Full text of DOI:10.1162/003355300554827

ABILITY-BIASED TECHNOLOGICAL TRANSITION, WAGE
INEQUALITY, AND ECONOMIC GROWTH*
ODED GALOR AND OMER MOAV
This paper develops a growth model characterized by ability-biased technologi-
cal transition in which the evolution of technology, education attainment, and
wage inequality is consistent with the observed pattern in the United States and
other advanced countries over the past several decades. It argues that an increase
in the rate of technological progress raises the return to ability and simultaneously
generates an increase in wage inequality between and within groups of skilled and
unskilled workers, an increase in average wages of skilled workers, a temporary
decline in average wages of unskilled workers, an increase in education, and a
productivity transitory slowdown.
I. INTRODUCTION
In the last two decades the United States, and other advanced
countries, has experienced rapid technological progress along
with fundamental changes in the pattern of wage inequality. The
wage differential between skilled and unskilled labor has risen
significantly despite the increase in the supply of skilled labor, the
wage dispersion within the groups of skilled and unskilled labor
has widened, and real wages of unskilled labor have declined.1
The phenomenon of rapid technological change along with a rise
in the skill premium, despite an increase in the supply of skilled
labor, has recurred in several time intervals in the last century.
* We are especially grateful to Lawrence Katz whose numerous insightful
suggestions significantly improved the paper. We also wish to thank two anony-
mous referees, Daron Acemoglu, Alberto Alesina, Costas Azariadis, Susanto Basu,
Roland Be´nabou, Herschel Grossman, Boyan J ovanovic, Fabrizio Zilibotti, and
seminar participants at the NBER Summer Institute, 1997, ‘‘Technology and
Employment,’’ Universitat Pompeu Fabra, 1997; ‘‘Technology, Human Capital and
Growth,’’ Hebrew University, 1999; and Universitat Autonoma de Barcelona for
their useful comments and suggestion. Galor ’s research is supported by the
National Science Foundation Grant SBR-9709941 and by the Israel Science
Foundation.
1. Katz and Murphy [1992] document this pattern of inequality in the United
States, and Berman, Bound, and Machin [1998] document this pattern of
inequality in the OECD. As to the change in the pace of technological progress,
Autor, Katz, and Krueger [1998] show that the pace of relative demand shifts
favoring more skilled workers is faster from 1970 to 1996 than from 1940 to 1970.
They provide evidence that this reflects an increase in the rate of skill-biased
technological change, although their study cannot separate whether this arises
from an increase in the overall rate of technological change or from a shift in the
direction of technological change.
2000 by the President and Fellows of Harvard College and the Massachusetts Institute of
Technology.
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The Quarterly J ournal of Economics, May 2000
469

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Over the period as a whole, however, wage inequality has evolved
in a cyclical fashion.2
This paper develops a growth model, characterized by ability-
biased technological transition, which accounts for the fundamen-
tal elements that have characterized the evolution of technology,
education, and wage inequality in the United States and other
advanced countries over the past several decades. The study
argues that an increase in the rate of technological change raises
the return to ability and generates simultaneously: a rise in the
wage inequality between and within groups of skilled and un-
skilled workers, an increase in the average wage of skilled
workers, a temporary decline in the average wage of unskilled
workers, an increase in education attainment, and a potential
coexistence of rising rates of technological progress and a transi-
tory productivity slowdown that may have been observed in
earlier parts of recent decades.
Earlier theoretical attempts to explain the recent empirical
regularities have focused on the role of skill-biased technological
change and globalization of markets in the increase of the wage
differential between skilled and unskilled workers. These theo-
ries, however, have treated the groups of skilled and unskilled
labor largely as homogeneous labor inputs and have therefore
failed to account for the contemporary phenomenon of widening
wage inequality within these groups.
The contemporaneous phenomena of persistent increase in
the relative wages of skilled workers and the rise in the wage
dispersion within the groups of skilled and unskilled workers,
suggest that the heterogeneity of ability is central for the analysis
of these empirical regularities. Furthermore, the coexistence of
rapid technological change and the observed pattern of wage
inequality suggests that the nature of the interaction between
technological progress and the relative return to ability may
provide the resolution for the puzzle as a whole. If rapid technologi-
cal progress raises the relative return to ability, then wage
inequality may rise within as well as across groups, provided that
the average level of ability is higher among skilled individuals. In
contrast, if technological progress would increase the return to
education without affecting the return to ability, individuals with
2. Goldin and Katz [1999] and Autor, Katz, and Krueger [1998] show that
wage inequality between groups declined in the United States from the 1900s until
the 1940s, as well as in the 1970s, and increased in the 1950s, 1960s, 1980s, and
1990s. In the 1970s, however, overall wage inequality expanded.

ABILITY-BIASED TECHNOLOGICAL TRANSITION
471
a lower level of ability would find it beneficial to acquire educa-
tion, and the ability dispersion would widen among educated
individuals and would narrow among the uneducated. The wage
inequality among the educated would therefore rise, but counter-
factually, wage inequality among the uneducated would decline.
The conjecture regarding the centrality of the positive interac-
tion between technological change and the return to ability for the
understanding of the observed pattern of wage inequality is
largely consistent with empirical evidence. Bartel and Sicherman
[1999] find that the education premium associated with technologi-
cal change is the result of an increase in demand for the innate
ability or other unobservable characteristics of more-educated
workers in the United States over the period 1979–1993. Mur-
nane, Willett, and Levy [1995] argue that during the 1980s the
return to cognitive skills had risen. Finally, Katz and Murphy
[1992] and J uhn, Murphy, and Pierce [1993] provide evidence
regarding the changing role of observed and unobserved compo-
nents of skills in the determination of earnings in the United
States in the past three decades. Their studies suggest that the
premium to unobserved components of skills has increased steadily
since 1970, and it preceded the increase in the return to education
since 1980.
The relationship between technology and inequality has been
the subject of intensive research in the last few years.3 Galor and
Tsiddon [1997], Greenwood and Yorukoglu [1997], and Caselli
[1999] argue that the increase in the wage inequality between
skilled and unskilled labor reflects the positive effect of technologi-
cal revolution on the demand for skilled individuals and thus on
the return to skilled labor. Further, Acemoglu [1998] suggests that
an exogenous increase in the supply of educated individuals in the
1970s induced the development of a skill-biased production
technology which has increased wage inequality. These papers do
not focus, however, on the contemporary phenomenon of an
increase in the wage inequality within groups.4
3. Other recent explanations for the pattern of wage inequality that are not
based on technological change include Acemoglu [1999]. In a search model in which
the composition of jobs changes endogenously and causes reallocation of capital
from unskilled to skilled workers, unemployment and between and within group
inequality rises and wages of the unskilled fall.
4. Galor and Tsiddon [1997] implicitly capture some of the patterns of within
group inequality. Caselli [1999] informally suggests a mechanism that may
account for some of the recent patterns of within-group inequality. Acemoglu
[1998] extends his basic model and argues that in the absence of perfect mapping
between education and skills, inequality within education groups increases as

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This paper, in contrast, develops a growth model with en-
dogenous determination of both technological change and the composi-
tion of the labor force in which ability-biased technological transition
generates patterns of wage inequality that are consistent with those
observed in the United States and other advanced countries over the
past several decades. The evolution of the economy and its impact on
wage inequality is based upon three central elements that appear
consistent with empirical evidence. First, an increase in the rate of
technological progress raises the rate of return to skills.5 Second, the
increase in the return to skills induces an increase in the supply of
educated individuals.6 Third, an increase in the level of human capital
increases the rate of technological progress.7 These three elements
generate a dynamic path characterized by a positive feedback loop
that permits a monotonic evolution of the rate of technological
progress in a transition to a steady-state equilibrium with perpetual
growth. The increase in the return to ability and education that
stem from the increase in the rate of technological progress brings
about a monotonic rise in wage inequality within as well as
between groups along the transition to a steady-state equilibrium.
The supposition that the state of transition brought about by
technological change positively affects the rate of return to ability
is at the heart of the model.8 Although the new technological level
may reflect in the long run either a skill-biased or skill-saving
technological change, it is argued that the transition to the new
technological state is mostly skill (ability)-biased in the short
run.9 In particular, it is assumed that the level of technology has
well. In contrast, Aghion, Howitt, and Violante [1999] focus on within-group
inequality rather than on between-group inequality. Moreover, an additional
aspect of the recent patterns of inequality, i.e., the decline in the wages of unskilled
workers, is captured only by Caselli [1999].
5. Goldin and Katz [1998] find evidence for technology-skill complementarity
throughout the twentieth century. See Foster and Rosenzweig [1996] for evidence
from the Green Revolution in India.
6. See Freeman [1975], Mincer [1994], and Kane [1994].
7. This link is commonly used in growth theory. It was first proposed by
Nelson and Phelps [1966]. It is supported by empirical evidence (e.g., Doms,
Dunne, and Troske [1997]).
8. This argument is raised in the seminal papers by Nelson and Phelps [1966]
and Schultz [1975]. See the recent paper by Rubinstein and Tsiddon [1999] as well.
9. If technological changes are skill-biased in the long run, then the effect will
be enhanced, while if technology is skill-saving, then the effect will be diluted. In
the current paper technological transition is ability-(skill)-biased only in the short
run, but it may be either skill-biased or unskill-biased in the long run. This
mechanism is related to that explored by Acemoglu [1998], where an increase in
the supply of skilled workers causes technologies to be more skill-biased in the long
run. Goldin and Katz [1998] provide evidence regarding technology-skill comple-

ABILITY-BIASED TECHNOLOGICAL TRANSITION
473
no effect on the relative demand for skilled workers, whereas a
faster rate of technological progress raises the relative demand for
skilled labor.
Individuals’ levels of human capital are determined by their
ability and education, as well as by the technological environ-
ment. Technological progress is assumed to reduce the adaptabil-
ity of existing human capital for the new technological environ-
ment. Able individuals, however, have a comparative advantage
in adapting to the new technology (i.e., their learning cost is
smaller). Individuals are subjected to two opposing effects due to
technological progress. On the one hand, the level of human
capital of each individual is diminished due to the transition from
the existing technological state to a superior one—the ‘‘erosion
effect.’’ On the other hand, each individual operates with a
superior level of technology—the ‘‘productivity effect.’’ Further, an
increase in the rate of technological progress raises the return to
skilled labor decreases the threshold level of ability above which
individuals would choose to become skilled workers. It increases
the number of skilled workers, decreases the number of unskilled
workers, and decreases the average ability in both groups. Hence
in addition to the ‘‘erosion effect’’ and the ‘‘productivity effect,’’
technological progress has a ‘‘composition effect.’’
A sufficiently large increase in the rate of technological
progress generates, due to the erosion effect, a slowdown in the
growth rate in Total Factor Productivity (TFP) in the short run.
However, once the rate of technological progress reaches a steady
state, the erosion effect is constant, whereas the productivity
effect grows at a higher constant rate.
The predictions of the basic model are consistent with the
evolution of wage inequality and the number of college graduates
in the United States economy over the past several decades. The
economy converges to a steady-state equilibrium with a positive
growth rate of output per worker supported by a positive en-
dogenous rate of technological progress. In the transition to the
steady state, the rate of technological progress increases monotoni-
cally, wage inequality within and between groups increases, the
average wage of skilled workers increases despite the increase in
their number, and the average wage of unskilled workers may
decline, despite the decline in their relative supply. The rise in the
mentarity which is consistent with our short-run view of the skill-bias of
technological change as well as the long-run view.

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wage dispersion within a group and the rise in wages of skilled
workers follows from the rise in the return to ability. The former
due to the heterogeneity in ability within a group, and the latter
due to the fact that in equilibrium the average level of ability is
higher among skilled workers. Further, consistent with the slow-
down in the growth of wage inequality in the United States in the
1990s [Autor, Katz, and Krueger 1998], as the economy converges
to the steady-state equilibrium, the rise in the rate of technologi-
cal progress diminishes, and the increase in the wage inequality
subsides.
The introduction of institutional changes into the basic model
permits the analysis to be consistent with those episodes in which
a decline in wage inequality was associated with an increase in
the fraction of skilled individuals in the labor force. In the
presence of capital markets imperfections, investment in human
capital is suboptimal. If economic development is associated with
institutional changes which reduce the effectiveness of imperfec-
tions in capital markets (e.g., the high school movement of 1910 to
1940 in the United States and the expansion in financial aid to
higher education in the United States from the 1960s to the early
1970s), they may generate a decrease in wage inequality between
groups along with an increase in education attainment. In particu-
lar, if the decline in the degree of credit market imperfections is
sufficiently large, the increase in the supply of skilled workers
would dominate the demand effect induced by the increase in the
rate of technological change, and wage inequality between skilled
and unskilled workers would decrease.
A cyclical evolution of the wage inequality between skilled
and unskilled labor, despite the monotonic increase in the supply
of skilled labor, would emerge from the effect of growth on
institutional changes.10 The pattern of increased wage inequality
due to the acceleration in the rate of technological progress would
be interrupted occasionally due to the feedback from growth to
capital markets that would increase the supply of skilled workers
and temporarily decrease wage inequality between skilled and
unskilled labor. This dynamic process would repeat itself and,
consistent with empirical evidence, would generate cyclicality in
10. Galor and Tsiddon [1997], in contrast, argue that the cyclical evolution of
the wage differential between skilled and unskilled workers is due to the cyclical
nature of technological progress (i.e., inventions followed by innovations). An
alternative mechanism is explored by Eicher [1996].

ABILITY-BIASED TECHNOLOGICAL TRANSITION
475
the wage differential between skilled and unskilled labor along
with a monotonic increase in the number of skilled workers.
II. THE BASIC STRUCTURE OF THE MODEL
Consider a small, open, overlapping-generations economy
that operates in a perfectly competitive world where international
capital movements are unrestricted and economic activity extends
over infinite discrete time. In every period the economy produces a
single homogeneous good that can be used for either consumption
or investment.11 The good is produced by physical capital and a
composite labor input (measured in efficiency units) that consists
of skilled labor and unskilled labor. The supply of all factors of
production is endogenously determined. The number of efficiency
units of skilled and unskilled labor in every period is determined
by occupational choices of the fixed number of individuals within a
generation, as well as by the state of technology. The stock of
physical capital in every period is given by the sum of the
economy’s aggregate saving net of international lending.
A. Production of Final Output
Production occurs according to a neoclassical, constant-
returns-to-scale, production technology that is subject to techno-
logical progress. The output produced at time t, Yt , is
(1)
Yt ϭ F (Kt , AtHt ) ϵ AtHt f (kt );
kt ϵ Kt /(AtHt ),
where Kt and Ht are the quantities of physical capital and
efficiency units of the composite labor input employed in produc-
tion at time t, and At is the technological level at time t, where A0 is
historically given. f (kt ) is strictly monotonic increasing, strictly
concave satisfying the boundary conditions that assure the exis-
tence of an interior solution to the producers’ profit-maximization
problem.
Producers operate in a perfectly competitive environment.
Given the wage rate per efficiency unit of labor and the rate of
return to capital at time t, wt , and rt , respectively, producers
choose the level of employment of capital, Kt , and the composite
labor input, Ht , so as to maximize profits. The producers’ inverse
11. The focus on a single industry in this context is justified by empirical
evidence which suggests that the increase in demand for skills comes from changes
within industries and not between industries [Autor, Katz, and Krueger 1998].

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demand for factors of production is therefore
rt ϭ f Ј(kt );
(2)
wt ϭ At [ f (kt ) Ϫ f Ј(kt )kt ] ϵ Atw(kt ).
B. The Internal Structure of the Composite Labor Input
The composite labor input Ht is a weighted sum of the number
of efficiency units of skilled labor, ht , and unskilled labor lt
employed in production at time t:12
(3)
Ht ϭ ␤ht ϩ lt (1 Ϫ ␦gt ),
where ␤ Ͼ 1, and 0 Ͻ ␦gt Ͻ 1 is the reduction in the aggregate
weight given to efficiency units of unskilled labor due to the rate of
technological progress from period t Ϫ 1 to period t, gt
(At Ϫ AtϪ1) /AtϪ1. It is assumed that13
ϵ
(A1)
0 Ͻ gt Ͻ 1.
␦ is therefore assumed to be in the open interval (0,1).
This formalization of the effect of an increase in the rate of
technological progress on the composite labor input is designed to
capture the spirit of the fundamental observation that technologi-
cal progress is skill-biased in the short run. Whereas the techno-
logical level At has no effect on the relative demand for skilled
workers, the rate of technological progress, gt , determines the
relative demand for skilled labor. For a given wage ratio, an
increase in the rate of technological progress would generate a
substitution of skilled for unskilled workers.14 This is a novel
formalization in which the change in the rate of technological
12. The introduction of imperfect substitution between skilled and unskilled
labor would not change the qualitative analysis. It would, however, make the
analysis complex and less transparent.
13. As will become apparent, Assumption (A1), which places restrictions on
the magnitude of the rate of growth, is used as long as technological progress is
exogenous. Once technological progress is endogenized, Assumption (A1) is
replaced by Assumption (A2) which restricts the magnitude of the exogenous
parameter ␥.
14. Formally, technological change erodes the aggregate stock of human
capital, Ht , although aggregate output may increase due to the productivity effect
captured by the rise in the technological parameter At . In the absence of changes in
the rate of technological progress, skilled and unskilled labor have a constant
weight in the composite labor input. A temporary increase in the rate of
technological progress, however, temporarily increases the relative weight given to
skilled labor and diminishes the aggregate number of efficiency units of labor. As
the rate of technological progress returns to the previous state, the aggregate
number of efficiency units increases, reflecting the adjustment of labor to the new
technological state.

ABILITY-BIASED TECHNOLOGICAL TRANSITION
477
progress endogenously determines the shares of skilled and
unskilled labor in production.
C. Factor Prices
Suppose that the world rental-rate is stationary at a level r.
Since the small economy permits unrestricted international lend-
ing and borrowing, its rental rate is stationary as well at the rate
r.15 Namely, rt ϭ r. Consequently, the ratio of capital to efficiency
units of labor in every period t, kt , is stationary at a level f ЈϪ1(r) ϵ
k, and the wage rate per efficiency unit of the composite labor
input is wt ϭ Atw(k) ϵ wAt . As follows from (3), each efficiency unit
of skilled labor generates ␤ efficiency units of the composite labor
input, whereas each efficiency unit of unskilled labor generates
(1 Ϫ ␦gt ) units of composite labor input. Hence, the wages per
efficiency unit of skilled and unskilled labor in period t, wst , and
wut , respectively, are
wst ϭ ␤wAt;
(4)
wut ϭ w(1 Ϫ ␦gt )At .
D. Individuals
In each period a generation is born. It consists of a continuum
of individuals of measure 1. Individuals, within as well as across
generations, are identical in their nonaltruistic preferences. They
may differ, however, in their cognitive ability and thus in their
education and their level of human capital. Ability is distributed
uniformly over the unit interval.16
Individuals live for two periods. In the first period, individu-
als who choose to become skilled workers acquire education and
work, whereas those who choose to become unskilled workers join
the labor force directly. The resulting wage income is allocated
between consumption and saving. In the second period, individu-
als retire consuming their entire savings. Individuals’ preferences
are defined over consumption in the two periods of their lives.
15. The removal of the simplifying assumption of a small open economy with
perfect capital mobility would not affect our analysis qualitatively. As will become
apparent, occupational choice and wage inequality are independent of the interest
rate.
16. As will become apparent, the qualitative effect of technological change on
within-group inequality is independent of the distribution of ability in society as
long as the distribution is continuous. The effect on between-group inequality,
however, may be sensitive to the choice of distribution.

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They are represented by a utility function that is strictly monotoni-
cally increasing, strictly quasi concave, and satisfies the conven-
tional boundaries conditions that assure the existence of an
interior solution for the utility maximization problem.
Members of generation t face an occupational choice in the
first period of their life. Individuals who choose to become skilled
workers devote a fraction 0 Ͻ ␶ Ͻ 1 of their unit time-endowment
(in either the form of formal education or on-the-job-training) to
the formation of human capital. They supply a fraction 1 Ϫ ␶, of
their potential efficiency units of skilled labor earning the competi-
tive market wage wst per efficiency unit of skill supplied. Individu-
als who choose to become unskilled supply their entire time
endowment, earning the competitive market wage wut per effi-
ciency unit of unskilled labor.17
Ability, Technological Change, and Human Capital. The
level of human capital of skilled and unskilled workers is deter-
mined by their ability as well as by the technological environment.
Technological progress changes the nature of occupations and
reduces the adaptability of existing human capital for the new
technological environment. That is, human capital is technology
specific, and technological progress that takes the form of creative
destruction erodes some of the existing stock of human capital.
Therefore, in the presence of technological progress, the applicabil-
ity of the level of human capital that can be absorbed from the
existing technological environment erodes, and individuals devote
time (on the job) for learning the new technology.
Consistent with empirical evidence, the time required for
learning the new technology diminishes with the level of ability
and increases with the rate of technological change.18 Hence,
following the insight of Nelson and Phelps [1966] and Schultz
[1975] discussed above, technological progress increases the re-
turn to ability. The efficiency units of labor of a member i of
generation t depends positively on individual i’s ability, a it ,
negatively on the rate of technological change, gt , and positively
on the complementarity of the rate of technological change and
ability.
17. In every point in time within a period skilled and unskilled workers are
jointly employed. That is, the time cost of education is uniformly distributed over
the period.
18. Bartel and Sicherman [1998] show that at a higher rate of technological
change, low skilled nonproduction workers receive significantly more training
than high skilled nonproduction workers, and the proportion of individuals
receiving training increases.

ABILITY-BIASED TECHNOLOGICAL TRANSITION
479
Suppose that the number of efficiency units of labor that a
member i of generation t supplies as an unskilled worker, lit , has a
simple linear representation:19
(5)
lit ϭ l(a ti, gt ) ϭ 1 Ϫ (1 Ϫ a it )gt .
The number of efficiency units of unskilled workers is subject
to depreciation due to technological progress, and ability lessens
the adverse effect of technological change. [(1 Ϫ a it )gt ] is therefore
the fraction of the working time of an unskilled worker devoted to
learning the new technology on the job. Individuals who choose to
become unskilled workers are endowed with one efficiency unit of
labor, regardless of ability. That is, the level of ability of unskilled
workers would not be rewarded in a stationary technological
environment.
Suppose that the number of efficiency units of labor that a
member i of generation t supplies as a skilled worker has a simple
linear representation:20
(6)
h it ϭ h (a it, gt ) ϭ (1 Ϫ ␶)[a ti Ϫ (1 Ϫ a ti )gt ].
Individual i’s level of human capital depends therefore on two
components: a it captures the direct positive effect of ability,
whereas [(1 Ϫ a it )gt ] captures the depreciation due to technologi-
cal progress.21 In particular, unlike unskilled workers, the level of
ability of skilled workers is rewarded even in a stationary
technological environment.
Consistent with Schultz’s observations, technological progress
complements ability in the formation of human capital. That is,
ability lessens the adverse effect of technological change. The
higher the rate of technological progress the higher the return to
ability. Individuals are subjected to two opposing effects due to
technological progress. On the one hand, the potential number of
efficiency units of labor is diminished due to the transition from
the existing technological state to a superior one—the erosion
19. Assumption A1 (i.e., 0 Ͻ gt Ͻ 1) assures that regardless of ability, the
number of efficiency units of any individual as an unskilled worker is strictly
positive.
20. As will become apparent, in equilibrium individuals whose ability level
would not assure a positive level of efficiency units as skilled workers would choose
to become unskilled workers.
21. [(1 Ϫ a i )gt ]/a i is the fraction of working time devoted for learning the
new technology ton thet job. As one would expect, this formulation implies that, for a
given level of ability, the time cost of unskilled workers is smaller than that of
skilled workers.

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effect. On the other hand, each individual operates with a superior
level of technology—the productivity effect. Moreover, once the
rate of technological progress reaches a steady state, the erosion
effect is constant, whereas the productivity effect and thus wages
grow at a constant rate. For the economy as a whole, the
productivity effect is dominating, and producers would find it
beneficial to adopt the new technology. However, for some individu-
als the erosion effect may dominate, and their wages would
decline due to technological change.22
Occupational Choice. Since skilled and unskilled workers
coexist in the labor market, additional structure is added to the
model so as to assure that in equilibrium the number of skilled
and unskilled workers is positive. In particular, the time cost of
education ␶ is required to be compensated by ␤—the added weight
given to skilled workers in the production technology so as to
assure that regardless of the rate of technological progress
investment in human capital is profitable. Although ␤(1 Ϫ ␶) Ն 1
would be a sufficient (additional) condition for the existence of
skilled workers in the economy, to simplify the exposition it is
assumed that ␤(1 Ϫ ␶) ϭ 1.23
A member i of generation t who chooses to become a skilled
worker supplies h it efficiency units of skilled labor. Given the wage
rate per efficiency unit of skilled labor at time t, wst , the individu-
al’s income, I it,s, is therefore
(7)
I it,s ϭ wst h it ϭ wAt [a it Ϫ (1 Ϫ a it )gt ] ϵ I s(a ti, gt , At ),
where as depicted in Figure I, ѨI s ( a ti , gt , At )/Ѩa ti ϭ wAt [1 ϩ gt ] Ͼ 0,
i.e., I it,s is an increasing linear function of a it .
Similarly, the income of a member i of generation t who
chooses to become an unskilled worker is
(8) I it,u ϭ wut lit ϭ (1 Ϫ ␦gt )Atw[1 Ϫ (1 Ϫ a it )gt ] ϵ I u (a ti, gt , At ),
where, as depicted in Figure I, ѨI u (a ti, gt, At )/Ѩa ti ϭ (1 Ϫ ␦gt , At)
wgt Ͼ 0; i.e., I it,u is an increasing linear function of a it .
As stated earlier, individuals’ utility function is defined over
first- and second-period consumption, and is strictly increasing in
22. The underlying assumption is that the new technology replaces the old
technology. This outcome can be endogenized in several ways (e.g., intertemporal
consideration of firms and cost of technology adoption that is convex in the
distance of the technological frontier).
23. The existence of unskilled workers in the economy follows directly from
(A1), (5), and (6), for any ␤ Ͼ 0.

ABILITY-BIASED TECHNOLOGICAL TRANSITION
481
FIGURE I
*
The Threshold Level of Ability in Period t, a t , and the Composition of the Labor
Force, Given a Rate of Technological Progress gt
both variables. Since individuals work only in the first period of
their lives, maximization of first-period income is a necessary
condition for maximization of utility. Individuals choose to become
skilled workers if and only if, given their ability and the rate of
technological progress, their income as skilled workers is higher
than that as unskilled workers. That is, a member i of generation t
whose ability level is a it chooses to become a skilled worker if and
only if I s(a it , gt , At ) Ն I u (a ti , gt , At ).
As follows from (7), (8), and (A1), there exists a unique,
*
interior, threshold level of ability 0 Ͻ a t Ͻ 1. Individuals whose
ability level is above this threshold would choose to become skilled
workers, whereas individuals whose ability level is below it would
s
*
choose to become unskilled workers. That is, I (a t ,gt , At ) ϭ
u
*
I (a t ,gt , At ):
1 Ϫ ␦gt ϩ ␦g2t
1 ϩ ␦g2t
*
a t
(9)
ϭ
ϵ a*( gt ),
where the steady-state threshold level of ability decreases mono-
tonically in the rate of technological progress, i.e., a *Ј( gt ) Ͻ 0, but
is unaffected by the level of technology.

482
QUARTERLY J OURNAL OF ECONOMICS
Figure I depicts the income of skilled and unskilled workers
as a function of ability. As follows from (7) and (8), the return to
ability is higher among skilled workers. The point of intersection
*
of the two curves is the threshold level of ability, a t above which
individuals choose to become skilled workers.
E. The Composition of the Labor Force, Aggregate Output,
and Income
In every period, given the threshold level of ability, the
number of skilled and unskilled workers in the economy is
uniquely determined. The number of unskilled workers at time t
*
*
is a t , whereas the number of skilled workers is Et ϵ 1 Ϫ a t .
The aggregate supply of efficiency units of skilled and un-
skilled labor is determined by the rate of technological progress
via two channels. Indirectly, by its effect on the threshold ability
*
level a t ϭ a *( gt ), which in turn determines the number of skilled
and unskilled workers, and directly by its effects on the supply of
efficiency units of skilled and unskilled workers.
The aggregate efficiency units of skilled labor, ht , and un-
skilled labor, lt , at time t, is
1
h ϭ
t
(1 Ϫ ␶)[a it Ϫ (1 Ϫ a ti )gt ] da ti ϵ h ( gt ),
͐
*
a
t
(10)
*[1 Ϫ (1 Ϫ a ti )gt ] dati ϵ l( gt ).
a
t
l ϭ
t
͐
0
The level of the composite labor input, as follows from (3), is
therefore
(11)
Ht ϭ ␤h ( gt ) ϩ l( gt )(1 Ϫ ␦gt ) ϵ H ( gt ).
As follows from, (7), (8), and (9), the average income at time t
s
u
˜
˜
of skilled individuals, It , and unskilled individuals, It , is
s
s
*
I (a t, gt , At ) ϩ I (1, gt, At )
s
˜
(12)
It ϭ
2
wAt (2 Ϫ ␦gt ϩ ␦g2t )
s
˜
ϭ
ϵ I ( gt , At );
2(1 ϩ ␦g2t )

ABILITY-BIASED TECHNOLOGICAL TRANSITION
483
u
u
*
I (0, gt, At ) ϩ I (a t, gt, At )
u
˜
(13)
I t ϭ
2
wAt (1 Ϫ ␦gt )(2 Ϫ gt ϩ (1 Ϫ gt )␦g2t )
2(1 ϩ ␦g2t )
u
˜
ϭ
ϵ I ( gt , At ).
The domestic output per worker produced at time t, ydt , given (1)
and (11), is
(14)
ydt ϭ AtH ( gt ) f (k) ϵ y( gt, At ).
III. EXOGENOUS TECHNOLOGICAL PROGRESS
This section analyzes the evolution of the economy as a whole.
It focuses on three central elements: the effect of the rate of
technological progress on (i) the return to skilled and unskilled
workers, (ii) the composition of the labor force and wage inequal-
ity, and the effect of the composition of the labor force on the rate of
technological progress. In order to distinguish between the short-
run effects and the long-run effects, the analysis is conducted in
two stages. First, technological progress is supposed to be exoge-
nous and its impact on the composition of the labor force, the
average income in each group and income inequality within and
between groups is thoroughly examined. Second, the rate of
technological progress is endogenized, and the joint evolution of
technological progress and wage inequality is characterized.
This section demonstrates that exogenous changes in the rate
of technological progress affect wage inequality. In particular, in
accordance with the pattern of wage inequality during the 1980s
and the 1990s in the United States, as long as the rate of
technological progress increases between two subsequent periods,
wage inequality within and across groups increases, the average
wage of skilled workers increases, and the average wage of
unskilled workers may decline.
A. Education, Average Wages, and Output
Technological change affects the average income of skilled
and unskilled workers via three channels. First, for a given
composition of the labor force, the rise in the level of technology
affects income of each group positively. Second for a given
composition of the labor force, the rate of technological change

484
QUARTERLY J OURNAL OF ECONOMICS
affects the income of each group negatively via the erosion effect.
Third, the rate of technological progress alters the composition of
ability within each of the groups. An increase in the rate of
technological change decreases the threshold level of ability above
which individuals chose to become skilled workers. The number of
skilled workers increases, the number of unskilled workers de-
creases, and the average ability decreases in both groups. Income
in each of the groups is therefore affected negatively, although due
to the optimal adjustment in the composition of the labor force the
average income in the economy as a whole is affected positively.
For a stationary rate of technological progress, g Ͼ 0 changes
in income are only due to the first effect discussed above. The
erosion effect is constant, and so is the composition of the labor
force. As follow from (9), (12), (13), and (14) and as depicted in
Figure II, for a given rate of technological progress g Ͼ 0, the
threshold ability is constant at a steady-state level, a * ϵ a*( g),
the number of skilled individuals is constant at a steady-state
level, E ϭ 1 Ϫ a*( g), the average income of skilled and unskilled
workers and output per worker increase monotonically, and their
growth rate is equal to the rate of technological progress g.
FIGURE II
The Threshold Level of Ability, the Composition of the Labor Force, and the
Income of Skilled and Unskilled Workers in a Steady State Equilibrium with a
Constant Rate of Technological Progress, g

ABILITY-BIASED TECHNOLOGICAL TRANSITION
485
PROPOSITION 1 (The effect of the path of technological progress on
average wages). Under (A1),
(a) The average income of skilled workers increases from
period t to period t ϩ 1, regardless of the time path of the
positive rate of technological progress.
(b) The average income of unskilled workers decreases from
period t to period t ϩ 1 for some time path of the rate of
technological progress 5 gt , gtϩ16.
Proof.
s
ˆ
ˆs
˜s
˜s
(a) Let Itϩ1 ϵ I ( gt , gtϩ1, At ) ϵ I ( gtϩ1, At (1 ϩ gtϩ1)) Ϫ I
( gt , At ) denote the difference in the average income of
skilled workers between periods t ϩ 1 and t. As follows
s
ˆs
ˆ
from (12), (A1), and ␦ ʦ (0,1), I (0, g tϩ1, At ) Ͼ 0, ѨItϩ1/Ѩgt Ͼ
ˆs
0, and hence, I ( gt , gtϩ1, At ) Ͼ 0.
u
ˆ
ˆu
˜u
(b) Let Itϩ1 ϵ I ( gt , gtϩ1, At ) ϵ I ( gtϩ1, At (1 ϩ gtϩ1)) Ϫ
˜u
I ( gt , At ) denote the difference in the average income of
unskilled workers between periods t ϩ 1 and t. As follows
from (13), (A1), and ␦ ʦ (0,1), for the extreme range of the
time path of the rate of technological change, i.e.,
u
ˆ
ˆu
5 gt , gtϩ16 ϭ 50,16, Itϩ1ϵ I (0,1, At ) Ͻ 0. Hence, it follows from
u
˜u
ˆ
the continuity of I ( gt , At ) in gt ʦ [0,1] that Itϩ1 is strictly
negative for some feasible range 5 gt , gtϩ16 in the open
interval (0,1).
ᮀ
*
Hence, since Et ϵ 1 Ϫ a t , Proposition 1 implies that for
monotonically increasing rates of technological change the aver-
age wage of skilled workers increases despite the increase in their
number, whereas the average wage of unskilled workers may
decline, despite the decline in their relative supply. The rise in the
average wage of skilled workers is due to the rise in the return to
(heterogeneous) ability despite the decline in the average ability
within the group, whereas the potential decline in the average
wage of unskilled workers is due to the erosion effect and the
reduction in the average level of ability within the group.
B. Productivity Slowdown
The predictions of the model reconcile the coexistence of
acceleration in the rate of technological progress and a productiv-
ity slowdown that may have been observed in earlier parts of
recent decades. As is established in Galor and Moav [1998], a

486
QUARTERLY J OURNAL OF ECONOMICS
sufficiently large increase in the rate of technological progress
generates a productivity slowdown in the short run. In the long
run, however, the growth rate of productivity is higher than
existed initially.
Due to the erosion effect, for a sufficiently large increase in
the rate of technological progress, the growth rate in Total Factor
Productivity (TFP) as measured by the Solow Residual declines.
However, once the rate of technological progress reaches a steady
state, the erosion effect is constant, whereas the productivity
effect grows at a constant rate. TFP therefore grows in the long
run at a higher constant rate.
C. Wage Inequality
This section analyzes the effect of an exogenous rate of
technological progress on income inequality: within the group of
skilled workers, within the group of unskilled workers, and
between skilled and unskilled workers. Income inequality be-
tween skilled and unskilled workers is naturally defined as the
ratio between the average wage of skilled and unskilled workers.
As follows from (12) and (13), income inequality between skilled
and unskilled workers, ␴s/u , is
t
2 Ϫ ␦gt ϩ ␦g2t
(1 Ϫ ␦gt )(2 Ϫ gt ϩ (1 Ϫ gt )␦g2t )
s
˜
I ( gt, At )
s/ u
t
(15)
␴
ϵ
ϭ
ϵ ␴s/ u ( gt ).
u
˜
I ( gt , At )
Income inequality within the groups of skilled and unskilled
workers is defined as the ratio of the top to bottom earners within
the group. This appears as a natural choice given the assumption
that ability is distributed uniformly, and income is linear in ability
within each group.24 As follows from (7)–(9), income inequality
within skilled workers, ␴st , and within unskilled workers, ␴u , is
t
I s(1, gt, At )
I s(a*, gt, At )
1 ϩ ␦g2t
1 Ϫ ␦gt
s
(16)
(17)
␴ ϵ
ϭ
ϵ ␴s( gt ).
t
I u (a*, gt, At )
I u (0, gt , At )
1
u
␴ ϵ
ϭ
ϵ ␴u ( gt ).
t
(1 Ϫ gt )(1 ϩ ␦g2t )
24. It should be noted that a Gini Index of inequality is monotonically
increasing in our measure of inequality. If wages, x ϳ U [xL,xH ], then the Gini index
is (xH Ϫ xL)/3(xH ϩ xL) ϭ [(xH/xL) Ϫ 1]/3[xH /xL) ϩ 1, which is monotonically
increasing in our index: xH/xL.

ABILITY-BIASED TECHNOLOGICAL TRANSITION
487
PROPOSITION 2 (The effect of changes in the rate of technological
progress on inequality). Under (A1), an increase (decrease)
in the rate of technological progress in period t increases
(decreases)
(a) Income inequality between skilled and unskilled workers
in period t.
(b) Income inequality within skilled workers in period t.
(c) Income inequality within unskilled workers in period t.
Proof. Follows from the differentiation of (15), (16), and (17)
with respect to gt .
ᮀ
u
As follows from (15), (16), and (17), ␴s/u , ␴s, and ␴ are
functions of a single variable—gt , and they are time independent.
Moreover, as established in Proposition 2, the functions are
monotonically increasing in gt . Hence the corollary follows.
COROLLARY (The effect of the time path of technological progress
on wage inequality). Under (A1), an increase (decrease) in the
rate of technological progress from period t to period t ϩ 1
increases (decreases) income inequality between and within
groups from period t to period t ϩ 1.
Hence, as depicted in Figure III, if the rate of technological
FIGURE III
The Effect of an Increase in the Rate of Technological Progress over Time on the
Composition of the Labor Force and Wage Inequality within and between Groups

488
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progress increases monotonically, wage inequality within and
between groups increases, the average wage of skilled workers
increases despite the increase in their number, and the average
wage of unskilled workers may decline, despite the decline in their
relative supply. The rise in the wage dispersion within a group is
due to the rise in the return to (heterogeneous) ability, whereas
the rise in the return to skills, despite the increase in the supply of
skills follows since cognitive ability is nonpurchasable.
Since the threshold level of ability above which individuals
choose to become skilled workers is independent of the distribu-
tion of ability, the qualitative effect of an increase in the rate of
technological change on the composition of ability within groups
and hence on wage inequality within groups is independent of the
distribution of ability. The qualitative effect of technological
change on wage inequality between groups may alter, however, if
the additional mass of individuals who choose to become skilled
workers due to the decline in the threshold level of ability is
relatively large. The sensitivity to alternative distributions is
mitigated, however, if the adverse effect of technological transi-
tion on the demand for unskilled workers is large (i.e., ␦ is large).
IV. ENDOGENOUS TECHNOLOGICAL PROGRESS
This section analyzes the evolution of the economy in the
presence of an endogenous technological change. The evolution of
the economy and its impact on wage inequality is based upon
three central elements that appear consistent with empirical
evidence. First, an increase in the rate of technological change
raises the rate of return to skills. Second, the increase in the
return to skills induces an increase in the supply of educated
individuals. Third, an increase in the level of human capital
increases the rate of technological progress. These three elements
generate a dynamic path characterized by a positive feedback loop
that permits a monotonic increase in the rate of technological
progress in a transition to a steady-state equilibrium with per-
petual growth. The increase in the return to ability and education
that stems from the increase in the rate of technological progress
brings about a monotonic rise in wage inequality within as well as
between groups along the transition to a steady-state equilibrium.
Suppose that gtϩ1 is a positive (linear) function of the number
of skilled workers in period t, or equivalently a positive (linear)

ABILITY-BIASED TECHNOLOGICAL TRANSITION
489
function of the proportion of skilled worker in the economy.25 That
*
is, gtϩ1 ϭ ␥Et , where ␥ Ͼ 0. Since Et ϭ 1 Ϫ a t , (9) implies that the
dynamic system is governed by a one-dimensional, first-order
nonlinear difference equation that is time independent:
␥␦gt
1 ϩ ␦g2t
(18)
gtϩ1 ϭ ␥Et ϭ ␥(1 Ϫ a*( gt )) ϭ
ϵ ␾( gt ),
where since ␦ ʦ (0,1) it follows from (A1) that ␾(0) ϭ 0, ␾Ј( gt ) Ͼ 0,
and ␾ЈЈ( gt ) Ͻ 0.
Hence, the evolution of the rate of technological progress is
governed by a strictly increasing, strictly concave function, ␾( gt ).
The existence of a positive steady-state equilibrium in the rate of
technological progress requires further restrictions on the value of
the parameter ␥. That is,
(A2)
1 ␦ Ͻ ␥ Ͻ 1 ϩ 1 ␦.
⁄ ⁄
LEMMA 1 (Existence of a stable positive steady-state growth rate).
If (A2) is satisfied, then there exists a unique steady-state
equilibrium in the rate of technological progress g ʦ (0,1).
The economy converges monotonically to g for all g0 ʦ (0,1).
Proof. Since ␾( gt ) is a strictly increasing, strictly concave
function of gt , and since ␾(0) ϭ 0, the existence of a unique,
globally stable, steady-state equilibrium in the open interval (0,1)
is established since ␾Ј(0) ϭ ␥␦ Ͼ 1 and ␾(1) ϭ ␥␦/(1 ϩ ␦) Ͻ 1 as
follows from (A2) and (18).
ᮀ
REMARK. As follows from Lemma 1, (A2) implies (A1). Hence an
assumption on the magnitude of the exogenous variable ␥
replaces the assumption on the endogenous variable gt .
Hence, for a given A0, the sequence 5 gt 6ϱtϭ0 fully determines the
time path of output per worker, average incomes of skilled and
unskilled workers, and wage inequality within and across groups.
The economy converges to a steady-state equilibrium with a
positive growth rate of output per worker supported by a positive
endogenous rate of technological progress. As long as the initial
rate of technological progress is lower than its steady-state level,
in the transition to the steady state the rate of technological
progress increases monotonically. Hence, as summarized in the
25. The second interpretation permits endogenous growth without scale
effect. That is, if population size increases, it has no effect on the economy’s growth
rate.

490
QUARTERLY J OURNAL OF ECONOMICS
following proposition, wage inequality within and between groups
increases, the average wage of skilled workers increases despite
the increase in their number, and the average wage of unskilled
workers may decline, despite the decline in their relative supply.
PROPOSITION 3 (The effect of the endogenous path of technological
progress on wages, inequality, and the composition of the
labor force). If g0 Ͻ g, then along the transition of the rate of
technological progress to a steady-state equilibrium, g,
(a) Wage inequality within and between skilled and un-
skilled workers increases.
(b) The average wage of skilled workers increases despite the
increase in their relative supply.
(c) The average wage of unskilled workers may decline,
despite the decline in their relative supply.
Proof. (a)–(b). Since, as follows from (18), the rate of techno-
logical progress increases monotonically in the transition to the
steady-state equilibrium, (a)–(b) are corollaries of (9), and Proposi-
tions 1 and 2.
˜u
˜u
(c) Since I ( gt , At ) Ͼ 0 for all g ʦ (0,1), and I ( g, At ) ϭ 0 if
[␦ ϭ 1 and ␥ ϭ 1 ϩ 1/␦ (i.e., g ϭ 1)], then for any g0 Ͻ 1 income of
unskilled workers decreases in the transition to a steady-state
˜u
equilibrium. Hence, it follows from the continuity of I ( gt , At ) in
g ʦ [0,1], and in ␦ ʦ [0,1], that I ( gt , At ) decreases in the
˜u
transition to a steady state, for some feasible range ␦ ʦ (0,1) and
1/␦ Ͻ ␥ Ͻ 1 ϩ 1/␦.
ᮀ
These qualitative results are robust under a different specifi-
cation of the rate of technological progress. Suppose that gtϩ1 is a
function of the number of efficiency units of labor of skilled
workers, ht . This formulation would not alter the qualitative
results as long as ␦ is sufficiently small. In particular, if gtϩ1 ϭ ␭ht ,
there is a unique globally stable steady-state equilibrium if
1/␦(1 Ϫ ␶) Ͻ ␭ Ͻ (1 ϩ ␦)2/(1 Ϫ ␶)␦. Furthermore, convergence to
the steady state is monotonic for a sufficiently low ␦.
As the economy converges to the steady-state equilibrium,
the increase in the wage inequality subsides. The study suggests
therefore that the slowdown in the growth of wage inequality in
the United States in the 1990s [Autor, Katz, and Krueger 1998]
reflects the slowdown in the rate of change of the rate of
technological progress as the economy approaches the steady-
state equilibrium.

ABILITY-BIASED TECHNOLOGICAL TRANSITION
491
A. Technological Shocks and Endogenous Adjustment
Suppose that the economy is in steady-state equilibrium with
a constant endogenous rate of technological progress g. Techno-
logical shock increases the rate of technological progress (in one or
several periods). Subsequently, the rate of technological progress
declines endogenously and converges back to the original steady-
state equilibrium g. As established in Proposition 2 and consistent
with the cyclical pattern of wage inequality between groups
documented earlier, major (exogenous) technological changes
initially increase wage inequality between groups, but once the
revolution is completed, the economy converges back to the
original steady-state equilibrium, and inequality between groups
declines to its preshock level. If one interprets the 1980s and the
early 1990s as periods of major technological breakthroughs (that
are independent of the level of education), the model predicts that
wage inequality between and within groups would rise and then
decline, TFP growth may initially decline, and the number of
skilled workers would initially rise and then would be expected to
decline.26
V. ECONOMIC GROWTH AND INSTITUTIONAL CHANGES
The introduction of institutional changes into the basic model
permits the analysis to be consistent with those episodes in which
a decline in wage inequality was associated with an increase in
the fraction of skilled individuals in the labor force. In the
presence of capital market imperfections, investment in human
capital is suboptimal.27 If economic development is associated
with institutional changes that reduce the effectiveness of imper-
fections in capital markets (e.g., directly via the expansion in
financial aid to higher education in the United States from the
1960s to the early 1970s, or indirectly via the high school
movement in the United States of 1910 to 1940), they generate a
decrease in wage inequality along with an increase in the number
of college graduates.
26. As elaborated below, if, in contrast, the increase in technological change is
an outcome of an exogenous increase in the supply of skilled workers in the 1970s,
then the supply of skilled worker would be expected to increase monotonically
toward its steady-state level.
27. For example, in the presence of differences in the rates of interest for
borrowers and lenders, as in Galor and Zeira [1993], investment in human capital
is persistently suboptimal.

492
QUARTERLY J OURNAL OF ECONOMICS
Consider a modification of the basic model where individuals
live three periods. In the first period of their lives, individuals
invest in human capital, in the second they work, and in the third
they are retired. In contrast to the basic model, the cost of
education for members of generation t Ϫ 1 who would like to
become skilled workers is an indivisible tuition payment equiva-
lent to the cost associated with hiring a teacher with e efficiency
units of a skilled worker. That is, ewAtϪ1. Moreover, for simplicity,
education is free for those who intend to become unskilled
workers. Individuals borrow the entire fund to finance the cost of
their education, ewAtϪ1. The loan repayment of a member of
generation t Ϫ 1, is therefore ewAtϪ1(1 ϩ ␪tr) in the working period
t, where ␪ Ͼ 1 is the ratio of the interest rate for borrowers and
t
lenders in period t.
Hence, a member i of generation t Ϫ 1 chooses to become a
skilled worker if and only if
(19)
I s(a it, gt, At ) Ϫ ewAtϪ1(1 ϩ ␪tr) Ն I u (a ti, gt, At );
that is, if and only if (1 ϩ gt )␤[a it Ϫ (1 Ϫ a ti )gt ] Ϫ e(1 ϩ ␪tr) Ն
(1 Ϫ ␦gt )(1 ϩ gt )[1 Ϫ (1 Ϫ a ti )gt ]. Provided that the number of
skilled workers in the economy is positive, i.e., provided that ␤ Ͼ
(1 Ϫ ␦gt ) ϩ e(1 ϩ ␪tr )/(1 ϩ gt ), the threshold level of ability in
**
period t, a t is
**
at ϭ a ( gt;␪t ),
(20)
**
**
**
where Ѩa t /Ѩ␪ Ͼ 0 and Ѩa t /Ѩgt Ͻ 0. That is a t depends
t
negatively upon the rate of technological progress, gt , and posi-
tively on the degree of imperfection, ␪t .
Hence, if economic development is associated with a reduc-
tion in the degree of imperfections in capital markets (i.e., a
reduction in ␪t ), it follows that the increase in the supply of skilled
workers due to the increase in the rate of technological progress
would be enhanced in the transition to a steady-state equilibrium.
The level of inequality between skilled and unskilled workers,
however, would be subjected to two opposing effects. The increase
in the rate of technological progress raises inequality between
groups. However, the reduction in imperfections increases the
supply of skilled labor and reduces the average ability of both
skilled and unskilled workers. Moreover, if skilled and unskilled
workers are imperfect substitutes, inequality between groups
declines.
The dynamic system in the presence of capital markets

ABILITY-BIASED TECHNOLOGICAL TRANSITION
493
imperfections is depicted in Figure IV. Suppose that the degree of
capital markets imperfections is initially ␪1. Modifying the analy-
sis in Section IV, the economy converges along the map ␾( gt ,␪1) to
a steady-state equilibrium g(␪1). If along the transition to the
steady-state equilibrium the economy experiences a discrete
improvement in the degree of capital market imperfections from
1
2
␪ to ␪ (e.g., the enhancement of subsidy for college loans in the
early 1970s), then the number of skilled workers increases. In the
next period the rate of technological progress rises discretely, and
the economy converges monotonically along the map ␾( gt ,␪2) to a
steady-state equilibrium g(␪2).
A. The Patterns of Wage Inequality in the 1970s
During the 1960s to the early 1970s, financial aid to higher
education expanded in the United States. As observed by Autor,
Katz, and Krueger [1998], although the demand for college
graduates in the United States has increased from the 1970s
faster than previously, the college wage premium declined be-
cause of the large increase in supply of college graduates. In
contrast, wage inequality within groups had increased over this
period [Katz and Murphy 1992].
As is apparent from the above analysis, if the decline in the
degree of credit market imperfections is sufficiently large, the
FIGURE IV
The Changes in the Evolution of the Rate of Technological Progress due to a
2
Reduction in the Degree of Capital Markets Imperfections from ␪1 to ␪

494
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increase in the supply of skilled workers would dominate the
demand effect induced by the increase in the rate of technological
change, and wage inequality between skilled and unskilled work-
ers would decrease. Moreover, wage inequality within groups and
average wages of each group may follow the pattern observed in
the 1970s. In particular, wage inequality within the group of
skilled workers would increase unambiguously due to the in-
creases in the heterogeneity in ability among skilled workers,
whereas wage inequality within the group of unskilled workers
would increase provided that the effect of technological progress
on the return to ability dominates the composition effect.28
B. The Patterns of Wage Inequality in the Period 1910–1950
The United States experience of the high school movement of
1910 to 1940 can shed light on the patterns of wage inequality
from 1910 to 1950. As established by Goldin and Katz [1999],
during this period wage inequality between and within groups
had declined.29 Unlike the experience of the 1970s, the improve-
ment in the accessibility of schooling was primarily geographical
in nature and consequently had no major effect on the composition
of ability among skilled workers.
As is apparent from the analysis above, if the decline in the
degree of credit market imperfections is sufficiently large, the
increase in the supply of skilled workers would dominate the
demand effect induced by the increase in the rate of technological
change (e.g., the introduction of network electricity), and wage
inequality between skilled and unskilled workers would decrease.
Moreover, wage inequality within groups would follow the pattern
observed in the period 1910–1950. Since the average ability
among unskilled workers declines due to the outflow of the upper
tail of the ability distribution, heterogeneity and wage inequality
among unskilled workers decline. Further, the increase in the
supply of ability among skilled workers reduces the return to
ability and consequently decreases wage inequality within skilled
workers.
28. Note that if the erosion effect with respect to unskilled labor is sufficiently
small prior to the 1970s then the increase in the erosion effect since the 1970s
would raise inequality within the group of unskilled workers unambiguously.
29. This pattern of declining wage inequality within and between groups is
consistent with the pattern observed in Europe in the period 1950–1980 [Freeman
and Katz 1995]. The diverging pattern of within- and between-group inequality in
the United States during the 1970s therefore appears to be the exception.

ABILITY-BIASED TECHNOLOGICAL TRANSITION
495
C. The Cyclical Pattern of Wage Inequality in the Last Century
The pattern of increased wage inequality due to the accelera-
tion in the rate of technological progress would be interrupted
occasionally due to a discrete feedback from growth to capital
markets which would increase the supply of skilled workers and
decrease temporarily wage inequality between skilled and un-
skilled labor. This dynamic process would repeat itself and,
consistent with empirical evidence, would generate cyclicality in
the wage differential between skilled and unskilled labor along
with a monotonic increase in the number of skilled workers. As
depicted in Figure IV, the increase in the number of skilled
workers would reinforce the acceleration in the rate of technologi-
cal progress and would enable wage inequality to increase once
again. This process would repeat itself, and wage inequality
would experience cyclical behavior despite the monotonic increase
in the supply of skilled workers.
V. CONCLUDING REMARKS
This paper argues that ability-biased technological transition
accounts for the evolution of technology, education attainment,
and wage inequality as observed in the United States and other
advanced countries over the past several decades. An increase in
the rate of technological progress raises the return to ability and
simultaneously generates a rise in the wage inequality between
and within groups of skilled and unskilled workers, an increase in
the average wage of skilled workers, a temporary decline in the
average wage of unskilled workers, an increase in education
attainment, and possibly a transitory productivity slowdown.30
The framework of analysis developed in this paper is suitable
for the examination of the unexplored territory of the interna-
tional spillovers of wage inequality. For instance, in the presence
of imperfect technological diffusion, wage inequality among tech-
nological leaders is likely to be larger than among followers.
Furthermore, institutional changes in a technological leader that
30. The proposed theory is indirectly supported by the apparent rise in the
tuition differential between prestigious private universities and public universi-
ties in the United States since the 1970s. If enrollment in prestigious private
colleges provides a signal about the ability of a student, and if tuition partially
reflects the value of this signal, then a possible rise in the importance of ability
since the 1970s would have increased the value of this signal, and tuition rates
would be expected to rise in these private institutions more than in their public
counterpart.

496
QUARTERLY J OURNAL OF ECONOMICS
reduces the wage differential between skilled and unskilled labor
and raises the rate of technological progress, would have an
increasing effect on wage inequality among follower countries.
BROWN UNIVERSITY, HEBREW UNIVERSITY, AND CEPR
HEBREW UNIVERSITY
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