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5
DEWEY
,
Massachusetts Institute of Technology
Department of Economics
Working Paper Series
FACTOR PRICES AND TECHNICAL CHANGE:
FROM INDUCED INNOVATIONS
TO RECENT DEBATES
Daron Acemoglu
Working Paper 01 -39
October, 2001
RoomE52-251
50 Memorial Drive
Cambridge, MA 02142
This paper can be downloaded without charge from the
Social Science Research Network Paper Collection at
http://papers.ssm.com/abstract^ 290826
MASSACHUSmTiNSTm^
DEC
200]
LIBRARIES
Massachusetts Institute of Technology
Department of Economics
Working Paper Series
FACTOR PRICES AND TECHNICAL CHANGE:
FROM INDUCED INNOVATIONS
TO RECENT DEBATES
Daron Acemoglu
Working Paper 01-39
October, 2001
RoomE52-251
50 Memorial Drive
Cambridge, MA 02142
This paper can be downloaded without charge from the
Social Science Research Network Paper Collection at
http://papers.ssm.com/abstract= xxxxx
Factor Prices and Technical Change:
Prom Induced
Innovations to Recent Debates*
Daron Acemoglu
Massachusetts Institute of Technology
October
22, 2001
Abstract
This paper revisits the induced innovation literature of the 1960s to which
Phelps was a major contributor (Drandakis and Phelps, 1965).
was the
first
I
first
This literature
systematic study of the determinants of technical change and also the
investigation of the relationship between factor prices and technical change.
present a
modern reformulation
of this literature based on the tools developed
by the endogenous growth literature. This reformulation confirms many of the
insights of the induced innovations literature, but reveals a new force, which I
refer to as the market size effect: there will be more technical change directed at
more abundant factors.
I
use this
modern reformulation
technical change often skill biased,
recent decades?
for
(2)
what
is
to shed light on two recent debates: (1)
and why has
the role of
income differences across countries?
it
human
become more
skill
why
is
biased during
capital differences in accounting
Interestingly,
an application of
this
mod-
ern reformulation to these debates also reiterates some of the insights of another
important paper by Phelps, Nelson and Phelps (1966).
JEL Classification: E25, J31, O30, 031, 033.
Keywords: Biased technical change, endogenous technical change, factor
dis-
tribution of income, growth, innovation, skill-biased technical change, technology.
*This paper
is
prepared in honor of
Edmund
participants at the Festschrift conference for
assistance.
Phelps. I thank Nancy Stokey, Jaume Ventura and
comments and Ruben Segura-Cayuela for excellent research
Introduction
1
In
many
ways, one can see the "induced innovations" literature of the 1960s as the har-
binger of the endogenous growth hterature of the 1980s and 1990s. While the endogenous
growth literature studies the process of growth
tions hterature attempted to understand
generate,
it
what type of irmovations the economy would
and the relationship between factor
was Hicks
in
induced innova-
at the aggregate, the
prices
The Theory of Wages (1932) who
innovation,^ the important advances were
and technical change.
first
made during
discussed the issue of induced
the 1960s by
Kennedy
Samuelson (1965), and Drandakis and Phelps (1965), who studied the
factor prices
Although
link
(1964),
between
and technical change.
However, during the 1960s the economics profession did not possess
necessary for a systematic study of these issues. In particular,
when
the tools
all
firms choose tech-
nology in addition to capital and labor, the notion of competitive equilibrirmi needs to
be modified or refined either by introducing technological externalities (Romer, 1986,
and Lucas, 1988) or by introducing monopolistic competition (Romer, 1990, Grossman
and Helpman, 1991, and Aghion and Howitt,
tools forced this literature to take a
arguments rather than
In this paper,
I
fully
briefly
number
1992).^
The absence
of shortcuts,
of the appropriate
and ultimately
rely
on
heuristic
micro-foimded models.
survey the approach taken and the problems faced by the
induced innovations literature, and then recast the results of this literature in terms of
models of endogenous technology (or directed technical change), based on
work
(e.g.,
Acemoglu, 1998, 1999, 2001, and Acemoglu and
Kiley, 1999). This
my own recent
Zilibotti, 2001, as well as
modeling exercise not only formahzes the contribution of the induced
innovations literature, but also highlights a
this hterature. In particular, like Hicks, the
new economic
force that did not feature in
induced innovations literature emphasized
'In particular, Hicks argued that technical change would attempt to replace the
factor.
He wrote "A change
in the relative prices of the factors of production
and to invention of a particular kind
is itself
more expensive
a spur to invention,
—directed to economizing the use of a factor which
heis
become
relatively expensive..." (p. 124).
^In addition, see the work by Segerstrom, Anant and Dinopoulos (1990), Jones (1995), Stokey (1995)
and Young (1993), and the survey in Aghion and Howitt (1998).
relative prices as the key
determinant of which factors new technologies would save on.
In models of endogenous technology, as emphasized by
size effect
Romer
(1990), there
because new technologies, once developed, can be used by
is
many
a market
firms
and
workers. This market size effect also features in the analysis of the direction and bias
of technical change: there will be greater incentives to develop technologies for
abundant
factors.
Th2 market
size effect is not only of theoretical interest,
more
but turns
out to play an important role in a number of recent debates.
In the second part of the paper,
the modern reformulation of
debates.
The first
its
I
discuss
how
the directed technical change model,
induced innovations hterature, sheds
relates to the question of
on two recent
light
why the demand for skills has been increasing
throughout the 20th century, and even accelerated over the past 30 years. The second
concerns the role of
human
capital in
of directed technical change provides
technical change to be
skill
human
himian capital differences
an explanation both
biased in general, and for
accelerated over recent decades.
interaction between
economic development.
I
will also
capital
show that
will
for
why
this
I
argue that a model
why we
may have
this skill biased
model points out an
and technology, and via this channel,
may be more
should expect
it
interesting
suggests
why
important in explaining differences in income
per capita across countries than standard models imply.
These two debates are interesting not only because they have been active areas
of recent research, but also because they relate to another important contribution of
Phelps, Nelson and Phelps (1966).
capital
is
Nelson and Phelps (1966) postulated that
essential for the adoption of
important implications:
are introduced,
first,
the
new
demand
technologies.
This view has at
for skills will increase as
and second, economies with high human capital
better technologies.
These insights are relevant
since they provide a theory for
why
for the
technical change
least
two
technologies
will effectively possess
two debates mentioned above,
may be
hiunan capital differences can be essential in accounting
capita across coiintries.
new
human
skill biased,
for differences in
and why
income per
Nelson and Phelps developed this insight in a reduced form
model. Interestingly, the directed technical model change provides a framework to derive
related results from a
more micro-founded model. But these
results differ in interesting
and empirically testable ways from the predictions of the Nelson and Phelps approach.
The
rest of the
paper
organized as follows. In the next section,
is
the induced innovations approach of the 1960s. In Section
of directed technical change based on
I
show how
my own
literature in a micro-founded model,
outline a simple
Acemoglu
research, especially,
model
(2001).
and without encoimtering some of the problems
that this earher literatvire faced. In Section
the role of
briefly survey
framework captures many of the insights of the induced innovations
this
to investigate
3, I
I
when and why the demand
human
4, I vise
the directed technical change model
for skills will increase. In Section 5,
capital in accounting for differences in
across countries, and then
I
I
disciiss
income and output per worker
use the directed technical change model to highlight
the interaction between technology and
how
can lead to large differences in income per
skills
capita across countries. Section 6 concludes.
A
2
Simple Induced Innovation Model
In this section,
I
model considered by Drandakis and Phelps
outline a version of the
(1965), which in turn
bmlds on Kennedy
of consimiers with constant savings rate
(1964).
The economy
is
populated by a mass
9.
All firms have access to a constant-elasticity of substitution (CES) constant returns
to scale production frmction,
Y=
where L
is
Nl and N^
labor,
which
are labor-
is
+
(1
-
7)
(NkK)-^
assumed constant throughout the paper
(1)
,
K
is
no depreciation of
capital.
''I
choose the
and
Although firms hire the profit-maximizing
of cost reduction" for given factor proportions
p.
capital,
the elasticity of substitution between labor and capital.^ For
amoiint of labor and capital, they choose their technologies to maximize
and Phelps, 1965,
is
and capital-augmenting technology terms, which are controlled by
each individual firm, a
simplicity, there is
7 {NlL)-^
824). This
CES form
is
(see,
Kennedy, 1964,
p.
"i/ie
current rate
543, Drandakis
equivalent to maximizing the instantaneous rate of
to simplify the discussion.
output growth, R, taking
K
and L as
simply take logs and differentiate
(1)
To
given.
calciilate this rate of
with respect to time, holding
K
output growth,
and L constant.
This gives:
where
s is
the share of labor in
GDP.
In maximizing R, firms face a constraint
I will refer
first
introduced by Kennedy (1964), which
to as the "innovation possibilities frontier" ^ This frontier
is
portance for the arguments of the induced innovations literature, as
technologically-determined constraints on
technical change can be traded
where F
is
off.
Let
of central im-
it
specifies the
how labor-augmenting and capital-augmenting
me
for
now
take a general form
a strictly decreasing a differentiable and concave function.
This frontier
captures the intuitive notion that firms (or the economy) have to trade-off a higher rate
of labor-augmenting technical change with a lower rate of capital-augmenting technical
As a
change.
as
shown
The
the innovation possibilities frontier traces a downward sloping
result,
in Figure
lociis
1.
solution to maximizing (2) subject to (3) takes a simple form satisfying the
first-order condition
(i-) + ^r'(§)=o.
Diagrammatically, this solution
is
drawn
the instantaneous rate of output growth,
as
shown by point A. Comparative
in
GDP,
reduces
s,
^.
in Figure 1 as the
(2),
Put
and of the innovation
statics are straightforward.
differently, technical change,
as a result, technical change
A
^Kennedy (1964)
very
much
like
greater share of labor
^
I
is
the
first
and
important
highlight for future reference:
called this "innovation possibility function", while
"invention possibility frontier"
and
Hicks conjectiued, tries to
becomes more labor-augmenting. This
which
for
facilities frontier, (3),
A greater s corresponds to labor being more expensive,
insight of the induced innovations literature,
it
tangency of the counters
makes labor-augmenting technology more valuable, and increases
replace the expensive factor.
called
(4)
Drandakis and Phelps (1965)
Result
1:
There
be greater technical change augmenting the factor that
will
is
more
"expensive"
Next note that the growth rate of output
is
given by
Y _1^, {NlLY-^ + (1 - 7) [Oi + §^) {NkKY-^
y
7 {NlL)^ + (1 - 7) {NkK)^
where
I
^
have replaced
by
9j^ using the constant saving rule. Let
lis
now
equilibrium satisfying the Kaldor facts that the output to capital ratio, ^,
and output grows
d^ =
=
is
constant,
and j^
—
y- Therefore, technical change has to be piirely labor-augmenting (or the tangency
point has to be at
pins
This necessarily implies that jf-
at a constant rate.
look for an
down the
B
as
drawn
in Figure 1). Moreover, the fact that
^—
immediately
equilibrium labor share from (4) as:^
(1
Intuitively, there are
-
s)
+ sT' (0) =
two ways of performing
0.
capital-like tasks in this
economy: accu-
mulate more capital, or increase the productivity of capital. In contrast, there
is
only
one way of increasing the productivity of labor, via technical change.^ In equilibrium,
all
technical change
is
of capital-like tasks.
directed to labor, while capital accumulation increases the supply
Therefore, this model not only gives us a theory of the type of
technical change, but also a theory of factor shares. This gives a second
Result
2:
result:
Induced innovations and capital accumulation determine equilibrium factor
shares, ensure that all technical
constant share of labor in
Finally,
major
GDP
change
will
be labor augmenting and imply a
in the long run.
Drandakis and Phelps (1965) also addressed the question of whether the
economy would tend to
this long-run equilibrium.
They showed that
as long as the
^Also this equation indirectly determines the capital-output ratio to satisfy the requirement that
^ =01.
He wrote "The general tendency to a more rapid
marked European history during the last few centuries has
^Interestingly, Hicks also anticipated this result.
increase in capital than labor which has
naturally provided a stimulus to labor-saving invention" (pp. 125).
elasticity of substitution
Intuitively,
(between labor and capital)
a greater share of labor in
this
1,
(4).
the share of labor
1,
leads to the third
Result
3:
1,
major
As long
1,
the economy
is
stable.
When the
elasticity of substitution is
labor-augmenting technical change increases the share of labor even
further, destabilizing the system. In contrast,
than
than
GDP encourages more labor-augmenting technical
change as shown by the first-order condition
greater than
is less
falls
when the
elasticity of substitution is less
and the economy converges to the steady
result of the
state.
This
induced innovations hterature:
as the elasticity of substitution between capital
and labor
is less
than
the economy converges to the steady state with constant factor shares.
Overall, the induced innovations literature provided the first systematic study of the
the determinants of technical change, and the relationship between factor prices and
technical change. Moreover, this literature obtained a
I
summarized
of important results that
in Results 1-3.
But there are
important
number
lies in
also
some problems with the approach
the assumption that firms simply maximize
profit-maximizing firms instead?
had to confront
of this literature.
The answer
in order to construct
relates to the
(2).
Why
The most
we have
can't
problems that Romer (1986)
a model of long-run growth.
If
aggregate tech-
nology has increasing-returns-type characteristics, there does not exist a competitive
equilibrium with complete markets. In this context, profit-maximizing- firms would solve
max
/
K,L,Nk
L,Nk,Nl J
wL — rK
^{NlL)-^ + {1-i){NkK)-
exp (—rt)'
^^
subject to (3), and taking the factor prices,
w
and
r,
as given.
But
this
dt,
I
problem does
not have an interior solution, since the production function exhibits increasing returns
to scale. Therefore, to go
cost reduction,
beyond the
heuristics of
we need a micro-founded model
maximizing the instantaneous rate of
of innovation.^
^See Salter (1960) and Nordhaus (1973) for some of the early criticisms.
A
3
Model
How do we
of Directed Technical Change^
incorporate profit-maLximizing firms in an economy with increasing returns,
and maintain the
flavor of
a competitive/decentraUzed equihbriiun? Romer (1986) and
Lucas (1988) achieved this by introducing technological externalities.
els,
investments (in either physical or
human
In these
mod-
capital) increase the productivity of other
firms in the economy, and because individual firms don't internalize this effect, they are
subject to constant "private returns" (in the sense that
their profits double, while total output
may
increase
when they double aU
by more).
As a
factors,
result, despite
increasing returns at the aggregate level, a competitive equihbrium continues to exist.
Romer
(1990),
oped a
different formulation
Grossman and Helpman
(1991),
and Aghion and Howitt (1992) devel-
by introducing monopolistic competition, and an
explicit
discussion of endogenous technical change. In these models final good producers (users
of technology) are competitive, but suppliers of technology
a result,
when
face.
Here
tral issues of
folds,
I will
but their profits only double because of the decline in the prices
build
on
this class of models,
and extend them to discuss the cen-
the induced innovations literature, the possibility of innovations benefiting
factors differentially;
3.1
power. As
these monopolistic producers double their inputs, total output increases
by more than two
they
command market
•
Baisics
Consider an economy that admits a representative consumer with logarithmic preferences
/>InCe'P^dt,
where
C
is
constant, p
is
(5)
the rate of time preference and the budget constraint
C+I<Y=
where / denotes investment.
I
also
£-1
'
lY^^ +{l--l)Yz'
(6)
impose the usual no-Ponzi game condition, requiring
the lifetime budget constraint of the representative consumer to be satisfied.
^The material here
liberally
is
borrows from Acemoglu (2001).
a heuristic presentation to save space and minimize repetition.
I
omit
many
The
pro-
of the details and opt for
duction function in
that consumption and investment goods are "produced"
(6) implies
from an output of two other (intermediate) goods, a labor-intensive good, Yl, and a good
that uses another factor, Z,
gate of li, and Yz).
Z, as
I
I
where P G
(or alternatively, utility is defined over to a
am being deliberately
want to think of
The two
Yz
it
CES
aggre-
vague about the other factor of production,
as skilled workers or capital in different apphcations.
intermediate goods have the following production functions
(0, !)•
The
labor-intensive
complementary machines, xl
good
is
produced from labor and a range of labor-
denotes the amount of the j-th labor-complementary
{j)
(labor-augmenting) machine used in production.
used with labor
is
denoted by
The range
The production
A^^.
uses ^-complementary machines and
function for the other intermediate
explained similarly.
is
of machines that can be
me to model
It is
important that these
the fact that some technologies
two
sets of
will
be augmenting labor, while others increase the productivity of Z.
machines are
Although,
diff'erent,
Nl and Nz,
for given
returns to scale,
enabling
when Nl and Nz
the production fiinctions in (7) exhibit constant
are chosen by the firms in the economy, there will be
increasing retiirns in the aggregate.
I
assimie that machines in both sectors are supplied by profit-maximizing "technology
monopolists". Each monopolist will set a rental price Xl
it
supplies to the market in order to maximize
all
machines depreciate
same
for all
machines and equal to
First suppose that
prices
Xl
fully after use,
(j) or
Xz U)
Nl and Nz
^p
its profits.
iJ) o^
Xz U)
fo'^
For simplicity,
I
^^^ machine
assume that
and that the marginal cost of production
in
terms of the
are given.
final
is
the
good.
Then an equihbrium
consisis of
machine
^^at maximize the profits of technology monopolists, machine
demands from the two intermediate goods
mediate good producers'
profits,
and
factor
sectors
Xl
(j)
or
xz
{j)
that maximize inter-
and product prices wl, wz, Pl, and pz that
clear markets.
This equilibrium
is
straightforward to characterize.
Since the product markets for
the two intermediates are competitive, product prices satisfy
p,Pi = i^(^)-*.
The
greater the suppfy of
Yz
(8)
VFl/
7
PL
relative to F/,, the lower
is its
relative price, p.
Firms in the labor-intensive sector solve the following maximization problem
max PlYl - wlL -
Xl U) ^l
/
Jo
taJking the price of their product, pl,
well as the range of machines,
the
Z
sector
The
similar.
is
and the
ij) dj,
(9)
rental prices of the machines, Xl{J)j
^
Nl, as given. The maximization problem facing firms in
first-order conditions for these firms give
machine demands
as:
The important
point that comes out from these expressions
employment of a
because
market
it
profits of
=
demand
for
machines complementing that
was emphasized
Xl
(xl
iJ)
(j)
a monopolist supplying labor-intensive machine
~
i')^L
Since the
(j)-
— Y^-
'^° simplify
demand curve
the algebra,
This implies that in equilibrium
Using
factor,
in the introduction.
(10), is iso-elastic, the profit-maximizing price will
cost:
that a greater level of
creates a greater market size for the machines. This observation underlies the
size effect that
The
ttl (j)
factor raises the
is
this price,
factor markets,
all
can be written as
machines facing the monopolist,
be a constant markup over marginal
normalize the marginal cost to
I
machine
for
j
prices will
be given by Xl
iJ)
if}
= \ — (3.
— Xz U) — ^
machine demands given by (10) and the assumption of competitive
we can
also calculate relative factor rewards as:
WL
\
1
J
\LJ
KNlJ
'
^^^^
where
a
=£-
(e
-
1) (1
Inspection of (11) immediately shows that a
factors,
which
in turn
is
is
-
/?)
the elasticity of substitution between
derived from the elasticity of substitution between the goods in
consvmiers' utility function,
e.
9
For a given state of technology as captured by Nz/Nl, the relative factor reward,
wz/wl,
effect:
decreasing in the relative factor supply, Z/L. This
is
the more abundant factor
marginal product
is
is
the usual substitution
substituted for the less abundant one, and
its relative
falls.
To determine the
we need
direction of technical change,
to calculate the profitability
of different types of innovations. Using the profit-maximizing machine prices,
Xz
iJ)
—
^^^ machine demands given by
1)
TTi
=
(10),
Pp]!^L and
TTz
we
find the
monopoly
Xl
iJ)
—
profits as:
= Pp'J^Z.
(12)
Then, the discounted net present value of technology monopohsts are given by standard
Bellman equations:
rVL
where r
=
i^l
+ Vl
or
-nz-,
and the appreciation of the
In steady state, the prices, pi or
Vl
=
vr^
+ Vz,
(13)
the interest rate. These value functions have a familiar intuitive explanation,
is
equating the discounted value, tVl or
-kl
and rVz
= Vz^Q
rVz-, to
the flow returns, which consist of profits,
asset at hand,
pz-,
and the
Vl or Vz-
interest rate will
be constant,
r,
so
and
Vl
=
and Vz
=
r
The greater Vz
is
(14)
.
r
relative to Vx,, the greater are the incentives to develop
Z-complementary
machines, Nz, rather than labor-complementary machines, Nl- Equation (14) highlights
two
effects
1.
The
on the direction of technical change:
price effect: there will
be greater incentives to invent technologies producing
more expensive goods {Vz and Vl are increasing
2.
The market
size effect:
The market
size effect
Vz
are increasing in
Z
a larger market
for
in
pz and
pl)-
the technology leads to more innovation.
encourages innovation for the more abmidant factor {Vl and
and L, the
total supplies of the factors
technologies).
10
combined with these
The
price effect
showing that there
the analogue of Result
of the induced innovations literature,
1
be more technical change directed towards more "expensive"
will
wl =
factors (note that
this
is
PNip]!'^/
model introduces a new
force,
and
role in the applications below,
(1
-
and wz
/?)
the market size
is
essential for
=
PNzP^J^/
which
effect,
-
P)).
In addition,
will play
an important
(1
a new result discussed below, that an
increase in the supply of a factor induces technical change biased toward that factor.
The Innovation
3.2
Instead of
(3),
which specified an innovation
types of innovations,
of the
we now need a
two types of innovations.
we have
addition,
possibilities frontier trading off the
frontier that transforms actual resources into either
This frontier will embed a specific form of
known
in the
endogenous growth
not enable long-run growth. In particular,
R&D,
sustained growth requires these factors to
time, for example
Here
due to
assume that
I
two
(3).
spillovers
R&D
is
when
literature,
many
specifications
there are scarce factors used for
become more and more productive over
from past research.^
by
carried out
scientists,
and there
is
a constant supply
N/N
of scientists equal to S.
With only one
proportional to S: that
current research benefits from the stock of past innovations,
With two
is,
sector, sustained
growth requires
sectors, instead, there is a variety of specifications,
between the two
In
to be carefvil in the choice of the form of the innovation possibilities
frontier, since, as is well
will
Possibilities Frontier
sectors. In particular,
its
own
A'^.
with possible interactions
each sector can benefit either from
of past innovations, or from a combination of
to be
its
own
stock
stock and the stock of the other
sector.
To
clarify the issues,
The degree
affected
it is
useful to
first
introduce the concept of "state dependence".
of state dependence relates to
how
by the current composition of R&D.
more from
own
its
other factor,
I
future relative costs of innovation are
When
current
R&D
in
a sector benefits
stock of past irmovations than past innovations complementing the
refer to the innovation possibilities frontier as "state
'See Acemoglu (1998, 2001)
and there are no spillovers.
for
models of directed technical change where
11
dependent".
R&D
A
uses final output,
flexible
formulation
Nl =
where 5 £
(0, 1)
is:
riLNi^^'^^'Nt'^^'S, and
measures the degree of state dependence: when 6
state dependence since both
in the
two
N, ^ VzNt''''Nt''^'S„
sectors.
N^ and Nz
there
0,
is
no
create symmetric spillovers for current research
when
In contrast,
—
(15)
^
=
1,
there
is
an extreme amoxmt of state
dependence because an increase in the stock of labor-complementary machines today
makes future labor-complementary innovations cheaper, but has no
efiect
on the
cost of
Z-complementary innovations. ^°
To
find the steady state equilibrium of this economy,
ative profitability of
profitability is
Z- augmenting technical change to
Vz/Vl given by
I
(dNLJdSj)
steady-state equilibrium condition
its relative cost.
The
rel-
relative
= Vz^VvlNI
^l
then:
is
rj^Ni7rL
Now
to equate the
(14), while the relative cost is
{dNz/dSz)
The
we need
= VzNl7rz:
solving condition (16) together with (12),
(16)
we obtain the equilibrium
relative
technology as
In
Acemoglu
here
I
(2001), I
show that the
equilibrirmi will
simply assume that this condition
is satisfied,
be stable as long as a
so
1
—
5cr
>
6^^,
and
0.
There are a niunber of important results that follow from equation
relative degree of
<
Z-augmenting technology simply depends on the
(17). First, the
relative supply of
Z. This captures both the price and the market size effects emphasized above, since in
equilibrium prices are also determined by relative supplies (from equation
in the case
when the
elasticity of substitution
between the two factors
is
(8)).
Second,
greater than
^"With existing data it is not possible to determine the extent of state dependence. In Acemoglu
I argued that results from the patent citations literature, e.g., Trajtenberg, Henderson, and
Jaffa (1992), suggest that there is at least some degree of state dependence in the innovation process.
(2001),
12
>
1, i.e., cr
in the relative supply of
an increase
1,
Z/ L leads to Z-augmenting
technical change. This
Greater relative supply of
effect.
this factor.
Z
Z
creates
is
Z
further.
demand curve for Z, which keeps Nz/Nl
endogenous-technology relative demand where
(11)), to the
With this piKpose,
greater
machines complementing
for
to illustrate the implications of the market size effect
constant-technology relative
is,
a consequence of the market size
more demand
This in turn increases the productivity of
One way
Nz/Nl- That
increases
compare the
to
is
constant (equation
Nz/Nl
is
given by (17).
substitute (17) into (11) to obtain the endogenous-technology relative
demand:
wz _ (rizy-'" /l-7\
^L
\VlJ
V 7 /
that with
relative
>
(J
demand
less
than
is flatter
This
for Z.
demand
increase the
Now
ETi
1,
demand
CT.
scarce.
Nz/Ni and
the
has become more abundant.
cr
<
1,
an increase
is
Z now
drawn
<
cr
in
the long-run relative
this
Nz/Nl
is
compare
(18) to (11)).
actually biased towards
Acemoglu, 2001). So irrespective of the
not equal to
it is
level,
in Figure 2 (again simply
a decline in
1,
reduces
the price effect dominates
Interestingly, however, the endogenoiis-technology relative
and the discussion
(as long as
supply of
in the relative
is
and new technologies are directed at the factor that has become
effect,
flatter, as
Because when
factor
raises
because, as pointed out above, changes in technology
is
for the factor that
Because with
1.
the market size
At some
straightforward to verify
Z/L
increase in
Nz/Nl, making technology more labor-augmenting. This
is still
It is
given by (18), ETi,
contrast the previous case to the one where the elasticity of substitution, u,
than
more
,^g.
demand curve
curve,
CT—the
1-*-
\L.
Figure 2 draws the endogenous-technology relative
together with the constant-technology
(Z\
'"*'
1, i.e.,
demand curve
is
as long as
is flatter
we
Z
demand curve
Why
is
this?
(see equation (11),
elasticity of substitution
are not in the
Cobb- Douglas
case),
than the short-run relative demand curve.
an application of the LeChatelier principle, which states that
demands become
flatter
when
all
other factors adjust (here these other factors
correspond to "technology").
But there
is
more to
surprisingly, the relative
this
framework than the LeChatelier
demand curve can be upward
13
principle.
sloping as
Somewhat
shown by ET2
in
Figure
This happens when
2.
a>2-8.
Intuitively, the increase in the relative
(19)
supply of Z raises the demand for ^-complementary
innovations, causing Z-biased technical change. This biased technical change increases
the marginal product of
Z
more than that of
labor,
and despite the substitution
effect,
the relative reward for the factor that has become more abundant increases. Inspection
of (19) shows that this can only
ative
demand
happen when a >
we need the market
curve,
of an upward-sloping relative
That
1.
size effect to
demand curve
first
for
an upward-sloping
be strong enough. The
it
will play
rel-
possibility
for skills is of interest not only to
strength of directed technical change, but also because
the
is,
show the
an important
role in
application of this framework below.
So we now have a micro-founded framework that can be used to study the direction
of technical change
biased. This
literature.
and to determine towards which
factors
framework also leads to an analogue of Result
Does
it
also capture the insights of the
new
1 of
technologies will be
the induced innovations
induced innovations literature related
to the behavior of the shares of capital and labor in
GDP? To
answer
this question, let
us look at the implications of directed technical change for factor shares. Multiplying
both
sides of equation (18)
sz
by Z/ L, we obtain
_wzZ _
relative factor shares as:
(r]zY-'- (l-l\^-'"
This equation shows that there
is
(Z\
1-*"
no reason to expect endogenous technical change
to keep factor shares constant. In fact, generally as
Z/L
changes
(e.g.,
due to capital
accimiulation as in the simple induced innovation model of Section 2), sz/sl will change.
However, factor shares
relevant, special case
ties frontier, that
is,
will be
where there
when
^
=
1
constant in an interesting, and perhaps empirically
is full
state dependence in the innovation possibili-
in terms of equation (15).
In this special case, the
accumulation equations take the familiar-looking simple form
Nl
-—
=
ij^Sl
and
14
Nz
-—
= rjzSz-
(21)
That
is,
sector,
research effort devoted to one sector leads to proportional improvements in that
and has no
effect
possibilities frontier
on the other
sector.
and multiplying both
Using this formulation of the innovation
sides of (11)
by Z/L, we now have:
^ = ^.
(22)
Hence, in this case, directed technical change works to stablize factor shares.
This
formulation of the iimovation possibilities frontier therefore leads to the second major
result, Result 2, of the
induced innovations literature, but with a micro-founded model
where firms maximize
profits
and with the caveat that
this result only obtains for
a
specific formulation of the innovation possibihties frontier.
Now
imagine that
Z
stands for capital as in the canonical model of the induced in-
novations literature. Capital accumulation
of the representative consumer.
given by the optimal consumption decision
is
Hence we have the Euler equation
^ = r-p,
where r
is
(23)
the interest rate, and capital accumulation
is
given by
Z = Y -C.
(24)
In steady state, equation (22) ensures that factor shares are constant. In addition, capital
accumulation, which follows from (24), implies that there will be labor-augmenting
technical change. This can be seen by
first
noting that the relative share of capital
is
given by
""'
sz
(l-l\^ fNzZ'
Sl
\
1
J
\NlL,
Inspection of this equation shows that this relative factor share can only remain constant
if
^
is
growing at the same rate as capital for worker, j. So technical change has to
be labor-augmenting. In
interest rate has to
(see
fact,
the result here
is
remain constant in the long
Acemoglu, 1999).^^
stronger than this: in steady state the
riin,
and so
Nz
has to remain constant
This model then predicts that the share of capital should
~ P) and to ensure balanced growth, the interest rate
^^ Briefly, the interest rate is r = PNzpJ
/ (1
has to be constant. Along the balance growth path, pz is constant, so Nz has to remain constant.
15
stay constant along the steady-state equilibrium, and technical change should be piirely
labor-augmenting.^^
Is this steady-state
a <
quires
6~^
.
we now have
6
equilibrium stable? Recall that in this framework stability re-
In addition, to ensure the constancy of factor shares in the long run,
=
1.
Therefore, as in Drandakis and Phelps (1965), stability requires the
elasticity of substitution to
duced irmovations
be
literature:
than
less
when
f^
1.
>
intuition
is
also similar to that in the in-
?^, the share of the
Z factor is sufficiently large
want to undertake Z-augmenting technical change.
that
all
new
technologies increases ^^ further, the
firms
The
economy
Therefore, for the steady state to be stable,
will diverge
If
the introduction of
away from steady
we need Z-augmenting
state.
technical change to
reduce the relative factor share of Z. This requires the two factors to be gross complements,
i.e.,
a
<1
(see
Acemoglu, 1999,
for details). Therefore, Result 3 of the
induced
innovations literature also follows from this more micro-founded framework.
I
next discuss
how the
directed technical change model, the
the induced innovation literature, sheds
Debate
4
1:
Why
Is
new
light
modern reformulation
of
on two recent debates.
Technical
Change
Skilled Bi-
ased?
Skill-Bieised Technical Chctnge
4.1
The
been
general consensus
among
labor and
skill-biased over the past 60 years,
macro economists
technical change has been favoring skilled workers
skills (the
my
model.
why we should
more than
number
^^The reader may notice one difference between the reasoning
innovations model and in
that technical change has
and most probably throughout the 20th century.
Figure 3 summarizes the most powerful argument for
a measure of the relative supply of
is
unskilled workers. It plots
of college equivalent workers
for constant factor shares in the
induced
In the induced innovations model, the constancy of the factor
shares follows from the requirement that there has to be steady capital accumulation.
equation
think that
consistent with different factor shares. In contrast, in
my model
Otherwise,
equation (22) implies
that "any technology equilibrium" has to give constant factor shares. Capital accumulation can then
be introduced into this framework, £is discussed briefly above and much more in detail in Acemoglu
(1999),
(4) is
and leads to the conclusion that
all
technical change has to be labor-augmenting.
16
divided by noncoUege equivalents) and a measure of the return to skills (the college
premium).^"'
shows that over the past 60
It
years, the U.S. relative supply of skills
has increased rapidly, and in the meantime, the college premium has also increased.
technical change
had not been biased toward
(and presuming that skilled
skilled workers
and unskilled workers are imperfect substitutes), we would expect a large dechne
returns to
On
skills.
the contrary, over this time period, returns to
The
the college premium, appear to have increased.
rapid increase in the supply of skills, the college
the
skill
Why
why has
bias of
it
is
become more
In the
first
skill
skill
is
this pattern to
an acceleration
explanation, technical change
it
sometimes
is
skill bias.
when
but
This approach can obviously
has enough degrees of freedom.
not a particularly attractive approach.
biased during the past 25 years, precisely
And
for
Moreover, according to this
the supply of
skills
skill-
has increased very
be viewed as a coincidence.
rapidly, has to
The second
explanation, interestingly, builds on another seminal paper by Phelps,
human
Nelson and Phelps (1966). Nelson and Phelps suggested that
are important for the absorption
for skills
And
skill-biased,
explanation the pattern whereby technical change appears to have become more
of the Nelson
in
biased over the recent decades? There are two popvilar
account for the patterns we observe, since
it
shows that despite the
biased throughout the 20th centru-y?
no theory for when we should expect more
this reason,
as proxied by
technologies.
has technical change been
explanations.
there
new
figure also
skills,
in the
premium has been increasing very rapidly
Most economists attribute
over the recent decades.
If
and Phelps model
and use of new technologies.
in the
(I
capital
and
skills
outline a simple version
Appendix). According to this view, the demand
has been increasing because there have been more (or more high-tech) new
technologies during the 20th century,
and perhaps because the
^^The samples are constructed as in Katz and Autor (2000).
I
rate of technical change
thank David Autor
for providing
me
with data from this study. Data from 1939, 1949 and 1959 come from 1940, 1950 and 1960 censuses.
The rest of the data come from 1964-1997 March CPSs. The college premium is the coefficient on
workers with a college degree or more relative to high school graduates in a log weekly wage regression.
The
relative supply of skills
18 and 65. It
is
is
calculated from a sample that includes
all
workers between the ages of
defined as the ratio of college equivalents to non-college equivalents, calculated as an
Autor, Katz and Krueger (1998) using weeks worked as weights.
17
has increased diiring the past 30 years. This explanation also has some drawbacks. First,
the original Nelson-Phelps model and
modern reformulations
its
(e.g.,
Greenwood and
Yorukoglu, 1997, Galor and Maov, 2000, Aghion, Howitt and Violante, 2000) are very
"reduced form"
intensive.
:
And
the adoption and use of
new
technologies
is
simply assimied to be
skill-
one can imagine new technologies simphfying previously complex
yet,
tasks, such as scanners.
Second, there are
many
historical
examples of skill-replacing
technologies, such as weaving machines, the factory system, the interchangeable parts
technology,
and the assembly
increase the
demand
I
will
for skills is
So the presumption that new technologies always
not entirely compelling.
next show that an approach based on directed technical change provides an
explanation for
became more
to be always
4.2
line.
why
technical change has been skill biased over the past century and
skilled biased over the past
and everywhere
skill
30 years, without assuming technical change
biased.
Directed Technical ChEinge and Skill
Consider the model of Section
3,
with
Z
Bicis^'^
interpreted as the
and L as the number of unskilled workers. Then, equation
bias of technology,
First,
number
of skilled workers,
(17) gives the degree of skiU
and leads to a number of interesting implications.
an increase
in the relative supply of skills will encourage the
skill-biased technologies.
Throughout the 20th century, the
increased very rapidly, both in the U.S. and in most other
development of
relative supply of skills has
OECD economies.
Therefore,
the framework here suggests that this increase in the supply of skills should have induced
new
technologies to
become more and more
Second, with the same reasoning,
degree of
skill
tion (19)
is satisfied,
curve for
skills.
bias of
skills.
when the supply
of skills accelerates,
we expect the
technologies to accelerate. Moreover, recall that
when
equation (18) traces an upward-sloping long-run relative
Therefore, the induced
pronounced that the
supply of
new
skill biased.
skill
skill
premium may
bias of
new
condi-
demand
technologies can be sufhciently
increase in response to a large increase in the
In fact, this model, together with condition (19), provides an attrac-
^*This material builds on Acemoglu (1998).
18
tive explanation for the behavior of the college
in Figure 3.
variables)
,
Because technology
it is
is
premium over the past 30 years shown
slow to change
reasonable to expect the
(i.e.,
are state
premium
to a large
response of the college
first
increase in supplies to be along the constant-technology
sponse to the increase in the supply of
Nz and Nl
because
returns to
skills,
demand
That
curve.
skills will initially
is,
in re-
dechne.
Then
once technology starts adjiisting, the economy will move to the upward-sloping long-run
demand
relative
curve,
and returns to
skills will increase sharply.
Figure 4 draws this
case diagrammatically.
Therefore, this theory can explain the secular
technical change has
become more
skill
bias of technical change,
biased during recent decades, and also
response to the large increase in the supply of
and then started a sharp increase
first fell,
skill
skills of
in the 1980s.
the 1970s, the college
Human
5.1
why
in
premium
^^
Debate 2: The Role of Human Capital
country Income Differences
5
why
in Cross-
Capitcd and Income Differences
There are large differences in human capital across coimtries. For example, while the average years of schooling of the population in 1985 was just under 12 in the United States
and
New
Zealand,
it
was
less
than 2 years in much of sub-Saharan Africa. Can these
differences in educational attainment
(more generally, human capital) be the proximate
or the ultimate cause of the large differences in income per capita across countries?
number
of economists, including Lucas (1988), Azariadis
Murphy and Tamura
emphasized the
growth
(1990), Stokey (1991),
role of
human
and Drazen (1990), Becker,
and Mankiw, Romer and Weil (1992), have
capital in cross-country differences in income levels
these effects be quantitatively large?
^^This framework also suggests a reason
may have been
skill-replacing.
why many
This
is
The
recent literature
on decomposing
technologies developed during the early 19th
because, during this time period, there was a large
increase in the supply of unskilled labor in British cities during that time period. See
for a
and
rates.
Can
century
A
more
detailed discussion.
19
Acemoglu (2001)
differences in
income per capita or output per worker across countries into
components concludes
tiiat
the answer
is
no.
Hall and Jones (1999) find that differences in
can accotmt
ical capital,
rest
due to
Both Klenow and Rodriguez (1997) and
human capital,
or even differences in phys-
only a fraction of the differences across coimtries, with the
for
differences in efficiency of factor use (or
me reiterate this
Let
different
somewhat
point
differently.
due to differences in "technology").
Figure 5 plots the logarithm of out-
put per worker relative to the U.S. for 103 coimtries against average years of schooling
The
in 1985.
ing.
In
figure
shows a strong correlation between output per worker and school-
the bivariate regression line plotted in Figure 5 has a slope coefficient of
fact,
0.29 (standard error 0.02)
and an R-square
appears that there could be a
ple calculation suggests that
lot in
it is
the differences in
To
human
difficult to rationalize
income as steeply as suggested by Figure
So
of 65 percent. ^^
in a regression sense,
capital.
However, a sim-
educational attainment raising
5.
—the increase
see this, note that the "private" return to schooling
ual earnings resulting from an additional year of schooling
Card, 1999)
—
is
(e.g.,
In the absence of human capital externalities, the contribution of a one-year
.
differences in schooling
come. More
in individ-
about 6-10 percent
increase in average schooling to total output would be of roughly the
But then
it
specifically,
deciles of the
can explain
little
same
magnitude.-'^
of the cross-country variation in in-
the difference in average schooling between the top and bottom
world education distribution in 1985
to schooUng around 10 percent,
is less
than 8 years. With the returns
we would expect the top
decile countries to
produce
about twice as much per worker as the bottom decile countries. In practice, the output
per worker gap between these deciles
So how could we
justify
human
is
approximately
15.
capital differences playing a
more important
role in
the world distribution of income? There are a number of possible avenues. First, formal
schooling
may be
is
only one component of
human
capital,
understating the true differences in
workers acquire
much more on-the-job
and
human
training in
differences in formal schooling
capital.
This could be because
some countries than
others, or because
^^Data on output per worker are from Summers and Heston (1991), with the Hall and Jones (1999)
from Barro and Lee (1993).
^^And if capital were in scarce supply, it would be lower.
correction. Education data are
20
the quality of schooling varies substantially across countries. There
truth to both of these points, but
undoubtedly much
appears unlikely that they can be the whole story.
it
who migrate
For example, workers
is
to the U.S. from other countries quickly converge
to the earning levels similar to those of U.S. workers with similar schooling, suggesting
that quaUty differences are not the major factor behind the differences in income across
Moreover, even without controlhng for education, these workers earn not
countries.
much less than
U.S. workers (certainly nothing comparable to the output gaps
across coimtries), so differences in output across coiuitries
we observe
must have more to do with
physical capital or technology differences (see Hendricks, 2001).^^
Second, perhaps the above calculation understates the importance of
because
it
human
ignores
capital externalities.
whole society benefits indirectly from the greater
After
all,
human
human
capital
quite plausible that the
it's
capital investment of a worker.
In fact, externaUties were the centerpiece of Lucas' (1988) paper which argued for the
importance of human capital differences, and have been a major building block
for
many
of the papers in the endogenous growth literature.
How
effect of
large
do hiuiian capital
human
relationship
externalities
capital differences
shown
justify a strong "causal"
on income differences consistent with the bivariate
A
in Figure 5?
need to be to
back-of-the-envelope calculation suggests that in
order to justify the magnitudes implied by Figure
5,
hiunan capital externalities need
to be very large.
The
social) returns to
education of approximately 34 percent (exp(0.29)
alternatively, the
comparison of the top and bottom decile countries implies returns
slope of the hue in Figure
on the order of 40 percent. To
externalities of 25-30 percent
5, 0.29, is
rationalize Figure 5,
we
consistent with (total or
—
therefore need
on top of the 6-10 percent private
1
~
0.34).
human
Or
capital
returns. In other words,
external returns created by education needs to be of the order of three to four times the
private retruns
What
human
is
—
^very large
capital externalities indeed!
the evidence? There have been a
capital externalities
'^ These
human
results have to
observed or unobserved
by exploiting
number
of studies attempting to estimate
differences in average schooling across cities or
be interpreted with some caution, since
skills
who
migrate to the U.S..
21
it
may be
workers with relatively high
states in the U.S. (e.g., Rauch, 1993). However, these studies face serioiis identification
problems. Cities with greater average schoohng
To
of other reasons.
also have higher
wages
for
a variety
solve this problem, one needs to find "quasi-exogenous" differences
Acemoglu and Angrist
in schooling across labor markets. In
attempted to do
may
this
and
(2000), Josh Angrist
by looking at variations in compulsory attendance laws and
I
child
labor laws in U.S. states between 1920 and 1960. It tiirns out that these laws were quite
important earlier in the centiuy in determining educational attainment, especially high
school graduation rates. For example,
strict child labor
we found that a person growing up
in a state with
laws was 5 percent more likely to graduate from high school than a
person growing up in a state with the most permissive child labor laws. Moreover, these
differences in laws
states.
do translate
into substantial differences in average
schoohng across
These laws therefore provide an attractive source of variation to identify human
capital externalities.
So how high are himian capital externalities?
found very small
Our
hmnan
Contrary to
1
is
required for
of the differences in
human
income per
capital to
symptom than
conclusion to draw.
more hne of
attack:
county adopts, and
level,
it is
human
how
capita.
differences across countries are
too early to
jump
effectively these technologies are
is
is
capital play a
developed in
the correct
is
one
effect
on income when they
interact
the insight that comes out of Nelson and Phelps (1966),
the induced innovations literature that
^^This point
more
being utilized. At an intuitive
discussed in the Appendix, and also follows from the
Can human
is
to this conclusion, since there
himian capital differences have a much larger
is
far
capital differences can affect the type of technologies that a
with technology choices. This
which
These are magnitudes
the cause of the differences in income? Perhaps this
But
0.
be a major ultimate or proximate cause
Are we then to conclude that himian capital
of a
from
or 2 percent (in other words, they imply plaiisible
externalities of the order of 20 percent of the private returns).
what
we
expectations,
capital externalities, often not significantly different
baseline estimates are around
short of
my
I
discvissed in Section 3 (see below).
much more important
my joint work
modern reformulation
^^
role in accounting for cross-coimtry
with Fabrizio Zilibotti (see Acemoglu and
22
of
Zilibotti, 2001).
income differences when
it
Although existing evidence does
interacts with technology?
not enable us to answer this question, there are a few pieces of evidence that suggest that
there might be something here. First, Benhabib
and Spiegel (1994) present cross-country
regression evidence consistent with this view. Second, there
with the notion that
human
productive technologies
is
micro evidence consistent
capital facilitates the absorption
and use of new and more
Foster and Rosenzweig, 1996).
Third, in Acemoglu and
(e.g.,
Zilibotti (2001), Fabrizio
and
I
undertook a simple calibration of a model with
technology mismatch and found that
differences in
Finally,
it
can account
income per capita with the differences
for
in
a large fraction of the actual
human
capital across countries.
a quick look at the cross-coiuitry data shows that there
between "technology" and human
skill-
is
a strong correlation
a measure of the relative supply
capital, especially,
of high him:ian capital workers. For example. Figure 6 plots the
TFP
measure
(relative
to the U.S.) calculated by Hall and Jones (1999) from a cross-country levels accounting
exercise against the ratio of college to
1985 (from Barro and Lee, 1993).
of
some other
on both
factors
countries as emphasized
noncoUege ratio of workers in the population
This correlation might of course
capital
it
by Hall and Jones (1999) and Acemoglu, Johnson and Robinson
suggests that a
and technology
so here instead
I will
the effect
variables, for example, institutional differences across
(2001), or the effect of higher (exogenous) productivity
Nevertheless,
reflect
in
is
more
on human capital investments.
careful look at the relationship
required. This paper, naturally,
is
between human
not the right forum for
this,
simply develop an alternative approach to analyze the interaction
between himian capital and technology based on the insights of the directed technical
change/induced innovations
5.2
literature.
Directed Technical Change, Appropriate Technology and
Human Capital
The notion of directed
OECD countries,
technical change implies that
which are often used by LDCs,
new technologies in the U.S.
will
be designed to work best with the
conditions and factor supplies in these technologically
these nations are
more abundant
in
hvunan
23
or in the
more advanced
nations. Because
capital, frontier technologies
they develop
Lack of
will typically require highly skilled workers.
making
create a technology-skill mismatch,
it
skilled personnel in
difficult for
LDCs
these countries to benefit from
frontier technologies. In other words, these technologies will be, at least to
LDCs' needs. This
"inappropriate" to the
directed technical change model, but
then
will
insight follows
some
degree,
from an application of the
also quite related to the insights of Nelson
is
and
Phelps (1966).
To develop
these ideas
world economy.
the technologies
copy these.
more
model of Section 3 applied to a
A technology leader that 1 refer to as the North,
Nz and
e.g.,
the U.S., produces
Nl, while the other countries, the South or the LDCs, simply
For simplicity,
I
take
workers and Z' skilled workers.
abundant
formally, consider the
A
all
LDCs
of the
key characteristic of the
than the North, that
in skilled workers
to be identical, with L' unskilled
LDCs
is
that they are less
is:
Z
Z'
Assume that LDCs can copy new machine
varieties invented in the North, with-
out paying royalties to Northern technology monopolists because of lack of intellectual
property rights. This assumption implies that the relevant markets for the technology
monopolists will be given by the factor supplies in the North.
of producing machines in the
LDCs may be higher,
in the North. This cost differential
may
result
1
also
assume that the cost
k~^/^^~^^ rather than
from the
-0
=
(1
fact that firms in the
—
/?)
as
LDCs do
not have access to the same knowledge base as the technology monopolists in the North.
I
also
all
assume that there
machines
will sell at
is
free entry to
copying Northern machines. This implies that
marginal cost in the LDCs, that
natural to think of k as less than
than in the North. Finally, there
1,
is
is,
at the price k'^^^^''^^ It
so that machines are more expensive in the South
no international
trade.
Using the above expressions, we obtain the output
levels of the
two
final
the North as:
yL
=
while in the LDCs,
Y^ [PLf-'^" NlL and Yz^^^ {p^f-^^'^ N^Z,
we
is
have:
24
goods in
where p"s denote
prices in the
LDCs, which
proportions are different and there
from those in the North because factor
differ
no international
is
trade.
The parameter k
features
in these equations since machine costs are different in the South. Notice also that the
technology terms,
Nl and Nz,
are the
same
as in the North, since these technologies are
copied from the North.
The
income in the South to that
ratio of aggregate
I
in the
North can be written
+
(1
-
7 (pt'^'N^L)-^ +
(1
- 7) [vr'"'NzZ)-
7 {{P'^i'-'"' N,L')-^
7) {{P'zf-'"'
NzZ')
K
(25)
Simple differentiation and algebra show that
dY'/Y
Since Z' /L'
< Z/L,
(i.e.
(see
(26)
this expression implies that
Nz/Nl
when a >
raises the
1, i.e.,
skilled workers, there will
technologies are less and less appropriate to the needs of the
What
number
of skilled workers to
make
best
LDCs
iise
be a tendency
Intuitively, these
LDCs who do
new
not have a
^°
of these technologies.
are the implications of directed technical change for income differences across
countries? Equation (26) shows that a greater
income gap between
skill
the two factors
income gap between the
income gap between the North and the South to increase.
sufficient
when
reduces Y' /Y). This implies that as technologies produced by the
North become more and more directed towards
for the
Acemoglu, 2001):
fN^
are gross substitutes, an increase in
and the North
as:
rich
skill
bias of technology will increase the
and poor countries (between countries with
different levels of
abundance). Directed technical change implies that technologies developed in the
when cr < 1, an increase in Nz/Nl narrows the income gap since the term in square
is now negative. However, when cr < 1, a lower Nz/Ni increases the demand for Z
relative to the demand for labor
that is, it corresponds to Z-biased technical change. Moreover, in
this case, the North, which is more abundant in Z, will invest in technologies with lower Nz/Nl than
^"in contrast,
brackets in (26)
is
—
appropriate for the South. In other words, exactly as in the
"too
skill- biased"
technologies, since with
cr
<
1,
lower
Nz/Nl
ceise
with
cr
>
1,
the North will choose
corresponds to greater
skill bias.
This
extends the results in Acemoglu and Zilibotti (2001) to a slightly more general model, and also more
importantly, to the case where the two factors are gross complements, i.e., a < 1. See Acemoglu (2001)
for
a more detailed discussion.
25
OECD
U.S. or the
will
be catered to their own needs, so
than woiild have been otherwise. As a
tjrpically
result, directed technical
more
change
skill
biased
will increase the
income gap across countries.
To gain
further insight, consider a special case with
derived as an equilibrium of a
Zilibotti, 2001),
(25)
is
more
detailed
and suppose that 5
=
in
=
cr
2 (this
model with many
terms of equation
was the case that was
sectors in
(15). In general,
complicated because domestic prices in the North and the South
on domestic
factor supplies
and world technology. However
Acemoglu and
differ
in the case with
equation
depending
cr
=
2, (25)
simplifies to
/ 7i(L-)-/-
Y'
+ (l-.)i(t^')'^V
U«(i)"' + {l-7)*(t2)"V
This expression shows explicitly that the extent to which
less
developed country can take
advantage of new technologies depends on the number of skilled workers.
few skilled workers
this technology
is
will
have
difficulty
adapting to the world technology, especially
highly biased towards skilled workers,
develop this point further, note that
A country with
when a
=
2
and
5
=
i.e.,
0,
when Nz/Nl
is
when
high.
To
the endogenous technology
equation (17) implies
Substituting this into (27)
where 7o
South
much
is
will
we
obtain:
a suitably defined constant. So the income gap between the North and the
depend on the himian capital gap between the North and the South, very
as in Nelson
and Phelps (1966).
It is also instructive at this
point to compare this approach based on endogenous
technology choice to Nelson and Phelps' original contribution. Despite the similarities,
there are also a
number
of important differences between this approach based on the
idea of directed technical change and appropriate technology, and the Nelson and Phelps'
26
approach.
The
first
difference
son and Phelps (1966),
human
is
more apparent than
real.
It
all
same technology
countries have access to the
not be differences in TFP/technology. This conclusion
TFP
differences are calcvilated as a residual
tween human
that
Y =
that in Nel-
capital differences translate into technology differences,
whereas in the simple version of the model of Acemoglu and
outlined here,
may appear
capital, physical capital
K-^^ {AHf-^'^, and A, the
presence of technology-skill mismatch as in
term,
it is
with Fabrizio
should
typically assiuned
Zilibotti,
TFP. Therefore,
human
I
specific relationship be-
calculated as the residual.
is
of hiunan capital on output will be counted as part of
differences in output per worker or
frontier, so there
particular,
my model
discussed here and in Nelson and Phelps (1966),
which
not correct, however, because
from assimiing a
and output. In
TFP
is
Zilibotti (2001)
In the
the effect
both the model
in
capital differences contribute to
income per capita because of
their interaction
with
technology adoption and the efficiency of technology use.
The second
difference
between the approaches
is
more
Inspection of
interesting.
equation (30) from the Nelson-Phelps model given in the Appendix shows that
capital should matter
more when the growth rate of the world technology,
contrast, (27) (or less transparently, (25))
when new technologies
are
human
g, is greater.
In
shows that human capital should matter more
more skill-biased. This
is
an interesting area to
investigate.
A
recent paper by Easterly (2001) finds that low himian capital countries lagged especially
behind the richer countries over the past 25 years. Interestingly, this period has been
one of slow world growth, so according to Nelson-Phelps' view, these low hrrnian capital
countries should have benefited relative to the technology leaders.
the past 25 years have also been characterized by very rapid
which suggests that, according to the model
in
could accoimt for this pattern, and more work
of these issues.
27
skill- biased
Acemoglu and
capital countries should have lagged further behind.
is
On
But of
the other hand,
technical change,
Zilibotti (2001),
course,
many
low
human
other factors
required to get a better understanding
Conclusion
6
This paper revisited the induced innovations Hterature of the 1960s to which Phelps was
a major contributor (Drandakis and Phelps, 1965).
This literature provided the
first
systematic study of the determinants of technical change, and also investigated the relationship between factor prices
of this literature based
on the
reformulation confirms
many
reveals a
at
new
force, the
more abundant
and technical change.
tools developed
I
presented a
by the endogenous growth
what
is
literature.
This
of the insights of the induced innovations literatiire, but
market
size effect: there will
be more technical change directed
factors.
This modern reformulation sheds light on two recent debates:
often skill biased,
modern reformulation
and why has
the role of
human
it
become more
skill
biased during recent decades?
capital diff"erences in accounting for
countries? Interestingly, an application of this
why is technical change
And
income differences across
modern reformulation to these important
debates also reiterates some of the insights of another important paper by Phelps, Nelson
and Phelps (1966). Despite the
similarities, there are also different implications of the
Nelson-Phelps approach and those of an approach based on the direct technical change
model.
To
investigate these differences empirically appears a fruitful area for future
research.
28
Appendix: The Nelson-Phelps Model
7
I
now
a version of the second model of Nelson and Phelps (1966).^^
briefly outline
Imagine that there
a world technology
is
frontier,
T {t),
advancing at an exogenous rate
9, i-e.,
T{t)
= T (0) exp {gt)
Countries can benefit from this world technology by incorporating
But
tion processes.
this
is
into their produc-
it
a h\maan capital-intensive task. For example, a country needs
highly skilled engineers to adapt world technologies to their conditions, to
sitions in the
these
new
coimtry
where
j,
hj
is
(t),
So Nelson and Phelps (1966) postulated that the technology of
would evolve according to the
human
the
their equation (8')).
Aj
{t)
A,
it)
human
first
A,
is its
'
^
it)
which
is
assumed to be timing variant
rate of progress.
Most
to be absorbed.
capital of a country
graduates, or engineers, or
The
equation
This equation states that the farther a country
be years of schooling,
hj can
diff'erential
ct>{hj){Tit)-Aj{t))
more technology out there
is
the greater the
^
capital in country j,
technology frontier, the faster
because there
key po-
implementation of these technologies and to train workers in the use of
techniques.
Aj
fill
is,
from the world
would be
>
so that,
But
also
(j)'
(hj)
the faster will this convergence be. Here
some other feature of the human
is
(see
plausibly, this
or the fraction of high skilled individuals,
implication of (29)
is
^
such as university
capital distribution.
that
d%
it)
I A,
(i)
'
dT{t)d(t>{hj)
so that
human capital becomes more valuable when technology is more
the reason
why
demand
Greenwood and Yorukoglu,
for skills to the
1997, Galor
Violante, 2000).
21
is
number
of
the Nelson-Phelps approach has provided the foundation for a
recent papers hnking the
(e.g..
advanced. This
See also Shultz (1975) and Welch (1970).
29
speed and extent of technical change
and Maov, 2000, Aghion, Howitt and
Second, note that although equation (29)
is
in terms of technological progress,
does have a unique stable stationary distribution as long as
In the stationary state,
all
cross-country distribution
is
Aj
(^)'s will
grow
at the
same
(l){hj)
rate g,
>
for all countries.
and
this stationary
given by
^.W = -T%rT^(^)9 + <p{hj)
Suppose now that output
in each country
then implies that countries with low
absorb
less of
human
is
human
across countries can be
capital to output,
more important
proportional to Aj
(30)
(t).
Equation (30)
capital will be poor, because they will
the frontier technology. This effect
contribution of
it
is
in addition to the direct productive
and suggests that human capital
in causing
income differences than calculations
based on private returns to schooling might suggest.
30
differences
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Political
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Instantaneous rate
of output growth
The innovation
possibiHties
frontier
Nk/Nk
Figure
1:
Equilibrium in the induced innovations model. Point
equilibrium with capital accumulation.
35
B
corresponds to the
Wz/Wl
ET2~endogenous
technology demand.
ET, —endogenous
technology
demand
CT— constant
technology
demand
Z/L
Figure
2:
Constant-technology and endogenous-technology relative
36
demand
curves.
o College
wage premium
J
I
A Rel. supply of college skills
J
I
L
- .8
.6
-
w
E
-
.6
!2
w
0)
E
.5
(D
-
O)
0)
a
0)
- .4
O)
CD
o
o
o
^
>.
D)
a
a
.4
-
W
O
- .2
o
.3
-
-
Relative Supply of College Skills and College
Figure
3:
Relative supply and relative
demand
Premium
for college skills in the U.S. labor
market
1939-1996, author's calculations from Census and Current Population Surveys data.
37
Relative
Wage
Long-run Rel Wage
Initial
Rel
Long-run
demand
Wage
relative
for skills
Short-run
Response
Exogenous Shift
Relative Supply
Figure
4:
supply of
Short-run and long-run response of the
skills.
38
skill
in
premium
to an increase in the
Figure
1
USA
ITA
UKG is^Jft^
Aufl©?
SPA
SGF
HKqRE
>
DEN
J5N-^
VEN
SYIJorMEX
ARG^
Brag
^**^"
KOR
POR
ALG,^^BRA
>
^^i^^G
URS
HUN
COL M
^^J^^^
EGY
SMt^^^-^ft
0)
-2-
o
PHL
^.--^^ IDN
^-^^^
PAp^^iM
2BW
Q.
^^^j^
Q.
^^^
NGHMB
O
CZE
SRL
MigJHOfraM
P8KN
L_
PAN
GUY
ROM
IND
LES
CHN
ZAM
D)
O
^°*brmmlw
1
1
1
1
1
1
10
years of schooling
Figure
5:
Cross-country relationship between years of schooling and logarithm of output
per worker. Data from Barro and Lee (1993) and Hall and Jones (1999).
39
NZE
TFP
Hall
Jones
(log)
*
ITA
SGpSfil^^^^
0BAN
M^Gp^^ ^mC^^FIN,,;;^
ARG J^eSWiyzE
COLugfeKKOR
IRN
SLE
USA^^
y^^
PAK
REU
SWZ
1
SRL
-
SEN^
^
RW/PEN^^
MOZ
GMB
PAIS
IND
JAM
MAtr
LES
^
2
-
CAF
MLW
P§i
pHL
ROM
m^^^
NGR
N?C
"UN
GUY
BRM
TOG
CHN
ZAM
-3
1
1
1
-6
1
-2
Ratio of college to non-college
Figure
6:
Cross-coimtry relationship between the ratio of college graduates to non-college
graduates and total factor productivity. Data from Barro and Lee (1993) and Hall and
Jones (1999).
40
1
6Sk'5
no6
Date Due
Lib-26-67
MIT LIBRARIES
3 9080 02246 2227