias of technical change
matters more for wage inequality in an open economy, see for example
Haskel and Slaughter (1998).

5. Equation (7) may imply a negative skill premium, i.e. [omega]^sup
j^ < 1, in which case skilled workers would prefer to work as
unskilled workers (and perhaps be more productive at these tasks than
unskilled workers themselves, receiving a positive skill premium).
Throughout the paper, I assume that H^sup j^ / L^sup j^ is such that
the skill premium is always positive (see footnote 16).

6. Hanson and Harrison (1994) show that the skilled-unskilled wage gap
in Mexico increased during the 1980's despite substantial trade
opening. Duryea and Szekely (2000) and Behrman, Birdsall and Szekely
(2001) find that between the early 1980's and mid-1990's, wage
inequality increased in Brazil, Mexico, Venezuela, Argentina and
Bolivia, and remained approximately constant in Chile and Costa Rica,
despite substantial global trade opening during this time period.
Robbins (1995) finds a sharp increase in the relative demand for
skills in Argentina, Chile, Costa Rica, Mexico, the Philippines,
Taiwan and Uruguay while these economics were opening to trade.
Desjounqueres el al. (1999) report increasing wage differentials
between nonproduction and production workers in Chile and Pakistan, no
change in India and Brazil, and a decline in Colombia, but an increase
in the demand for skills in all the cases. Davis (1992) reports
declining wage inequality in South Korea, Venezuela and Colombia, and
a slight increase in Brazil during the 1980's.

7. More generally, this factor-content approach is correct when
countries are in a diversified equilibrium both before and after trade
opening, see Dearoff and Staiger (1988).

8. Using a different methodology Krugman (1995) calculates the same
number to be 3[middot]7%.

9. There are many possible reasons for this inappropriateness of
technology. Countries require crops suitable for their own climate,
vaccines that deal with the prevalent diseases in their region, and
technologies that exploit their existing know-how. So technologies
developed in the U.S. may be partly "inappropriate" to different
environments, and hence less productive when used in other countries.
Atkinson and Stiglitz (1969), Stewart (1977), Basu and Weil (1998) and
Acemoglu and Zilibotti (2001) emphasize the importance of
"appropriateness" of technologies in the context of economic
development.

10. This might imply that the x's here may better correspond to
intermediate goods rather than machines. This is without any
subst\antive implications. Moreover, it is straightforward to
introduce slow depreciation of machines, which complicates the
expressions, but does not affect any of the results.

11. Throughout LDC firms are not allowed to re-export to the U.S.
market, so [mu] does not affect domestic revenues for U.S. R&D firms.

12. Because of the copying cost, [xi], only one firm will copy each
U.S. technology. If more than one firm did so, they would compete a la
Bertrand, and would make negative profits. If [xi] = 0, then there
would be zero profits from machine sales in the LDCs, and the results
would be identical to the case with [mu] = 0 here.

14. Q^sub h^/Q^sub l^ is a measure of skill-complementary technologies
relative to labour-complementary technologies. The fact that Q^sub
h^/Q^sub l^ also corresponds to the "skill bias" of technology is a
consequence of the elasticity of substitution, [epsilon], being
greater than 1. See Acemoglu (2002).

15. See Acemoglu (2002) for the analysis of the case in which
[epsilon] < 1. Even in this case, a greater relative supply of skills
causes skill-biased technical change.

16. Notice that to ensure a positive skill premium in equations (26)
and (27), we need ((1 - [gamma])/[gamma])^sup -[epsilon]^ > (H^sup
U^/L^sup U^)^sup [eta]^.

17. The working paper version, Acemoglu (1999b), presented evidence
consistent with a negative relationship between skill premia and the
supply of skills across a set of countries using data from Barro and
Lee (1993) and Psacharopoulos (1994).

19. Because the degree of enforcement of property rights has not
changed, the market sizes for different types of technologies remain
the same as before trade.

20. Very different results would be obtained, however, if property
rights were not enforced in LDCs before trade, and trade led to the
full enforcement of these rights. In this case, the impact of trade
(and the change in property rights enforcement regime) on the U.S.
skill premium would be given by considering an increase in H/L in
equation (24) in Section 3.

21. Nickell and Bell (1996) argue that U.S. high school graduates are
less skilled, so one might be tempted to think that supply of skills
is not necessarily greater in the U.S. However, Devroye and Freeman
(2000) show that there is no support for this presumption when
comparing native born Americans with Europeans. all internationally
comparable statistics, in turn, suggest that the fraction of workers
with high education is greater in the U.S.

22. In practice, inequality and returns to schooling seem to be higher
in the U.S. than in Europe, despite the greater supply of skills in
the U.S. For example, in 1984, the log difference of the 90-th and
10-th deciles of the hourly wage distribution was 1-40 in the U.S.,
1-16 in Britain, 1-23 in France, 1-01 in the Netherlands, 0-88 in
Germany, 1-01 in Sweden and 1-04 in Japan (Freeman and Katz, 1995,
Table 2). In the context of this framework, this pattern arises
because the skill-abundant U.S. develops more skill-biased
technologies than European countries.

The standard explanation for this pattern is institutional wage
compression in Europe. The purpose of the exercise here is not to deny
the importance of wage compression in Europe, but to offer a
complementary explanation.

23. I am using p^sup t^ to distinguish this fixed technology case from
the case where technology adjusts, p .

24. This result depends on the assumption that the U.S., Europe, and
the LDCs all start trading with each other. It is of course possible
that the world was characterized by free trade between the U.S. and
Europe in the 1960's, and the big change was opening of trade between
these countries and the LDCs. In that case, trade will cause
skill-biased technical change in both the U.S. and Europe. However,
the data suggest that trade between the U.S. and Europe grew at least
as fast as trade between the U.S. and the LDCs (see, for example,
World Bank, 1997).

Moreover, the results outlined here with goods produced by different
countries as perfect substitutes, may appear somewhat extreme. The
working paper version, Acemoglu (1999b) shows that the same results
hold when different countries produce goods that are imperfectly
substitutable.

25. In other words, this model suggests that the empirical
relationship between the skill premium or inequality in country j and
trade opening should be

[omega]^sup j^ = a [middot] measure of trade opening in j + b [middot]
measure of trade opening in the U.S., with a < 0 and b > 0.

26. Freeman and Oostendorp (2000) and Behrman et al. (2001) find no
change in inequality when an LDC opens up to trade, but a general
increase in inequality in the LDCs over this period of global trade
opening.

27. This is only an approximation because it does not take into
account the agents who have chosen to acquire skills, and are in the
process of doing so. As [upsilon] [arrow right] 0, this expression
becomes exact.

REFERENCES

ACEMOGLU, D. (1998), "Why Do New Technologies Complement Skills?
Directed Technical Change and Wage Inequality", Quarterly Journal of
Economics, CXIII, 1055-1090.

ACEMOGLU, D. (1999a), "Changes in Unemployment and Wage Inequality: An
Alternative Theory and Some Evidence", American Economic Review, 89,
1259-1278.

ACEMOGLU, D. (1999b), "Patterns of Skill Premia" (NBER Working Paper No. 7018).

ACEMOGLU, D. (2002), "Directed Technical Change", Review of Economic
Studies, 69, 781-810.

ACEMOGLU, D. and ZILIBOTTI, F.