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working paper
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of
economics
TFP DIFFERENCES
Daron Acemoglu
Fabrizio Zilibotti
No. 98-15
September 1998
massachusetts
institute of
technology
50 memorial drive
Cambridge, mass. 02139
WORKING PAPER
DEPARTMENT
OF ECONOMICS
TFP DIFFERENCES
Daron Acemoglu
Fabrizio Zilibotti
No. 98-15
September 1998
MASSACHUSETTS
OF
TECHNOLOGY
INSTITUTE
50 MEMORIAL DRIVE
CAMBRIDGE, MASS. 02142
MASSACHJSetfSliSTITUTE
OF TECHNOLOGY
LIBRARIES
First Version:
August 1998
This Version: September 1998
TFP
Differences*
Daron Acemoglu^
Fabrizio Zilibotti*
Abstract
We suggest
tivity.
Many
a possible explanation for cross-country differences in total factor produc-
technologies used by
are designed to
make optimal use
LDCs
are developed in
OECD
economies, and as such,
of the skills of these richer countries' workforces.
some
Due
to
by skilled workers in richer
be carried out by unskilled workers in the LDCs. Since the technologies in
these tasks are designed to be used by skilled workers, productivity in LDCs will be low.
Even when all countries have equal access to new technologies, this mismatch between
skills and technology can lead to sizable differences in total factor productivity, in the
differences in the supply of skills,
economies
of the tasks performed
will
order of 40 to 70 percent of the variation
we observe
in the data.
Our theory
also suggests
that the trade regime and the degree of intellectual property right enforcement in
have an important
on productivity
JEL
effect
on the type of technologies developed
in richer
LDCs
economies and
differences.
Classification: F43, 014, 034, 047.
Keywords: Development, Directed Technical Change,
Intellectual
Property Rights,
Skills,
Technology, Total Factor Productivity.
We
Ventura
thank Chris Mazingo and Marcus Salomonsson
for
comments. Acemoglu acknowledges
for research assistance,
financial support
from
NSF
and Josh Angirst, Jonathan Temple, Jaume
Grant SBR-9602116.
NBER and CEPR. Address: Department of
MA 02142-1347. Ph.: (1) 617 253 1927; fax: (1) 617 253 1330;
'Daron Acemoglu: Massachusetts Institute of Technology,
Economics, E52-371, MIT, 50 Memorial Drive, Cambridge,
e-mail: daron@mit.edu.
^Fabrizio Zilibotti: Institute for International
Economic Studies and CEPR.
Address: Institute for Inter-
national Economic Studies, Stockholm University, S-106 91 Stockholm, Sweden. Ph.: 46-8-16 22 25; fax: 46-8-16 14 43;
e-mail: zilibotti@iies.su.se;
web
page: http://www.iies.su.se/data/home/zilibott/homepage.htm.
Introduction
I.
Most economists view technological
parities in per capita
differences as
income across countries
(e.g.
an important part of the large
dis-
Romer, 1993; Prescott, 1998). This
view receives support from a number of recent studies, such as Klenow and Rodriguez
(1997), Caselli et
tor productivity
technology are
al.
(1997),
(TFP)
and Hall and Jones (1998), which
Large cross-country differences in
differences across countries.
difficult to
find significant total fac-
understand, however. Ideas, perhaps the most important ingre-
dient of technologies, can flow freely across countries,
by
technologies, can be imported
less
motivated papers such as Mankiw,
and machines, which embed better
developed countries. This compelling argument has
Romer and Weil
(1992), Chari,
Kehoe and McGrattan
Rogerson and Wright (1998) and Jovanovic and Rob (1998) to model
(1997), Parente,
cross-country income differences as purely driven by differences in factors rather than in
technology.
In this paper,
even when
approach
is
we
that
many
are imported from
make optimal use
technologies,
an explanation
is
TFP
for cross-country
differences
The
same technology.
countries have access to the
all
North, which
offer
which applies
center-piece of our
technologies used by less developed countries (LDCs/the South)
more advanced countries (the North) and,
of the prevailing factors
more abundant
and conditions
as such, are designed to
in these richer countries.
The
in skills, tends to develop relatively skill-complementary
and these are only of limited use to the countries in the South.
The main
result of our
paper
developed in the North and the
is
skills
that,
due to the mismatch between technologies
of the South's labor force, there will be
TFP
differ-
ences between the North and the South, even in the absence of any barriers to technology
transfer.
The South must use
unskilled workers in tasks performed by skilled workers in
the North. Since the technology imported from the North
skilled workers
not suited to the needs of un-
performing these tasks, the South will have low TFP, even after controlling
for the contribution of
Figure
is
1 plots
human
capital to output.
TFP
(the logarithm of) the level
in 1985 calculated
by Klenow and
Rodriguez (1997) and the ratio of college graduates to non-college graduates in a sample
of 96 countries (data details in Section
between the relative supply of
skills
positive correlation is encouraging for
III),
and points to a high
and TFP.
1
Though not a
positive correlation
test of
an approach attempting to explain
with differences in the relative supply of
skills.
2
It
our theory, this
TFP
differences
might be more important, however,
producing countries and Trinidad, an outlier, the R2
increases to 0.59. One standard deviation increase in H/L is associated with an increase in the TFP level
of 21%. Similar results are obtained using TFP measures from Hall and Jones (1998).
2
The TFP measures control for the contribution of human capital to output, so there is no mechanical
1
The
R2
of the regression
is
0.53.
Excluding
oil
.036099
£
r
c
o
a
o
J
.967086
-6.90675
'
Logarithm of H/L
Figure
1:
TFP
Ratio of College Graduates to Non- College Graduates.
vs.
to investigate whether the
model
of
its
By
mechanism we propose can be quantitatively
gives a simple expression for the
TFP of a country relative to the U.S.
ratio of skilled to unskilled workers
and the equilibrium
choosing this equilibrium bias to match the U.S.
skill
as a function
premium, we perform a simple
by our model are sizeable
approximately between 40 and 70 percent of the
for
Our
skill-bias in U.S. technology.
calibration. This exercise suggests that the differences predicted
and can account
significant.
TFP
differences
observed in the data.
A number of other interesting results also follow from of our analysis.
First,
LDCs
are
predicted to have productivity levels comparable to advanced economies in very unskilled
and very
skilled sectors
most complex
tasks,
and
tasks,
medium
but lower productivity in
even very skill-scarce
LDCs
have to use
skilled tasks. In the
skilled workers.
These
skilled
workers can use the skill-complementary technologies developed in the North and achieve a
high level of productivity. In contrast, there will be large productivity differences in sectors
where workers are
skilled in the
North but unskilled
in the South, since the technologies
are not developed for the unskilled workers in these sectors. This pattern receives
some
support from the casual observation that there are pockets of efficient high-tech industries
such as software programming in India.
Second,
there
is
sectors
we show that
international trade reduces
factor price equalization,
where technology
is
TFP
TFP
differences. In particular, if
differences disappear because
LDCs
specialize in
appropriate to unskilled workers. Therefore, the
commonly
between TFP and the ratio of college graduates. Nevertheless, part of the correlation may be
due to the fact that the productivity of skilled workers is underestimated. Also countries with high
productivity may choose to invest more in education, contributing to this correlation (e.g. Bils and
Klenow, 1998, for a discussion of these issues).
relation
held view that in a world with free access to
differences
correct
is
price equalization
is
less
there
is
free trade
and
technologies there will be no
factor price equalization.
generally found not to hold, however, our
developed countries.
model suggests that
Interestingly, despite reducing
GDP divergence.
international trade causes
TFP
Since factor
be widespread even when technology and ideas can flow
differences should
advanced to
if
new
TFP
freely
TFP
from
differences,
Trade reduces the prices of unskilled goods in
the North, and discourages investment in unskilled technologies, which were those most
beneficial to the South.
skilled workers,
As a
result, trade increases the relative productivity
and widens the output gap between poor and
and pay of
rich countries.
Third, intellectual property rights are an important determinant of technological
When
development.
such property rights are enforced internationally, firms in the North
have more incentive to develop technologies suited to the
However, each
less
skill
requirements in the South.
developed country individually benefits from not enforcing these rights,
creating a potential for a classic Prisoner's Dilemma.
Finally, our theory suggests
and GDP.
a stylized pattern of cross-country convergence in
A less developed country diverges from the technological leader when it chooses
to use local technologies for which there
some
TFP
point,
and cross-country
TFP
is
no R&D, but
and income
this process necessarily stops at
differences tend to
become
stable as the
LDCs start importing the leading technologies developed in the North. On the other hand,
TFP
(and income) convergence occurs when a country improves
its skill
base relative to
the North, which concurs with the experiences of Korea and Japan (see for example, Rhee,
Ross-Larson and Pursell, 1984; Lockwood, 1968).
The two
building blocks of our approach, that most technologies are developed in the
North and that these technologies are designed
for the
needs of these richer economies,
90% of the R&D expenditure in the world is carried
35% in the U.S.. 3 Moreover, many of the technologies
appear plausible. For example, over
on
in
OECD
economies, and over
developed over the past twenty years in the U.S. and the
OECD
appear to be highly
skill-complementary and substitute skilled workers for tasks previously performed by the
unskilled (e.g.
Katz and Murphy, 1992; Berman, Bound and Machin, 1998). So
perhaps not be surprising that there are
in unskilled workers,
skills.
This has led
many examples
,
should
of developing countries, abundant
which adopt labor-saving technologies requiring specialized technical
many development
economists, like Frances Stewart (1977, p.
to conclude that "...the technology Third
inappropriate"
it
which
is
World countries gets from
xii),
rich countries
is
consistent with the approach in this paper.
A number of other papers have emphasized the difficulties in adapting advanced tech3
of
Authors' calculation from
GNP, and we
UNESCO (1997). UNESCO (1997) gives R&D expenditure as a percentage
OECD share using the Summers and Heston (1991) data on GNP.
calculated the
LDCs. Evanson and Westphal (1995) suggest that new technoloamount of tacit knowledge, and such knowledge cannot be transferred,
nologies to the needs of
gies require
a large
thereby slowing
down
propriateness" of technology has also received
Atkinson and
The importance
the process of technological convergence.
Stiglitz (1969)
some
attention, for
of "ap-
example Salter (1966),
and David (1974). Diwan and Rodrik (1991) use some of
the insights of this literature to discuss the incentives of Southern countries to enforce
we do
intellectual property rights, as
the appropriate technology literature
and
of Atkinson
Stiglitz
Basu and Weil
is
important recent contribution to
(1998),
who adopt
the formulation
whereby technological change takes the form of learning-by-doing
and influences productivity
at the capital labor ratio currently in use (see also
Basu and Weil characterize the equilibrium
1998).
An
in Section V.
Temple,
world where the
in a two-country
less
advanced economy receives productivity gains from the improvements in the more advanced economy. Our paper
differs
from Basu and Weil, in particular, and the rest of the
appropriate technology literature, in general, in a number of ways. First, what matters in
our theory
not capital-labor ratios (as in Atkinson and Stiglitz and Basu and Weil) or
is
size of plants (as in Stewart),
but relative supplies of
skills,
which we believe to be more
important in practice. Second, our results do not follow because productivity depends on
the exact capital-labor or skilled-unskilled labor ratios in use, but because skilled workers
use different technologies than unskilled workers, and in the North skilled workers per-
form some of the tasks performed by unskilled workers in the South. Third, and perhaps
most important, technological change
but a purposeful
is
activity. In particular,
not an unintentional by-product of production,
R&D
firms in the
towards different technologies depending on relative
from the
fact that the relative
novations. In this respect, our
abundance of
model
is
Finally, there
fer, for
as
now a
large literature
example, Vernon (1966),
Batiz and
Some
is
Romer
(1991),
Krugman
its
Acemoglu
implications for
more
(1987), Feenstra (1991)
over, in our model, trade affects
GDP
however,
is
levels,
which models
wage
inequality.
on innovation, imitation and technology
(1979),
Grossman and Helpman
traditional
and Young (1991), obtain the
TFP
and
not long-run growth.
GDP
(1991), Rivera(1997).
result that trade
is
economy
may
very different. More-
in opposite directions,
The most important
that these papers do not analyze an
trans-
models of trade and innovations, such
reduce the growth rate of less developed countries, but the channel
relative
(1998),
Eaton and Kortum (1997) and Barro and Sala-i-Martin
of these models, as well as
Krugman
our results originate
the North induces "skill-biased" in-
closely related to
on
direct their innovations
profitability. All
skills in
directed technical change, but primarily focuses
North
and
difference
affects
only
from our work,
in which technological knowl-
edge flows freely across countries, and they do not allow technical progress to be directed
towards different
levels of skills.
The plan
of the paper
Section
as follows.
is
II
introduces our basic model and
North and the South
characterizes the equilibrium in the
in the
absence of commodity
trade and intellectual property rights in the South. Section III shows that
is
higher
North than the South and performs a simple calibration of our model to see to
in the
what extent the model can explain the
and
technical change,
It
TFP
TFP
and income
shows that trade eliminates
V
Section
TFP
TFP
IV analyzes
variations in the data. Section
differences in
a world with commodity trade.
differences but leads to further
income divergence.
analyzes the impact of property rights enforcement in the South on technical
change. Section
VI endogenizes
skill
acquisition decisions
and shows that improvements
TFP
convergence, and Section VII
in the relative supply of skills in the
LDCs
lead to
analyzes the choice between local and imported technologies in the South. Section VIII
concludes, while
Appendix
additional results,
is
A contains the main proofs.
available
upon
Appendix B, which contains some
request.
II.
The Basic Model
A.
Countries, Agents and Preferences
We consider a world economy consisting of two groups of countries.
advanced country which we
which we
refer to as the South.
to be identical.
sizes, is
call
What
that
H
n
n
/L >
New
H
s
/L s
,
To
simplify the analysis,
H
s
skilled workers
so the North
is
we assume
H
n
skilled
and
perform no
R&D.
new
more abundant
technologies, as
we
their relative
Ln
workers and
unskilled
We
Due
to the
market
will see shortly, countries in the
size effect
South
All technological progress will therefore originate in the North.
an extreme assumption, but helps to
emphasized in the previous
clarify
how TFP
assume
in skills.
South can adopt these technologies without any impediments or
factors
one large
Southern countries
U unskilled workers.
technologies are developed using final output.
in the creation of
all
and the South, other than
The North has
skills.
workers, whereas the South has
is
the North, and a set of small less developed countries
distinguishes the North
the abundance of
There
differences
This
costs.
is
will
But the
obviously
can occur without other
literature.
oo
All consumers have linear preferences given
by / Ce~ rt dt where
C
is
consumption
interest rate.
We suppress
,
o
and r
is
the discount rate, which
is
assumed to be equal to the
time indexes when this causes no confusion.
>
Technology
B.
We
first
describe the production technology which
is
common
across countries.
The
equations in this and the next subsection therefore apply both to the North and the South,
and we omit the country indexes. Consumption and investment come out of an output
aggregate,
C + I + X<Y = exp
hxy(i)di
/
(1)
Jo
where /
of the
investment in machines, and
is
X
expenditure on
is
consumption aggregate in each period to
y(i)
l
kL {i,v) -Pdv
\
Jo
Good
1.
f
[(l-i).l(i)f+
z
i is
produced
N"
kn(i,v)
/
1-3
p dv
this
(i.e.
sector
is
and
as:
[i-Z-h(i)]
p
,
[0,
machines j €
Nh] used with
[0,
take the form of increases in
of machines that can
skill-specific capital).
skilled workers.
Nl and Nh,
in sector
There
is
i
together with workers of
a continuum of machines,
that
is,
skilled workers.
(see also
This
is
similar to the
Grossman and Helpman,
1991), but
Acemoglu
(1998).
that each good can be produced by skilled or unskilled workers,
The terms
using the technologies suited to their needs.
(1
— i) and
imply, however, that
i
unskilled labor has a comparative advantage in producing goods with low indexes.
1
Jo h(i)di
Z
will
technical change expands the range
allows for technical change to be skill-or labor-complementa / as in
(2) also implies
economy
Technical progress in this
be used with unskilled and
expanding variety model of Romer (1990)
parameter
(2)
N£\, that can be used with unskilled workers, and a continuum of
denoted by j £
Equation
the price
Jo
where kz (i,v)is the quantity of machines of type v used
skill level
R&D. We normalize
enables a positive
skill
premium.
The
Feasibility requires that /q l(i)di
<L
and
wL
and
%,
1
< H.
Producers of good
and the rental
G
i
[0, 1]
take the prices of their products, p(i), wages,
prices of all machines, Xl( v )
and Xh( v )>
^ given
>
and maximize
profits.
This gives the following sectoral demands for machines:
=
[{l-0)-P®-{{l-i)'l(i)) P /xM]'
kH (i,v)
=
[(l-P)-p(i)-(i-Z.h(i))e/xH(v)}
1
that
(technology) monopolist
it
also
owns the patent
owns machines and rents them out to
and investments
owning the patent to a machine v
demand
for
machine v
for skill
(3)
l/P
A
depreciate at the rate 8
olist
1/0
kL (i,v)
for
each type of machine.
users at the rental rates Xzi v )-
K
z (v)
time
0.
assume
Machines
in machines are reversible. Consider the
for skill class z, invented at
type z as
We
monop-
Define the total
= $ k(i, v)di. The monopolist
chooses an
investment plan and a sequence of capital stocks so as to maximize the present discounted
6
value of profits, as given by
K
to
z
—
{v)
Iz {y)
— 8Kz {u) and
we have suppressed time
assumed to be constant;
when the
at the time
Vz {v) = J™ e~
variety v
-
Xz {v)Kz (v)
demand
9Iz (u)) dt
- 6KzQ {v),
constraints given
by
subject
where
(3),
denotes the marginal cost of machine production,
the quantity of machines produced by the monopolist
is
is
[
to the set of
indexes.
K® (y)
rt
invented (in this case, at time
0);
and lz {y) denotes gross
investment.
Since (3) defines isoelastic demands, the solution to this program involves
XzW) —
+
assume 9
K
=
z (u)
K
z
=
{y)
same quantity
all
—
£)/(!
P)i tna t
i
s
>
a^ monopolists charge a constant rental rate, equal
mark-up over the marginal cost times the
to a
We
@( r
—
(1
—
2
/5)
K
+ 6), so that x = (1 — 0)I^v) — 8Kz {v) = 8KZ that
/(r
and
z
interest rate plus the depreciation rate.
,
Profit-maximization also implies
is,
each monopolist rents out the
of machines in every period. Notice also that
machines produced
Vz (u) = VZ
for all v, that is
type z are equally profitable (though this profitability can
for skill
change over time).
Substituting (3) and the machine prices into (2),
y(i)
= plif-WP
,
NL
- .*)
(1
•
l(i)
+p(i)(
we obtain
1
-W -Nff-i-Z-
h(i).
Therefore, increases in iV# (Nl) improve the productivity of skilled (unskilled) workers
in all sectors.
R&D
A^
and Nl are the only state variables of
(in the
technical change
this
economy.
We
North) leads to increases in the range of machines.
is
directed, in
skill-complementary
is
the sense that the degree to which
new
assume that
technologies are
determined endogenously (see Acemoglu, 1998). Some firms im-
prove technologies complementing unskilled workers, while others work to invent
complementary machines.
Nz =
In particular,
<j>
(Xz /Nz )
X
resources (final output) devoted to improve the technology of
that there
sector,
is
z
where
X
R&D
effect of its
denotes total
skill class z.
a large number of small firms which can enter to perform
and each firm ignores the
z
skill-
We
R&D
assume
for either
expenditure on the productivity of others.
(Xz /Nz ) as given when it decides its research expenditure. A firm which discovers a new machine becomes the monopolist producer of
-7
that machine. We assume 4>(x) = Tx
< 7 < 1. This pawhere x z = Xz /Nz and
More
formally, each
firm takes
<fi
,
rameterization of the
4>
function simplifies the analysis of transitory dynamics. If
then there are decreasing returns to research investment within a period.
4
7 >
0,
We can write
the law of motion of technologies as follows:
N =T
z
x\-i
N
7 = 0, then our balanced growth path results are unchanged, but there
we change preferences to Constant Relative Risk Aversion, then there
dynamics, even when 7 = 0, but these are somewhat more complicated.
4
If
ics. If
(4)
z.
are no transitory
dynam-
are once again transitory
Observe that directed technical change
is
a crucial ingredient in our
the North to develop the technologies most suited to
its
results;
it
will
enable
needs, which are different from
those suited to the countries in the South.
Analysis
C.
We
Nl and Nh
take the technology variables
first
equilibrium in the North and the South.
as given
we
In this section,
no commodity trade between the North and the South, so
two
We
sets of countries.
start with
otherwise stated, the proof of this
Lemma
1 There exists
In words,
labor,
all
an
lemma
J such that
for
i
prices will differ across the
in
<
J, h(i)
=
i
(2).
and
>
i
J, l(i)
Using
_ p(i)<i-0//> .{l-i).NL l(i)
~\p(i)^-^-i-NH -Z-h(i)
.
Utility maximization, in turn, gives the
Lemma
=
0.
this
only.
This
is
natural
lemma, we can write the
as:
f
[0, 1].
proofs, unless
Appendix A.
is
and those with indexes above J are produced with skilled labor
y{)
€
is
goods with indexes below the threshold J are produced with unskilled
production in sector
i
assume that there
lemma. As with other
intuitive
given the structure of comparative advantage in
all
also
and characterize the
if
<i< J
if
J<i<l
[b)
*
consumer indifference condition:
p(i)y(i)
=Y
for
These equations enable us to prove:
2 In equilibrium,
for any
i
for any
<
i
J, p(i)
>
= Pi
J, p(i)
—
(1
= PH
i)~^
i~ p
and
and
l(i)
h(i)
=
=
L/J, and
H/(l
-
(6)
J),
(7)
where Pi and P# are appropriately defined price indexes, and
PH = (NH
-pL
\-NL
J
T^J—)
Goods with higher indexes produced with
and command higher
prices.
The
ZHY+
converse
is
(8)
unskilled labor have lower productivity,
true for skilled goods.
then obtained using the consumer indifference condition.
It exploits
markets have to clear in the North and the South separately.
8
Equation
(8) is
the fact that goods
To
Nl and Nh, we must
fully characterize the equilibrium for given
Good J can be produced by either skilled or unskilled workers, and must
in either case, thus, when i = J, both (6) and (7) apply. This implies:
Ph
determine J
yield zero profit
J
(
Hi^)'-
Pl
and
(8)
(9) therefore
determine equilibrium relative prices and the threshold sector
given state of relative technology,
is
the numeraire,
we
obtain:
PL =
Noting that
simplifying,
Y=
NH /NL
Using the
.
fact that the
exp(-/3)
J~p and
PH = exp(-/5)
and combining
with
this
we obtain a simple reduced form equation
•
(1
consumption aggregate
Since wages are equal to marginal products,
m
we
mL = z (NE \ J
combining (12) with
of skilled workers in labor costs
is
always
x 2
(8)
1
GDP:
for
(10)
.
and
(10),
and then
6
2
(11)
.
]
also have:
fZH\-^
itj
and
—
J)~ p
-
(5), (8), (9)
Y = exP (-P)[(NL LY' 2 + (NH ZH)V 2
D.
a
5
Jq p(i)y(i)di,
Finally, notice that
for
(9),
<
we
i2 >
find that the equilibrium share
J.
Technological Progress in the North
We
start
South, so
with the assumption that there are no intellectual property rights in the
R&D
firms in the
North cannot
relevant market for technologies
equilibrium
R&D
in the
is
sell their
technologies to Southern firms.
therefore the North. Since there
is
no commodity
The
trade,
North can be determined without any reference to the South.
Recalling the above discussion regarding profits of technology monopolists, and using
(6)
and
(7),
the return to inventing a
new machine
rVz =
ir z
+ Vz
for skill class z
(13)
,
= 0(1 - /?) (P£) 1//? / J n(i)di = 0(1 - /5) (P£) Ln and
1//?
n
7T H = (3(1 - /3) (P£)
ZH n Ln and
/] h (i)di = 0(1 - 13) (P£)
1//3
where nL
l
1//?
.
5
6
That
is,
is:
we use the normalization exp
\f ]np(i)di
=
Hn are effectively the
1.
For future reference, observe that we cannot use this expression for
librium capital stocks have already been substituted in.
TFP
comparisons, as the equi-
new
"markets" for
technologies since technology monopolists can only
sell
machines to
Northern producers employing Northern workers. The time derivative captures the
that
PH
fact
and P£ may be changing out of the balanced growth path, so that the value of
may be
the patent to a certain machine
different in the future.
Free-entry implies that
the value of a technology monopolist must be equal to the marginal cost of innovation,
hence T~ l x~ 1 Vz
=
7
at all points in time.
1
NL
Along the Balanced Growth Path (BGP),
and
thus the same research effort must be allocated to
vations (xl
in
— xH
This
).
is
only possible
skill-
= h
if -k l
NH
must grow
same
rate,
and labor-complementary inno-
BGP, Vl
(since in
tt
at the
= Vfi = 0).
Hence,
BGP, we need
fZHn
pn
Using
(8)
and
Ln
\
-p
^
(14)
1
j
(9), this implies:
H
h
1- Jn
ZH n
Jn
Ln
~~
(15)
This equation uniquely defines the relative productivity of skilled and unskilled workers
along the
BGP
as a function of the relative supply of skilled workers in the North. It also
determines the threshold sector J n along the
The next
BGP
the
proposition summarizes this result and the dynamics of the
exists
a unique and globally stable
BGP,
given by
Nh
grow
at the rate
(15), and along this growth path, output,
g
There
to this
economy outside
in the North.
Proposition 1 There
and
BGP.
=F^
1
[exp(-l)
•
-
(1
Nl and
0)
(L
a unique BGP, and starting from any
is
BGP. Along
economy grows
this path,
n
+ ZHn
Since
rate g, the relative productivities of skilled
/r\
Nl and Nh,
^)h
.
the economy converges
R&D, and the
both Nl and Nh grow at the common
a constant fraction of output
at the constant rate g.
{l
)
(9), (10), (12)
is
devoted to
and unskilled workers are constant. Relative
productivities can change along the transition path, however.
We
can note that, as in Acemoglu (1998), an increase in
technical change.
premium
in the
North
by an increase in
relative
7
wages
Notice that
7)r~ 1 a;J 7 Vr2
=
As equation
H
n
is
/L
n
(15) shows,
always
w H /vfl =
an increase
Z.
The
in
Hn /Ln leads to skill-biased
Hn /Ln raises Njj/Nl-
skill-biased technical
The
skill
change induced
exactly cancels the negative direct impact of this variable on
(see equation(12)).
if
1.
there were a consortium of
The
R&D
firms rather than small ones,
qualitative results are identical in the two cases.
10
we would have
(1
—
Equilibrium in the South
E.
The
R&D
process specified above entails a market size effect.
GDP
international intellectual property rights, the share of
To
creasing function of the country's market size.
implies
ilar
x
c
=
7r
c
=
/r
[exp(— 1)
—
(1
•
(L
•
/?)
C
is
L +
c
an increasing function of
ZH
C
.
BGP,
not invest in
More
the North.
ments
producers will instead import
Our assumption
below).
in-
free entry
GDP
spent on
the South, collectively,
all
R&D
invest-
the discussion in
skills (see
that each Southern country
from
their technologies
one could also motivate the lack of substantial
generally,
an
each country c (a sim-
for
R&D, and
South by weak property rights and scarcity of
in the
Remark
R&D. Southern
is
Since the South consists of a set of "small"
economies, each will have an infinitesimal market for
the
/r]
1
argument also applies away from the BGP). Therefore, the share of
R&D
will
)
1'
R&D
devoted to
see this, recall that in
+ ZH
c
Since there are no
small captures these
is
considerations in a simple way.
We now discuss
TFP
whether
differences
might emerge even when firms in the South
have equal access to the technologies in the North. To achieve
new technology
patents at zero cost and sells machines embodying this
country
—no other firm
prices in the
is
allowed to
same capital/labor
R&D
in the
North as
Proposition 2 There
C
exists
machine rental
i
< Js
and technologies
Output grows
,
hi
Nh
at the
The equihbrium
=
and k
(NH ZH
s
\NL L
= Ls /Js
(1
— P) -1
-
South and
and Nl are
still
given
Thus (proof omitted):
,
and
and Nl are determined
same
Nh
=
in the
a unique equilibrium in the South where J s
Js
for all
be used in production
therefore apply, while
in subsection D.
l-J
where
technologies. This implies that
ratios will
the North. Equations from subsection
new
to the producers in
South are the same as those faced by firms in the North, x z ( v )
Accordingly, the
by
sell
we assume that there
each Southern country which copies
exists a statutory technology "monopolist" in
its
this,
is
given by
1/2
S
\
(16)
s
for all
in the
i
> Js k =
and h
,
North
(e.g.
t
=
H
s
/(1 —
given by (15) in
Js ),
BGP).
rate g as in the North.
in the
South therefore takes a very similar form to that in the
North, with the only exception that technology parameters, N'{ and Nl, are taken from
the North. Hence,
is
constant (although
ratio of
in
when the North
is
J s > Jn ), and
consumption to
GDP
is
in
BGP,
the South
the growth rate
is
is
also in
BGP.
equal to that of the North,
higher in the South, however, as there
R&D.
11
Js
The
In particular,
is
g.
no investment
Remark:
It
can be noted at this point that similar results would be obtained
were performed by skilled workers rather by using
workers would perform
is
its skilled
workers to
obtain exactly the same results as here. Moreover, in this case, even
the South consists of large countries, there will only be limited
skilled
wages are high.
We
With
small and does not enforce international
property rights, the South would once again not allocate any of
South because
R&D
output. In the North, h skilled
final
R&D while the remaining H — h would work in skilled tasks.
our assumption that each Southern country
R&D, and we
if
R&D
when
investments in the
prefer the specification in the text as
it
leads
to simpler expressions.
Productivity Differences Between the North and the South
III.
TFP
A.
Differences
The concept
of
TFP,
first
introduced by Stigler (1947), decomposes output (or output
growth) into a component dependent on factors of production and a component dependent
on "technology"
distinction
measure
.
Since technology
often
is
embedded
not always clear, and, consequently, there
is
TFP
(e.g.
is
example
capital, the
a large literature on
how
to
Jorgensen, 1995).
TFP is
of TFP
In our model the definition of
there are two natural definitions
not completely unambiguous, either. In
here
(TFP1 and TFP2), both
factoring out output into the contributions of skilled
fact,
obtained by
and unskilled workers, capital and a
The former is implied by the logic of the theory, while the latter corresponds more
residual.
closely to
sectoral
in factors, for
what
is
estimated in practice. Both
TFP
TFPs, which are obtained by rewriting
yL (i)
=
aL (i)
KL
1
{i)
-?
•
l{if and yH (*)
measures originates from aggregating
(5) as:
= aH (i)
KH
l
(i)
-P
[Z
h(i)f
,
where the a z (z)'s are the sectoral TFPs, given by8
aL {i)
and
KL
(i)
=
L
/<f
=
[(1
-
i)
NL f
and a H
=
[i-
NH f
= NlPI'^L/J for i < J, and
= NH P^ZELj{^ — J) for i > J denote the capital stocks
(17)
kL {i,v)
Kff(i)
= J^H k H (i, v)
sector
i
used in
(obtained using (3)-(6)-(7)).
Notice that Z h(i) is the "quantity of human capital" employed in sector i using Z as the skillpremium. Z should not be part of sectoral TFP, since otherwise sectors and countries with more skilled
workers would mechanically have higher TFP.
8
•
12
The alternative definitions of TFP
in
two
The
different ways.
first
arise
because these sectoral
definition comes, simply,
from
(1)
TFP can be aggregated
and
(17).
1
Y=
A{J,
L
H ) exp (j
,
=
where A(J, Nl, Nh)
exp
1
(/q
\nKL {i)
]na(i)dij
content from the technology terms.
first
By
x
+
-^l{ifdi
is
J
hxKH {i) 1 -^
[Zh(i)f di\
(18)
,
obtained from separating the terms with factor
using (17) and solving the integral
we obtain our
measure of TFP, TFP1:
TFP1 =
To introduce the
by
tal stock
NH PH
'
A(J,
NL NH =
)
,
[NlNJT
J
(1
-
TFP,
alternative definition of
J)~
(1
- J)
J-'f
(19)
define the value of the aggregate capi-
K = KL + KH where KL = tf KL (i)di = NL PL
l ll3
ZH. Output can be
exp[-/3].
L, and
KH = /] KH (i)di =
written as (details in the Appendix):
Y = B(J,NL Na
)
,
^ [ZHf] ^
[Kl-W] ' [K
where our second measure of TFP, TFP2,
TFP2 = B(J,NL ,NH = [N[NH J (1 )
1
(20)
,
is
J)
_(1_J)
J~ J ^
[(1
-
J)-(
w
)j- J exp[-/3].
]
(21)
we use the
In (19),
correctly aggregated labor
structure of our model, so (19) measures "true"
structure
is
and
TFP
differences. In contrast, this sectoral
ignored in (21), and only aggregate stocks of labor and capital are factored
out. This adds the
term
[(1
- J)-^-^ J~A
correct measure in our model, (21)
TFP
to the
closer to
is
using the exact sectoral structure of the
what
economy
is
is
Notice also that (18) and (20) already factor out
(3J for unskilled workers,
and
/?(1
—
measure. Although (19)
often infeasible.
skills
using the correct factor shares,
on output are already controlled
do not directly depend on
because both
TFP
the
estimated in empirical work, where
H and L,
and
TFP
for.
(19)
and
(21),
differences will not arise in our
model due to mismeasurement of the human capital of workers. Instead,
will arise
is
J) for skilled workers, which means that the direct
effect of differences in skill supplies
therefore,
capital inputs, given the sectoral
measures depend on the threshold sector,
TFP
J.
differences
J determines
the extent to which skilled and unskilled workers are employed in sectors (tasks) for
which they
may
productivity,
We
Lemma
of
not have a comparative advantage. So the level of
and economies with
start our analysis with
3 For given
J with a unique
affects aggregate
have different
TFP levels.
a simple lemma (proof omitted):
NH and NL
global
different threshold sectors will
J
A(J,NL
maximum at Jm
,
,
NH (TFP1) an inverse U shaped function
= Nl /(Nl + Nh))
13
is
TFP.1/0
Jm
Figure
Lemma
1
Sectoral TFP's.
3 has an intuitive geometric representation.
transformation of the sectoral
TFPs
the two schedules cross. Hence,
figure also
(a(i)
TFP1
1 / /3
is
denned
)
Figure 2 plots a monotonic
in (17).
At Jm
=
NL /{NL + NH
),
maximized, when an economy adopts the un-
< J m and
skilled technology in all sectors j
The
2:
J
J
the skilled technology in
draws an arbitrary value of the threshold sector
all
where
(J),
> Jm
sectors j
TFP
is
.
not
maximized.
Proposition 3 Suppose
(15).
Nh/Nl
1.
Then, A(Jn ,NL ,NH )
2.
If either (i)
then B(
Therefore,
given by the
n
or
,
)
is
S
,
Moreover,
).
L n and \ZHn /L n >
is
not very abundant in
skill
endowments
of the
may appear
to have lower
allocates skilled workers to tasks
those sectors with
this is not the case. In
in this case,
n
ZH < L
i
<
TFP2.
1/2).
S
/L S where A <
1,
also larger in the
or otherwise,
if
there
is
North
a large
North and the South. The reason why
is
that the
skill
In particular, an
TFP, according
and sectors where
The
TFP2 is
skills,
second measure might give ambiguous answers
unskilled workers
ZH
).
,
labor force has an independent effect on
(e.g.
NH
always larger in the North, and
North
enough gap between the
ZH n >
NL NH
(ii)
\ Nl N*H > B(J
TFP1
,
BGP equilibrium condition in the North,
> A(J S ,NL ,NH ).
ZH n < Ln
as long as either the
this
is
Then, J > J = J m = argmax^J, NL
n
s
composition of the
economy with very few
to this measure, because
their productivity
is
relatively
it
low
conditions in part 2 of the proposition ensure that
our calibration below, we will take the North to be the U.S., and
n
is satisfied,
so that
North.
14
TFP2
is
also
unambiguously larger in the
Intuitively, this proposition
and
no
directed,
is
TFP
will
shows that when
R&D
carried out in the North only,
is
be larger in the North than in the South, even though there are
barriers to technology transfer.
In particular, as
H
s
/L s <
Hn /Ln
TFP
,
larger in
is
the North than in the South because some sectors in the South employ unskilled workers,
though productivity would be higher
The reason
using skilled technologies.
workers in the South to allocate to
As we
more
will see in
if
all
production were carried out by skilled workers
is
that there
is
an
insufficient
number
of skilled
tasks performed by skilled workers in the North. 9
detail in section V,
R&D
if
firms could sell to Southern producers,
they would invest more in unskilled technologies, and productivity in the South would not
be as low.
Similarly, as
noted above,
to unskilled machines, and the
TFP
if
the South could perform
gap would be smaller.
of the South importing technologies from the
North that underlies the
TFP
R&D,
it
would
direct
it
the combination
It is therefore
North and directed technical change
in the
between the South and the North.
differences
Proposition 3 has an immediate corollary (proof omitted):
Corollary 1 There are no
i
for all
ie(J
s
< J
%
,J
s
or
i
> J
n
TFP
differences
Sectoral
.
TFP
is
between the North and the South
larger in the
is
in the
South
).
=
Js
o
sectoral
,
TFPs
will
make
the North
it
more productive
2. If
be as drawn by thick
using unskilled workers in sectors j
G (j m ,J), where
the South sets the threshold
lines in the figure.
The South
the technologies developed by
to use skilled workers.
All productivity differences
between the South and the North therefore originate in these "medium-tech"
i
s
n
G (J ,J
).
The South
highly complex tasks.
and
in the sectors
as the North.
concentrates
Since technology
where the North
The
its
scarce
is
endowment
common
This pattern
TFP
knowledge, in these complex tasks
South
is
as productive
productivity gap emerges instead in those sectors where
may
explain
why
India,
—
sectors,
of skilled workers in a few
also uses unskilled workers, the
to substitute unskilled workers for skilled workers
i's.
for all
n
This Corollary can also be illustrated using Figure
sector at
North than
in sector
i.e.
easier
those tasks with intermediate
which has relatively few
compared to the U.S. (approximately half of the U.S.
it is
level),
skilled workers
and low
has a relatively
efficient
software industry, but appears to have low productivity in a range of
more
traditional
industries.
9
TFP
between the North and the South would arise even for
and unskilled workers would be performing different tasks in the
two sets of countries. However, in this case, the South could have higher TFP than then North. Directed
technical change ensures that the North has higher TFP than the South, as it implies that Njj/Nl takes
the value that maximizes North's TFP (using TFP1
whereas using TFP2, directed technical change
does not maximize the North's TFP, but tends to increase it).
Notice that in this model
arbitrary
Nh
and Nl, because
differences
skilled
—
15
A
B.
Simple Calibration
In this subsection,
we investigate whether the TFP
are quantitatively important. Equations (19)
different measures) in
and
(21) give the
TFP
TFP
levels (with the
two
a country as functions of the world technology and the country's
we can determine
threshold sector, J. Given the technology parameters,
the
by our model
differences predicted
by our model using the
differences predicted
J,
relative skill supplies
and
calculate
we observe
in
the data.
We construct
H/L
the variable
as the ratio of the population over age 25 with higher
education to those over 25 without higher education in 1985 from the Barro-Lee data set. 10
=
We
choose
set
Z to make the predicted U.S.
(3
the share of labor in national income in our economy, and
0.7, since /? is
skill
premium equal
to 1.82, that
u which
the college
is
premium
Z = 1.82. With
these assumptions, we can use equations (19) and (21) with the values for H/L for each
country and calculate the predicted TFP relative to the U.S. (whose TFP is normalized
in the U.S. in 1988 (Katz
to
and Murphy, 1992,
p.
43),
1).
We denote these predicted
A value of 0.5,
for
(relative)
TFP1) and by B (TFP2).
question is predicted to have TFP
TFP levels by A
example, implies that the country in
(for
equal to one half of the U.S. TFP. Notice that in this calculation,
about these countries'
level of
income or investment. The
those predicted by our theory given each country's
transfer, are likely to create
capital used in practice
TFP
differences.
A
H/L. In
and
practice, a
and
B
are simply
number
of other
barriers to technology
human and
Moreover, measures of
physical
may understate true differences in the amount accumulated factors
across countries (e.g. our calculations
same
we are not using any data
levels of
factors, including distortions, corruption, wars, slow diffusion,
as a college graduate in the
between our predicted
importance of predicted
is
implies
TFPs and
TFP
assume that a
LDCs).
We
the data.
differences
and
college graduate in the U.S.
is
should therefore not expect a perfect
the
fit
Nevertheless, evaluating the quantitative
their correlation
with the actual differences
informative.
Klenow and Rodriguez (1997) (based on
(1998) (henceforth,
tively,
KR
and HJ) calculate
Bils
TFP
and Klenow, 1998) and Hall and Jones
levels for
98 and 127 countries, respec-
using data on output, capital, labor and school attainment.
The
on higher school attainment reduces the two samples to 96 and 102
we exclude
10
oil
availability of
data
countries. Moreover,
producers and Trinidad (a total of eight countries) from the
KR sample,
Web address for Barro-Lee data http://www.worldbank.org/html/prdmg/grthweb/ddbarle2.htm, see
Barro and Lee (1993). We thank Pete Klenow for the data on TFP levels from Bils and Klenow
Klenow and Rodriguez (1997) and Chad Jones for data from Hall and Jones (1998).
11
The results are not sensitive to variations in /3. If instead of /? = 0.7 as in Klenow and Rodriguez
(1997), we choose /? = 2/3 as in Hall and Jones (1998), the results are almost identical.
also
(1998) and
16
TFP
according to Klenow and Rodriguez (1907)
.2
TFP gap
Figure
3:
Actual (KR)
vs.
.3
.4
from the
Predicted
US
TFP
.5
<KR)
Gap.
since these countries appear to have unrealistically high
natural resources on output
effect of
is
TFP
TFP
measure: A.
suggesting that the
levels,
not well accounted for by measured inputs for
these countries.
We
TFP
denote the (relative)
measures of
KR and HJ
by
Bkr and B HJ and
,
them, as well as our measures, in our Appendix Table Al. 12
our
A measures to BkrS
and
BH /s,
which
will
be "true"
TFP
flow freely. It
sizeable.
account
is
by comparing
start
be informative regarding the quantitative
importance of our predicted TFPs. In particular, recall that our
will
We
report
m
/del
(productivity) differences across countries, even
however important to determine whether these
suggests that there
when technology can
TFP
differences
can be
We next turn to 5's to evaluate the potential importance of our mechanism to
for TFP differences in practice. Since Z?'s are more closely related to measured
TFPs, they are more appropriate
for this latter
Figures 3 and 4 plot the relative
and the TFP
— BHJ on the
vertical axis,
=
TFP
comparison.
measures calculated
=
— A) on the
by KR and HJ (gapKR = 1 — Bkr and
of each country (gapA
I
We also draw the 45° line in all figures. A
country further away from the origin has lower TFP relative to the U.S., whose observation
lies exactly on the origin. Since our first measure A (TFP1) corresponds to true TFP
differences, but not necessarily to the way TFP is calculated in practice, we only want
to evaluate how large these TFP differences are. We can get a sense by comparing
the variance of A to the variance of Bkr and Bhj- The variance of our measure is
9&PHJ
12
1
HJ and
)
KR
horizontal axis.
report productivity differences per unit of
human
capital.
Since they use a Cobb-
Douglas framework, these can be easily transformed into TFP differences. In particular, denoting the
0.42
and
labor productivity differences estimated by these papers by bKR and bn j, we have Bkr = (bKR)
Bhj =
(bij j)
.
It is
these
TFP
numbers that we
use.
17
TFP
according to Hall and Jones (1998)
a
s
a
a
IL
Figure
approximately
the largest
TFP
i
.1
Actual (HJ)
4:
20%
i
O
i
.3
Bkr
of the variance of
KR
i
.4
the
.5
US
TFP
<HJ)
Gap.
TFP
measure: A.
and 10% of the variance of Bhj- For example,
gap predicted by our model
this evidence that
i
Predicted
vs.
whereas the largest gaps are in
level,
i
.2
TFP gap from
is
TFP
a
We
and HJ are 82% and 62%.
our model predicts sizable true
TFP
30%
level equal to
differences even
of the U.S.
conclude from
when
all
countries
have access to the same technology, though these differences are smaller than those found
in the
data by
KR and HJ.
As noted above, however,
TFP1
does not correspond to the
So to evaluate how much of the variation in the data could actually be driven
in practice.
by our mechanism, we need to compare
= 1~B
6 plot gaps
on the horizontal
on the
axis,
Bkr and Bhj
vertical axis,
linear regression of
and show a much better
our measures on
to our B's
and the gapKR
For a quantitative comparison, in Table
a
TFP measures estimated
Bkr
fit
1
(TFP2
— 1 — Bkr
,
s).
Figures 5 and
and gapnj
= 1 — Bhj
between the data and our model.
we
report the coefficients
and Bhj
(for
and
R2
from
completeness, Table 1 also
A perfect fit would correspond to a constant equal
to 0, slope coefficient, d, equal to 1 and R2 = 1. Obviously, measurement error and
other important determinants of TFP ignored in our theory imply that there will not
reports the
same
be a perfect
fit,
regressions using A).
but
how
close
we
are to such a
also identical to the statistic suggested
is
by
fit is
KR
as
informative.
The
slope coefficient
a summary measure of how much
a variable explains variations in another variable in a similar context (their suggested
measure
2
i? ",
2
9ft
a = Cov((Bs ,B)/Var(B s )). As an alternative, we also report a "constrained
= 1 — Var(Bs — B)/Var(Bs ). This is the R? from a regression if we constrain the
is
slope to be equal to 1
fit
and the constant
0.
2
3ft
would be equal to
between our model and the data. All three measures, a,
regarding
how much
of the
measured
TFP
differences our
18
R
2
1, if
and
there were a perfect
2
9ft
,
are informative
model can account
for.
Table
TFP
Comparison between predicted and actual TFPs.
from
KR
HJ
B
B
0.02
0.07
0.02
0.04
0.11
0.04
0.09
0.01
(2.21)
(3.64)
(1.79)
(3.86)
(5.22)
(3.55)
(4.05)
(1.02)
0.34
0.68
0.71
0.19
0.39
0.46
0.42
0.48
(11.2)
(11.0)
(18.7)
(8.10)
(8.08)
(13.7)
(9.70)
(16.0)
0.60
0.59
0.80
0.40
0.39
0.68
0.49
0.74
0.49
0.57
0.79
0.29
0.40
0.61
0.48
0.65
or
B=TFP2)
More
(1998).
the constrained
B
R
B
Each column reports the
Note: t-statistics in brackets.
(A^TFPls
from
A
2
is
CTFP
B
HJ
B
R2
3ft
from
B
a
and Jones
TFP
A
c.
5R
1.
linear regression of the specified measure
measures calculated by Klenow and Rodriguez (1997) and Hall
we regress gap^ =(1-A) or gap B =(1-B) on gap s =(1-TFP S ).
TFP
on the
specifically,
measuring the
fit
constraining the constant to be zero and the slope coefficient
TFP2
measures constructed using the skill variables of Klenow and Rodriguez (1997)
instead of using fraction of population with higher education divided by fraction with no higher education.
CTFP includes an adjustment to the TFP calculated by HJ which is discussed in the text.
to be one.
Our
is
first
the
measures of how much of the
by our mechanism, the slope
dicted
ries,
e
measure of
are olkr
fit,
we
=
2
(KR
obtain: ^t KR
=
variations in the data could be explained
from the regression of actual TFPs on our pre-
coefficients
0.68
TFP
data) and
a HJ =
0.57 and $1% 7
=
0.39 (HJ data).
0.40.
As
for
our other
Therefore, despite the absence
of any barriers to technology adoption, slow diffusion or other factors affecting technol-
ogy choices
model accounts
in our calculations, our
between 39 and 68 percent of the
for
variation in the data.
More
practically
the U.S.
concretely, for example, our
model predicts that Mozambique, a country with
no workers with higher education
level,
while the relative
TFPs
in 1985, should have a
calculated by
KR
and 47%. Indonesia, on the other hand, should have a
model, while measured
model
is less
TFPs
vary between
successful in capturing the
and the Philippines, which have very low
gap
for
levels,
equal to
are, respectively,
TFP
53%
of
of the U.S. level, while India's
and HJ.
13
TFP
is
of
53%
according to the
(HJ). Nevertheless, our
some other
countries, like India
even relative to their low
educational attainment. In the case of India, for example, the model predicts a
74%
42%
and HJ
62% (KR) and 39%
TFP
TFP
TFP
between 40% and 50% of the U.S.
levels of
TFP
level in
of
KR
13
At this point, we can note that there
advantage of skilled and unskilled workers
one degree of arbitrariness in our calibration: comparative
— i) and i. For any increasing function
—
using
/(l
i)
and
would
give
similar
theoretical
results
but different quantitative results. We
f(i)
/(.),
chose (1 — i) and i for analytical tractability. Also as we will see in the next section commodity trade
reduces TFP differences, and here we are making the calculations assuming no trade.
is
is
parameterized by (1
19
TFP
„
.8
ti
T!
.7
E
.6
in
.5
according to Hall and
J
ones (1903)
-
~
~
Jr
+
*+
-
*
4+
t/i
.4£
+
2-
L
•-
a
.1
s
+
+
.3+
,
~
+
*
t
.
+
+
,
4
a
* *
+
*
*
+
4
+
+
+
*jr
+
*
+
*>
**
E
+
+ J
+
+
+
M
+ ++
+
+
**
+
+
* *
*
I
0.
IL
F
I
I
I
.2
.1
c\
Figure
5:
Actual (KR)
TFP
US
the
TFP
Predicted
vs.
.4
.3
TFP gap from
I
I
I
I
.5
.6
.7
.8
<HJ>
TFP
Gap.
measure: B.
according to Klenow and Rodriguez <1G97)
7 ~
e -
5+
+
4 -
+
3~
+
t
*
I
a
1-
a.
+
IL
o
F
+
+
/^
4
+
*
jf
+
2"
a
6:
*
+
v**
/*
+
*
+
.
<*
+
*
+
+
+
*
,
+
+
+
+
A
I
I
.2
.3
I
TFP gap from
Figure
>*
0<
+
yr
*
o
L
»-
j*r
_>r+
+J/S^
+
t
*s
+
+
+
E
+
+
+
Actual (HJ)
vs.
Predicted
20
.4
the
US
TFP
I
I
.5
.«
(KR)
Gap.
TFP
measure: B.
might be argued, however, that by using variations in the number of workers
It
H/L
with higher education only, our approach exaggerates differences in
Moreover,
tries.
sometimes suggested that the contribution of higher education
it is
smaller than that of secondary schooling.
come
closest to
results
14
H/L
it is
H/L
by using an alternative measure of
and secondary school attainments as
useful to check the robustness of our
estimated using differences in primary
TFP2
For this purpose, we reconstruct our
well.
reported by Klenow and Rodriguez (1997) which are based on
educational attainments, quality of schooling and labor force experience. Using this
ternative measure of relative skill
The
series.
(KR
l).
endowment
actually improves the
slope of the two regression lines increase to
measure
data), while our
is
Although college-noncollege distinction may
our skilled-unskilled distinction,
measure (B) using
across coun-
3£
2
2
increases to %l KR
=
a KR =
0.79
0.72,
and
$l
fit
of our predicted
and to a H j
Hj =
2
al-
=
0.46
0.61 (see Table
15
Table
1
shows that our calibration results are somewhat better with the
KR
sures calculated
by
HJ -
many
as well as
to be perfect substitutes,
- implicitly assume
and use the same
endowments of countries with
skill
premium
skilled
mea-
may be
than those calculated by HJ. One possible reason
earlier authors
TFP
that
and unskilled workers
to calculate the
human
capital
model, this
different relative supplies of skill. In our
is
not
the correct procedure, as skilled and unskilled workers are imperfect substitutes, and the
skill
premium
premia
for
varies across countries (see Psacharopoulos, 1973, Table 8.4, p. 132 for skill
a number of countries).
numbers from those of HJ. In
It is,
however, possible to construct "corrected"
particular, let estimated
TFPs
be:
]nTFP = \nY-(l-P)]nK-p]n(L+(— )
whereas according to our model the correct
InCTFP =
We
In B(J,
TFP
H
J
is:
NL NH = lnF - (1 - P) InK - /31n (L J {ZH)
l
)
,
can then calculate an estimate of corrected
In
measure
TFP
from
TFP
HJ and
-J
)
KR as follows:
CTFP = \nTFP - (3(1 - J)ln(^) + /?ln (l + l-82y)
S
s
14
Even the contribution of secondary schooling to output has been challenged, e.g. Benhabib and
and Pritchett (1997). However, Krueger and Lindahl (1998) show that this is due to
measurement error, exacerbated by the methods used in these papers.
15
KR's appendix reports estimates of Y/L and H/Y (where Y stands for GDP) relative to the U.S..
From these date, we calculate H/L relative to the U.S. and also report these in Table Al. The H/L
Spiegel (1994)
ratio in the U.S.
is
normalized to 0.508, which corresponds to the ratio of workers with higher education
Although we only report results for TFP2,we also obtain similar results the
to those without in 1985.
above
if
we combine the
KR measure of H/L
with our
21
TFP1.
=KR and HJ.
for s
TFP
Using this corrected
to the
HJ data
(see Table 1). This
is
use the alternative measure of
when we
regress our predicted series
constant
falls
increases to
in
a =
to
SR 2
-
0.48 (our
Overall,
variation
and
H/L) and
of our predicted
of
H/L
KR (B).
TFPs
(B),
and
In particular,
on the corrected TFPs, the estimated value of the
H/L) and a =
9£
2
=
that the
and can account
we observe
by
intensity provided
in
TFPs
0.63 (KR's
alternative
H/L).
also increase
measure of fit
also increases
The
16
mechanism suggested
for
R2
H/L).
0.48 (KR's
Our
0.74, respectively).
we conclude
tively important,
fit
one case becomes non-significant, while the slope of the regressions
0.42 (our
significantly (to 0.39
skill
improves the
when we use our measure
true both
when we
and
(CTFP)
measure
in this paper can
be quantita-
approximately between 40 and 70 percent of the
across countries.
Trade and Technology
IV.
We now
consider a world where
all
commodities
i
G
[0, 1]
are traded internationally.
We assume that intellectual property rights are not enforced in the South. The main result
in this section is that free trade implies TFP convergence, but causes GDP divergence.
We use the convention that H s is the total number of skilled workers in the South
and L s
is
the supply of ui^killed workers, as well as the supplies in a representative
country in the South. International trade implies that commodity prices are equalized in
all
countries.
Moreover, since different commodities can only be produced by skilled or
unskilled workers, factor price equalization
is
also guaranteed.
now adopt the same technology (same threshold JT ). More
pi _
(
Pl'V-jr) ~\Nl
V
result, countries will
specifically,
y _ (Nizii^y
J?
As a
we have
12
{U)
'
)
and
<-.
1/2
7
(^kY
Nl)
wi
where L w
prices
n
H
w
H
H
n
/7t7tu\-l/2
(^EL
\
L™
)
= S+
and
are the world supplies,
and wjj and w r
L are world wages with free trade.
= L +L
s
Pj and Pj
are the world
As patents
tion, (14), is
are not enforced internationally, the balanced growth equilibrium condin
unchanged; Northern
and Ln as their
firms continue to consider
H
R&D
While KR do not assume skilled and unskilled workers to be perfect substitutes, they use - like HJ
- the same skill premium to calculate the human capital endowments of countries with different relative
supplies of skill. If we apply to the TFP calculated by KR the same correction which is applied to the
TFP calculated by HJ, the results of Table 1 do not change substantially, and, in fact, the fit of our
model improves marginally. For example, we obtain 3J2 = 0.71 (our H/L) and 3?2 = 0.79 (KR's H/L).
16
22
markets. Thus, (world) prices have to adjust in order to satisfy (14). This implies that
in the
BGP, world
depend on the
relative prices will only
factor
endowment
of the North.
Formally,
Pi
V_
JT
(
T
PT~[l-J
L
This equation implies that along
will
(
ZH n
U"
BGP with trade,
(23)
world prices and threshold sector, J7
,
be equal to those prevailing in the North before trade. However, world prices must
market clearing equation,
also satisfy the world
(22),
The
rather than the supplies of the North only.
which depends on world supplies
state of relative technology therefore
In particular, since the supply of unskilled workers has increased, the
has to change.
relative productivity of skilled workers has to increase to ensure that (23)
More
and
specifically, (22)
(23)
JVg
which
larger
is
imply
n
_ fZH
\
ratio, since
trade induces skill-biased technical change.
change depends on the relative market
in the
--i.e.
North
17
sizes
More
(H n /L n > (H w /L w ).
)
specifically,
(H/L) and
But
trade, at
first,
In other words,
the direction of technical
Market
relative prices (ph/pl)-
do not change, because inventors continue to
equation (22) at a given
profitable
BGP,
only.
1/2
-i
1/2
(24)
than the closed economy
sizes for technologies
is satisfied.
machines
sell their
increases the relative price of skill intensive goods
Nh/Nl- This makes skill-complementary
innovations more
and accelerates the creation of skill-complementary machines. In the after-trade
the South, therefore, concentrates
its
unskilled production in fewer sectors
and uses
a larger number of skill-complementary machines, while the structure of production in the
North reverts back to
its
now more
pre-trade form. Nevertheless, since technologies are
skill-complementary, skilled workers have higher relative productivities and wages.
In the next proposition,
opening.
To
we
characterize
simplify the discussion,
we
how
the world economy adjusts to trade
limit our analysis to
from a world of completely closed economies to one of
an unanticipated switch
free trade:
Proposition 4 Suppose that the relative technologies and prices before trade, (Nh/Nl)*,
relative prices
thresholds
and wages
Jn and J s
in the
are as given
North (Ph/PlY and
by
(12), (14), (15)
and
(
w Hl wl) n
(16).
i
and the equilibrium
Consider an unanticipated
opening of the world economy to free trade. Then, upon trade opening Ph/Pl,
J and
North and decrease in the South, and are equalized. The system
71
while the
then converges to a new balanced growth path, with (Nh /Nl) t > (Nh/Nl)
wh/wl
increase in the
,
17
This possibility
is first
raised
by
Wood
(1994),
has in mind. Acemoglu (1998) also establishes this
though
it is
effect in
23
not clear what the mechanism that
a model of directed change.
Wood
(Ph/Pl)
(Ph/Pl)Z
{Ph/PlT
time
{NH /NL Y
(NH /NL
n
)
time
to
Figure
Dynamics of
7:
prices
and technology
after trade opening.
Ph/Pl decreases to (Ph/Pl) = (Ph/Pl)™ and the world threshold
n
sector J decreases to J7 = J
w H /w L the world skill-premium, continues to increase
t >
after trade opening and reaches a new level (w h /wl)
The PGP growth
(wh/wl)
world price ratio
.
,
71
-
rate of the
economy
The dynamics
the same as before trade
is
of prices
the trade regime changes
effects are therefore
abundant
theory, however,
and
and technology are described
(to),
the level of technology
is
i.e.
falls
As the North
goods and the
What
the South (upper quadrant).
the adjustment after this
At the moment
-
the same as in the standard trade theory.
North and
is
in Figure 7.
predetermined at (Nh/Nl) u The
in skills, the relative price of skilled intensive
increases in the
prices,
(g).
initial response.
is
skill
is
more
premium
different in our
The change
in
commodity
the higher level of Ph/Pl, encourages more skill-complementary innovations,
Nh/Nl
increases (lower quadrant).
The world economy
reaches a balanced growth
path, as the productivity of skilled workers increases sufficiently, and the relative price
of skill intensive goods return to their pre-trade levels in the North,
(Ph/Pl)
11
-
The
reasons, but also
skill
premium
in the
due to the induced
technologies implies that the skill
standard trade
effect is
North
increases, not only
skill-bias technical change.
premium
in the
i.e.
(Ph/Pl) t
=
due to standard trade
Moreover, the change in
South may also increase, because the
being countered by skill-biased technical change induced by trade
opening. Accordingly, increased trade openness in this model can raise wage inequality
both in the North and the South, and
may have
24
larger effects in the
North than predicted
by
traditional calculations.
18
Since the world relative price of
intensive goods returns to that of the
skill
before trade, and the North and the South use the
same threshold
employ
sectors
skilled workers in the South, however,
J free trade
J s falls. Which
sector
implies that unskilled workers are used in fewer sectors in the South,
i.e.
North
1*,
indeterminate as any part of
is
the skilled production could be carried out in the North and imported to the South or
What
vice versa.
is
unambiguous
is
South
that, overall, the
import skill-intensive
will
goods and export unskilled goods. Finally, because the market
size for
new
technologies
unchanged and world prices return to those of the North before trade, the long-run
is
growth rate
is
The next
unaffected and remains at g.
GDP
proposition compares the
levels
between the South and the North
before and after trade:
Proposition 5 Let
trade and
GDP
be the
Vj and Yj GDPs
GDP
opening,
Yn
differences
in the
after trade,
Y
North and
then
s
the
GDP
Y? /Yj > Yn /Ys
in the
That
.
South before
after trade
is,
between the North and the South widen.
Trade unambiguously amplifies
GDP
differences
As we saw above, trade induces new technologies
between the South and the North.
to be further biased towards skilled
This reduces the productivity of unskilled workers both in the South and the
workers.
North, and because the South
is
more abundant
in unskilled workers, its relative situation
A
with respect to the North deteriorates after this change.
obtain the result that trade
Krugman
may
lead to
(1987), Feenstra (1991)
these papers
is
more
number
relative inequality
of other papers also
among
countries (e.g.
and Young (1991)). Nevertheless, the mechanism
in
quite different from ours. Typically, trade induces less developed countries
to specialize in sectors which benefit less from learning-by-doing than the sectors in which
the North specializes. In contrast, in our model, trade changes the direction of technical
progress in the North, and leads to larger income differences via this channel. Additionally,
in these
models trade leads to both
result, as
we
TFP
GDP
and
divergence, which
is
different
from our
see next:
Proposition 6 Let A„ and A£ denote
respectively, using
TFP1, and
let
TFP in the North and in
the TFP2 measures in the
after trade
B% and BJ
be
the South,
North and
18
Thus, trade opening may be the cause of the increase in wage inequality in the U.S. over the past
twenty years. Some of the arguments against the trade explanation, that wage inequality also increased
in
many LDCs, and
setting.
that skilled-unskilled labor ratios increased
These changes
may be due
all industries,
to skill-biased technical change induced
by
may be
trade.
invalid in this
Another critique
of the trade explanation, that the prices of skill-intensive products did not increase in the U.S.,
be
less valid in this
model, as in the long-run
Ph/Pl
25
returns to
its
pre-trade
level.
may
also
South.
Then, A„
= Aj
and
B% =
Bj. That
is,
after trade opening,
TFP
differences
between the North and the South disappear.
Despite causing
GDP
thermore, not only do
TFP
for
equalization
TFP
is
TFP
divergence, trade therefore leads to
convergence.
The reason
differences decrease, but they actually disappear.
TFP
factor price equalization.
workers perform tasks for which they have
little
trade, however, ensures factor price equalization
is
Fur-
low in the South when unskilled
comparative advantage.
and induces firms
in the
Commodity
South to em-
ploy unskilled workers only in the tasks performed by unskilled workers in the North.
Since the productivity of unskilled workers in these sectors
the South, and likewise for skilled workers,
An
TFP
implication of Proposition 6
differences
correct in
is
is
TFP
the
is
same
in the
North and
differences disappear.
that the intuition that technology flows eliminate
an economy with
free trade
and
factor price equalization.
Access to the same technology and factor price equalization ensure the production structure to be the
all
same
in all countries.
In other words, there
common JT such that
< J1 This emphasizes,
a
is
countries use unskilled workers only in sectors (tasks) with j
.
however, that free technology flows, by themselves, are not sufficient for
tion.
TFP
equaliza-
Countries with different factor prices will use available technologies in different ways,
causing unequal TFPs.
In fact,
if
we introduce
iceberg transport costs at the rate r in international trading
— r units arrive at the destination country), then we
lose factor price equalization and TFP differences re-emerge. In particular, when r > 0,
H n /L n > H s /L s implies that {Ph/PlT < (Ph/Pl) s —more specifically, if there is actual
2
s
Then equation (9)
trade, it is straightforward to see that {Ph/Pl) = (1 — t) {Ph/Pl)
n
s
implies that J < J
so there will be TFP differences. We state this as a proposition
(so that
when
1
unit
is
exported,
1
71
-
,
(proof in the text):
Proposition 7 Suppose there are
then for r
More
>
0,
there will be
TFP
(iceberg) transportation costs in international trade,
between the North and the South.
differences
generally, other sources of deviations
ensure that
TFPs
from factor price equalization
are not equalized. Since factor price equalization
as a description of international factor prices (e.g.
1987),
19
we conclude that
international trade,
TFP
between
less
strongly rejected
Bowen, Learner, and Sveikauskas,
international trade will reduce
differences
is
will also
TFP
differences,
but even with
and more developed economies
will not
disappear, even though they have equal access to the leading technologies.
19
and
Here we refer to absolute factor price equalization, not to conditional factor equalization of Leontieff
Trefler (see Trefler, 1993).
26
A
TFP
central result of this section, that international trade affects
A
tween the North and the South, receives some empirical support.
TFP
non-OECD
estimates for
=
(t
4.4,
KR) and
0.30
(t
=
data) and of 0.105 (HJ data).
is
HJ
HJ). Quantitatively, a
4.0,
one standard deviation increase in the index of trade openness
(KR
regression of the
countries on the index of trade openness provided by
yields a slope coefficient of 0.25
increase of 0.088
differences be-
associated with a
TFP
20
Property Rights and Technology
V.
Intellectual
A.
Equilibrium with Full Property Right Enforcement
property rights were enforced in the South, revenues from technology
If intellectual
sales in these countries
firms in the North. This
R&D
would accrue, not to statutory monopolists, but to the
R&D
would encourage
new
firms to design
technologies for the
Southern market, too, potentially reducing the "inappropriateness" of technologies to the
South. 21 This possibility
investigated in this section.
is
We
assume that there
the
sum
of the
are
still isoelastic,
is
R&D
r
the North under
NL
two
'
full
is
rate of the world
where
//
This
H
hn
= (H
s
=
is
—
(1
where P£
it
H =
Given
ir L .
exp(-l)
is
•
(1
- 0)
/L s )/(H n /L n ) <
Nh
II. C.
It
and
21
NL
Ln
and
7t
H =
the equilibrium in the South and
,
can be shown that the steady-state growth
1
(3
[L
and o
n
is
+ U + Z {^Hn + ^JiH
a constant,
a 6
[fi,
1]
North and the South economy. In particular, a
is
s
))
which depends on the
increasing in
only evidence of a positive correlation between trade openness and TFP, as
gap between
non-OECD
U + (P2)
given by:
sample, and obtain similar results, using
TFP
machines
for
the price index for unskilled goods in
is
correcting for the possibile endogeneity of trade openness.
the
now
price as above. Then, profits for
(P£)
/?)/?
is
are determined, as before, to equate returns to innovating in the
economy
relative size of the
20
/p
"
determined as in subsection
g
machines
property right enforcement, and the other price indexes are defined
sectors, thus ensure
North
=
tc l
"'
s
NH
and
same
firms continue to set the
(p^ Hh° ++ (P£J
(p%y
- P)PZ (P£J
similarly.
for
demands from the South and the North. Since demands
the two types of innovations are
(1
The demand
no commodity trade.
rich
and poor
OLS and
countries,
HJ run
L s /Ln
we
22
.
are not
a similar regression for their whole
IV. Since our theory implies that trade should reduce
we have repeated
here the regression for the subsample of
countries.
This point, though not other results of this paper or this section,
is
also noted
by Diwan and Rodrik
(1991).
and (16). Also a =
(Nh/Nl)/Nh/NI where "denotes full property right enforcement and denotes no property right enforcement. Lemma 4 in Appendix B provides a more detailed characterization of the term a.
22
The
expression for g
is
obtained using the expressions
(8),
(9),
(10), (15)
*
27
GDP
differences
compare between the worlds with and without international enforcement of
intellectual
The main question
property rights.
We
Proposition 8 Let
right enforcement,
Yn /Y
s
for the focus of the
with
start
GDP
paper
differences.
is
how TFP and
23
GDP in the North and Y GDP in the South without property
Yn and Y GDPs with property right enforcement, then Yn /Y <
Yn
be
and
s
s
s
.
GDP
Property right enforcement leads to
rights enforced in the South, technologies
convergence.
With
intellectual property
produced in the North are more suited to the
This leads to faster improvements in labor-complementary tech-
needs of the South.
nologies than skill-complementary technologies,
and narrows the output gap between the
South and the North.
The
results
on
TFP
When
convergence are more complicated.
enforced, two changes occur relative to the environment of Section
is
directed towards unskilled technologies (the
BGP Nh/Nl
property rights are
II.
First,
more
R&D
TFP
ratio falls), leading to
convergence. Second, both the South and the North increase the range of goods which
are produced with unskilled technologies, as implied by equation (9).
second force
reduces
is
TFP
Numerical calculations show, however, that the region of the
differences.
TFP
leads to divergence
it
in
but this condition
Appendix
B
is
is
extremely small.
parameter condition which rules out
exists a relatively non-restrictive
prove
effect of this
ambiguous, and we cannot conclude that property right enforcement always
parameter space where
analytically,
The
complicated, so
(available
upon
request).
we
Moreover, there
this possibility
state the relevant proposition
Here,
we simply note
that for most
parameterizations, enforcement of intellectual property rights leads not only to
convergence but also to
23
to
TFP
convergence.
and
GDP
24
An important issue in this section is the transfer of machine sales revenues from Southern monopolists
R&D firms in the North.
and
sell
the
new machines
To
simplify the analysis,
we assume that these monopolists continue to
now owned by Northern inventors. So
to local producers, but they are
exist
their
GDP in the South is unaffected by
whether these rents remain in the country or not, and can be compared to the GDP without property
rights. However, GNP and consumption in the South cannot be directly compared, and even when there
is GDP convergence, as shown here, there may be consumption divergence.
24
For the parameters we used in the calibration of Section III.B (which were chosen to match the
wage premium and educational attainment of the U.S. i.e. Z = 1.82, H/L — 0.51), the introduction of
property right enforcement leads unambiguously to TFP convergence as long as the South has a relative
s
skill endowment less than 0.0225 the endowment of the North (i.e.
/L s > 0.0225Hn /Ln Moreover,
revenues are tranferred to the North. This assumption implies that
H
even
if
we consider
the case in which the South has no skilled workers at
).
all,
the result that
TFP differences
be reversed when that the market size of the South is more than a
thousand times larger than that of the North. This is, clearly, highly unrealistic. This numerical result is
highly robust, and even very large perturbations of the parameters do not lead to any significant change.
decline with property rights can only
28
A
number
made
of interesting observations can be
at this point. First, although the
introduction of intellectual property rights will generally reduce
ensure
not, in
itself,
in the
North
make use
is
TFP
equalization. In particular,
TFP
will
and the same
TFP in the North than in
differences in TFP to be valid we do
then imply larger
in the previous section will
For our explanation for cross-country
the South.
not need property rights not to be enforced. Even with
there will be
TFP
full
differences. Interestingly, however, if the
North, in a world with
property right enforcement,
South
is
much
larger than the
property right enforcement, the South might have higher
full
than the North. The reason
that, in this case,
is
does
be designed to
of North's labor force even with property right enforcement,
argument as
it
the market size for technologies
if
than the one in the South, new technologies
larger
differences,
R&D
TFP
would design
firms in the North
technologies complementary to unskilled workers to exploit the larger Southern market,
and
this time, skilled
reverse
TFP
workers in the North would have low productivity, leading to the
differences.
Second, the introduction of intellectual property rights
slowdown
in the North. If
of output
and
TFP
will
sufficiently negative
is
(jj
not be
much
in the absence of property rights,
(i.e.
7
may
large), the eventual
North
will
grow
TFP
growth rate
higher with than without property rights. However,
TFP
in the
North
is
at a slower rate
than usual
not
when
adjustment process,
TFP
maximized, whereas
intellectual property rights are enforced. Therefore, during the
in the
lead to a temporary
for
it is
a while, and grow faster due to
the larger market size of the world. Essentially, the introduction of intellectual property
rights
would
needs of the North, which
Finally,
forcement,
change towards the needs of the South, and away from the
direct technical
if
is
we have both
TFP
the source of the temporary
will continue to
as above,
we can show that
This implies that the
GDP
slowdown.
free trade (factor price equalization)
and property
right en-
a result of free trade
—see previous
section).
differences will disappear (as
But there
TFP
be
GDP
differences. In particular, using the
N„T
1-J1
Nl
JT
gap
will
ZH n + ZH
"
S
Ln + L s
depend on the
lation relative to that of the North. If the
South
is
size of population of the
relatively small,
in this case will
N^/Nl
is less
than
NH /NL
be smaller than those in Section
enforcement).
29
II
South popu-
most technologies
continue to be developed for the North's workforce, and the North will
the South. However, since
same arguments
still
given by (15),
be
GDP
richer
will
than
differences
(without trade and property right
B.
Prisoner's
The
Dilemma
in
Property Rights Enforcement
analysis in the previous subsection shows that the South
enforcement of intellectual property
When
rights.
produced in the North are more appropriate
An
important question
The
is
therefore
why
that even
first possibility is
benefit from the
these rights are enforced, technologies
for the
needs of the countries in the South.
intellectual property rights
if
may
may
property right enforcement
South, contracting problems in these less developed countries
is
not be enforced.
beneficial to the
may make
it
difficult to
R&D
enforce intellectual property rights. Second, even with property right enforcement,
firms in the North
may be
differences in other factors
be made
unable to
may
sell their
technologies to firms in the South, because
require adjustments in these technologies which can only
locally.
There are
also three other reasons suggested
may
help making
payments
which deserve a
brief
in
not want property right enforcement. Property right enforcement would
new
as noted above,
analysis,
a social planner aiming at maximizing the consumption of the agents
discussion. First,
the South
by our
technologies
it
also causes
for machines).
more suited
to the needs of the labor force of the South, but
a transfer of resources from the South to the North (via the
Second, enforcement of intellectual property rights would destroy
the monopoly rents accruing to the statutory monopolies in the South. Accordingly, they
may campaign
Mokyr
(19^0), Krusell
and Rios-Rull (1995) among
be destroyed by a change in economic organization
Finally, there's also
To
As
against the introduction of property rights.
it is
also
emphasized by
others, the presence of rents that will
may
a classic prisoner's dilemma
block progress.
among
the countries in the South.
see this, consider a situation in which property right enforcement decisions are taken
by each country's government, which has the objective of maximizing
GDR
Assume
that property right enforcement increases the present value of consumption in the South.
Suppose that property rights are enforced in
ernment
in the South, however, has
property rights within
market
its
for technologies,
all
Southern countries. Each individual gov-
an incentive to deviate and reduce the enforcement of
borders. This change will only have a small effect
and hence, on the technologies developed
individual country has therefore
little
on the
in the North.
to lose by this deviation, but gains a large
by saving the transfer of income to the
R&D firms in the North.
small countries in the South, the unique equilibrium in the
overall
As a
result,
The
amount
with
many
game where each government
chooses the degree of enforcement will be one with no property rights enforcement. This
suggests that the enforcement of intellectual property rights internationally
a coordinated
effort.
30
may
require
Human
VI.
Capital and Convergence
Since differences in
may end up
countries
we endogenize the
this section,
we
why
useful to understand
it is
composition are the source of income and
skill
skill
with different
TFP
levels of skills.
acquisition decision of individuals.
model
consider an overlapping generations
differences,
In
In particular,
where within each
in continuous time,
generation agents are heterogeneous in the length of time that they need to spend at
become
school in order to
We
skilled.
characterize the equilibrium of this economy, and
show that within the context of the model,
differences
between the South and the North
can be captured as a difference in the distribution of schooling
We then show that a
costs.
Southern country which experiences a reduction in the costs of schooling
more
and the gap of GDP and
skills,
death equal to
faces a flow rate of
chard, 1985).
to
become a
in country
the population
Tx
skilled worker. It takes
The
c.
distribution of
assume that there
T
is
there
is
BGP
and v
a single-crossing property:
is
small,
it
Tx < Tx
all
When
fine
_
talent
T
where r
exp [_( r
+v
is
C
(T) has no mass points.
_|_
W )( T
_
right enforcement in the South.
an individual with
cost of education
also acquire skills.
Therefore, there
Tx > T do not
GC (TC
skills, his
t)]wL {r)dT
acquire education. Although
if
we assume
that
and
not.
)
return at time
= wL /
the effective discount rate and
contrast the agent with
T
We
takes the simple form:
wages grow at the rate g as given in Section
If in
G
and
rest of the setup is
needs to be indifferent between acquiring
he does not acquire any
j-oo
if
must
>
IP
The agent with
G C (T)
in innate ability,
a complicated function of past education decisions,
in general
are near
given by the function
H/L and the skill premium remain con-
which
as a situation in
a cutoff level of talent, T, such that
is
(as in Blan-
the only source of heterogeneity in this economy,
is
no commodity trade and no property
chooses schooling, another with
H/L
we
BGP,
is
by government policy towards education. The
We now define a BGP
exists
1
and each
periods for agent x to become skilled, and during
unchanged. To simplify the exposition, we assume that
Tx
constant at
market imperfections, or to differences
credit
also influenced
stant. In
is
period,
Each agent chooses upon birth whether to acquire the education required
and may be due to
it is
v, so that
he earns no labor income. The distribution of Tx
this time,
accumulate
TFP between this country and the North will decline.
v of unskilled agents are born every
In each country, a continuum
will
II,
°°
skills
t is:
exp[-(r
+ v — g)r]d,T = w L (r + v — g)
we have used
the fact that along the
BGP,
the rate of technical progress in the North.
decides to acquire education, he receives nothing for a
segment of time of length T, and receives
wH
31
thereafter. Therefore, the return to agent
f
from acquiring education,
t)]w H (T)d,T
=
R e (T) = R ne
R
e
can be written
(T),
Re (T) =
as:
J^j.exp[— (r
+
v)(r
—
+ v — g)T]w H /(r + v — g). In BGP, for T to be indifferent, we need
c
times, so in country c, wH
/w Lc = exp (r + v — g)TA. Inverting this
exp[— (r
at all
equation and substituting into (25),
we obtain the
relative supply of skills as a function
of the skill premium:
EL =
L*
The equihbrium
in turn
the
skill
skills
c
(\n(w%/wl)/(r
is
premium
of the North,
H/L, there
is
'
given by the intersection of the relative supply (26)
H
w^/w^l
H/L, and
{
+ v-g)y
determined by (12) above
determined from (15) given
decreasing function of
We
l-G
of each country
with the relative demand for
is
G c (ln(w<H /wi)/(r + v-g))
n
/L
=
n
,
Nh/Nl- Nh/Nl
a given
which can be calculated by substituting
Z, into (26).
(26) traces
for
wh/wl
Since (12) defines
as a
an increasing relation between vjh/wl and
always a unique equilibrium for each country.
need the supply of
skills to
above shows that
in the North, so fewer people should choose
This implies that the function
to acquire skills in the South.
first-order stochastically
be larger
dominate that in the South. To see
premia are higher in the South
skill
Psacharopoulos, 1973, Table 8.4).
then more, rather than
If
less people,
(in
G
c
in the
this, recall
that our analysis
accordance with the findings of
the South and the North had the same
would acquire
the South.
skills in
a number of reasons for this difference in the propensity to invest in
differences in G"s).
North should
Government subsidies
for education are
G
function,
There could be
skills (i.e.
more extensive
for the
in the North,
reducing the costs of education as captured by G, and individuals have better access to
credit
more
and typically longer
life
expectancy. All these factors
make investments
in skills
desirable.
The next
proposition summarizes the equilibrium in this case:
BGP equihbrium with endogenous skiU acquisition is characterized
wH /w l = Z and (26) for c = n determine the relative supply of skills in the
Proposition 9 World
as foUows:
r
North, equation (15) then determines the relative state of technology,
Nh/Nl, equations
BGP
is
(12)
and
(26) for c
=
s determine the
equihbrium in
Nh/Nl- Given
the South. The
locally stable.
The most
interesting conclusion of this analysis with endogenous skills
change in the function
to the North,
is
run relative supply of
that the
G c for a country will lead to a change in its supply of skills relative
and therefore to
balanced growth path
is
stable,
TFP
convergence or divergence. In particular, since the
when the North is
skills will
in
BGP, a country with less than its long
gradually accumulate
32
skills
and experience
faster
than
average
TFP
growth. Therefore, countries that improve their
to the U.S. should also experience
from the
historical accounts of
of adopting
with rapid
TFP
composition relative
skill
convergence. This pattern receives
some support
development of Korea and Japan, whereby the process
new
technologies and productivity convergence for these countries coincided
skill
accumulation (see for example, Rhee, Ross-Larson and Pursell, 1984;
Lockwood, 1968).
Local Technologies and Divergence
VII.
So
our analysis has assumed that firms in the South use technologies developed in
far,
the North. In practice, Southern firms
may
decide not to import Northern technologies,
and use instead
This
is
Many new
can be
"local technologies".
especially relevant for unskilled workers.
unskilled technologies turn formerly
efficiently
performed by unskilled workers. But, when these technologies are not
may
advanced, they
sufficiently
complex tasks into simpler ones that
not be very useful to unskilled workers in relatively
skill-
For example, advanced computers and software enable firms to use
intensive sectors.
but this would not
relatively unskilled workers, while tracking inventories automatically,
have been possible with the computers of twenty years ago.
A
firm employing unskilled
workers would then have been obliged to find other methods of inventory control.
To
we assume,
discuss these issues,
produce output in sector
local technologies
owns each
i
by using
in this section, that unskilled workers can also
local technologies.
To
simplify the analysis,
symmetric to those imported from the North, that
local technology
and
sells
a local monopolist
machines embedding the relevant technology to the
local producers. In particular, equation (2)
k L {i,v)
/
is,
we make
l
-p
now changes
dv
to:
[(l-i).l(i)f;M(i)k^l{if
Jo
+
where M(i)
is
/
Jo
kH {i,v)
l
-p
[i-z- h{i)f
dv
,
the productivity of local technology in sector
marginal cost of local machines
is
(r
+ 6)/(l — P),
North, so that they will have the same prices.
imported from the North improve steadily
—
i.
We
also
assume that the
as for the machines imported from the
The only
at the rate
g in
difference
is
that technologies
BGP— while the productivity
of local technologies remains constant at M(i).
The next
proposition follows immediately (proof omitted):
Proposition 10 Producers
M(i)
>
(1
— i)NL-
in the
Eventually,
all
South use local technologies in sector
local technologies are
33
i
< Js
as long as
abandoned. Suppose the North
is
in
BGP,
then, until
all local
technologies are abandoned,
GDP
and
TFP
in the
South
diverge from their values in the North.
When
local technologies are available, the
of the North, even though
it
has access to
South does not always use the technology
In particular,
it.
when
the labor-complementary
may
technologies of the North are not very advanced, local technologies
of a country better than the skill-complementary Northern technologies.
suit the needs
Our assumption
that most technical change takes place in the North implies that local technologies will
not improve as quickly as Northern technologies. Thus, while
both the
GDP
point,
will
it
and
TFP
become
of the South will
beneficial for the
North, and income and
TFP
fall
it
uses local technologies,
relative to the North. Nevertheless, at
some
South to start importing technologies from the
inequality between the South
and the North
will eventually
stabilize.
VIII.
Conclusion
In this paper,
we have developed a model with TFP
and advanced economies. Richer countries have higher
firms in
all
differences
same
countries have access of the
is
the difference in the supply of
North has more
skilled workers,
in the South. Furthermore,
differences
TFP
between
levels, despite
developed
the fact that
The source
set of technologies.
skills
less
of
TFP
between the South and the North. The
and employs them in tasks performed by unskilled workers
we made two
technologies are developed in the North,
crucial,
but plausible, assumptions: most new
and technical change
is
directed, in the sense
that more profitable technologies get developed and upgraded faster.
of skills in the North implies that
new
The
larger supply
technologies are relatively skill-complementary,
whereas the South, which employs unskilled workers in most tasks and sectors, needs
more labor-complementary
technologies. This
and technologies imported from the North
In the data, there
TFP
is
TFP
Moreover, even though
it
skill
skills
of the South
differences.
composition and the
ignores a range of relevant
such as distortions in technology transfer, slow diffusion, corruption,
model can account
As
the source of the
a high degree of correlation between the
differences across countries.
factors,
is
mismatch between the
for
TFP differences we
for TFP differences,
a sizable fraction of the
well as proposing
a new explanation
number of potentially important determinants of TFP.
First,
etc.,
our
observe in practice.
our model suggests a
commodity trade
influences
technological developments. In particular, free-trade implies that the South specializes in
tasks that can be performed efficiently
by unskilled workers, and ensures
TFP convergence.
Nevertheless, trade without property right enforcement also encourages the North to
develop further skill-complementary technologies, which do not yield
34
much
benefit to the
So despite causing
South.
TFP
convergence, trade amplifies
GDP
differences
between
the South and the North. Second, the extent of intellectual property rights in the world
is
also a
major factor
TFP
in
differences. If the South, collectively, enforces intellectual
property rights, this will encourage Northern
R&D
firms to develop technologies
gap between
rich
stylized pattern of convergence
and
suited to the needs of the countries in the South, reducing the
and poor
Finally, our
countries.
divergence of
TFP
and
GDP
model suggests a
Southern countries which improve their
across countries.
skills
base relative to the North will experience faster
TFP
and income
the North
TFP
growth, and converge to the
levels of these richer countries. In contrast, countries will diverge
when they
in the North.
TFP
But
prefer to use local technologies, rather
this process will eventually
countries start importing
more
come
from
than import those developed
to an end,
and
as all less developed
and using Northern technologies, cross-country income and
TFP
differences will stabilize.
Clearly, our
diffusion of
new
model has abstracted from important determinants of TFP, such
technologies,
and economic and
as slow
political distortions in the process of
technology adoption. This has been done in order to emphasize that even in this environ-
ment
less
of free technology flows
and more developed
and no
distortions, there will
countries, essentially because
to suit the needs of advanced economies.
differences
Our
distortions interact,
is
new
TFP
differences
an area
between
technologies are developed
results suggest that this source of
might be considerable and should be taken into account when
sources of output differences across countries.
paper
be
How slow
diffusion of
new
asse; jing the
technologies and
both qualitatively and quantitatively, with forces emphasized
for future research.
35
TFP
in this
Appendix A: Proofs of Main Results
Proof of
Lemma
The
1:
a firm using technology z in sector
profit of
= p(i)y(i) -
II z (i)
Xz(v) kz(i, v)dv
/
i is:
- wz z
(27)
{
Jo
We proved in the text that profit maximization implies that x z u =
J
zjt where Dz = 1 if z = L
(1 - 0) and kz (i, v) = k z (i) = (p ((1 - ifD z + i^(l - D Z
)))
and D z = if z = H. Thus, we can use (27) to write per worker profit:
where z G {L,H}.
(
)
{
Ml = (p(i){(i-if Dz + i^l-D )))^N
Ui) =
-
(1
where competition implies
C L (z)
is
a strictly increasing function of
i
over
all
goods
i
G
or
Ch(0
have either Cl(0
=
=
Hz^i)
some
that in equilibrium
=
Thus a
skill class falls
positive
such that ( H (J)
0,
- wz
Now,
(28)
note ( H (i)
first
—
have to be produced. So Vi we must
(0, 1)
=
or both. Finally,
not possible
it is
workers are unemployed, because this would
to zero, hence, from (28), there
would
exist a
measure of variety of goods must be produced using
< J<
alH > J and vice versa for i <
skilled (unskilled) workers. It therefore follows that there
— (l(J) =
0, Vz.
z
Next, observe that Cobb-Douglas
[0,1].
n^-(i)
skilled (unskilled)
imply that the wage of this
profitable deviation.
<
that, in equihbrium, Tl z (i)
technology in (1) implies that
N
- t)'^ + 0(1 - D z
))f
0) (p(i) ((1
-
z
z
and C# (0
— Cl(^) >
f° r
must
exist
J (where
1)
J.
QED
Proof of
J
is p(i') (1
it
Lemma
2:
^
—i'f
To
derive a contradiction, suppose that for
— i'Y
p(i'){l
Consider two firms in sectors
unskilled technologies. In equilibrium, these
substituting
Pl
(1
—
for
i)
We
Dz =
Thus,
can then rewrite equation
_
/
Pt 0W NL
Then, since
all i
>
J,
and y(l)
p(i)
Pjr,
we have y
=
{
P\j
(skilled) workers.
''
(1
=
— i)
i(i)(i
.
-
i)-e
l(i)
=
However,
J, p(i)
J, p(i)
=
=
Pni~®
<i<J
o
if
J,
we have
yi
=
y(0)(l
Furthermore, (29) imphes that
Nnh{l). Hence,
Thus,
<
for all i
,
y(l)i~ p
<
both using
<
i
i"
(5) as follows:
Next, recall that consumers' utility maximization implies that piyt
=
for all
<
i'
profits.
A similar argument establishes that for all i >
some Pl.
v(i)
i',i",
two firms must make zero
in equation (28) gives a contradiction.
1
some
L/(l
l[i) {h(i))
-
must be equal
J) and h(i)
^
36
=
H/J.
=Y
—
j/(0)
for alii
G
(0, 1)
i)~P. Similarly, for
=
1-/3)//3
P[
iVL Z(0)
in all sectors using unskilled
We
need to prove that Ph/Pl
finally
(and, in particular, p{0)y(0)
h
y(l)
Ptf
2/(0)
where the second equahty
(30) establishes (8).
= p(l)y(l)),
x
=
that
(Fir/r)
7T
=
1'
BGP
(g).
tt l
,
and g
=
=T
now
(6), (7)
,
then:
J)
{
and
BGP
(29).
1 /7
in the text.
is
= Tx ^
BGP x# — x^ =
1
we know that g
(4)
Tx' 1
= Vz =
t/tt z
(1_ "' 7
(7r/r)
j
Rearranging terms in
- p)L /J =
Define
Nl/Nl and k/k = x H /x H —
n
xl/xl).
We start with the growth
= Tx ^ 1 = Tx 1-7 where
1
Recall,
x.
first,
that free
Thus, in a balanced growth equilibrium,
.
-
exp(-l)/3(l
and the second follows from
stability.
1
In order to derive the expression of
.
n
exp(-l)/?(l
equality follows from (10)
Consider
= PH
pi
1:
From
implies that
1
Pi and
=Y
piyi
QED
the last equality exploits the fact that in
R&D
Observe that, since
(8).
Pg-MNHH/jl Pt PW NL L/J
Proof of existence and uniqueness of
entry in
=
p(0)
obtained by using
is
Proof of Proposition
rate along the
given by
is
= Nh/Nl
p) (L
n
+ ZH
n
,
)
rr,
observe
where the
first
(15).
=
and k
xh/xl
(so,
n/n
=
Recall that free entry implies Yx'^Vz
NH /NH —
=
1
at all
points, so
xz
Vz
r
7r 2
xz
lVz
7
^Txl
(n)
= p(l~P) {PI) "3 Ln = exp[-l]p(l-p)L n (l + ^jn ZH n /L n ) and7r H (n) =
Hn = exp [-1] p(l-P)Hn (l + (l/y/n-ZHn /Ln ))(the second equalities
P(l-P) (PS)
1
where n L (n)
l/l3
in
both expressions follow from
observe that (4) implies that
system of
Clearly,
(8)-(9)-(10)).
h/n
= x^
1
1
(1
—
ac
)
differential equations describing transitory
n
n
k
XH
xH
The stability
properties of this
=
^(l-* -7
.
We
and
H {n) <
Tt'
0.
Next,
can then write the following
dynamics:
1
= [iTxVT
1
[*H(n)
T_
TTg(^)
7
l rx H
(31)
)
- n L (n)]
dynamic system are "block-recursive" Note,
.
that although x H affects the speed of growth of both
it
>
L (n)
7r'
1-7
n and k
in first
in particular,
two equations,
does not affect the sign of the dynamics of neither of these two variables.
therefore determine first the stability of n
and
k,
can
and then characterize the behavior of xh-
Figure 8 gives this argument diagrammatically. Recall that
37
We
n
is
the only predetermined
=
k
h
Figure
<
from any n
variable. Starting
monotonically converges to
n
Transitional dynamics.
8:
n*, (e.g.-
= n*
=
and k
n
=
in Figure 8)
1.
The
we have k <
converse applies
Finally, the inspection of the third equation of (31)
1,
and the system
when
n> n*.
shows that given the dynamic
adjustment of n and 7r#(n), there exists a unique trajectory of x H converging to the
with
±h =
Since
0.
Xh
is
not predetermined, xjj will be set in equilibrium along this
QED.
converging trajectory at every point of time.
Derivation of Equations (20) and (21): Substitute
h{i)
=
H/{\ -
Y =
exp
(
J), kL (i,v)
f log(l
-
'NL (Pl' p L/j)
Now, using the
fact that
Y=
=
Pl
ifdi
l
/P
L/ J and k H (i,v)
+
defined in
in all
Lemma
)
=
P]j
p
for y(i) using (2), l(i)
ZH/{\ -
=
L/J,
J) in (18):
x
i-j
x [nh (P]I P ZH/{1 -
J)Y'\ZH/(1 - J)Y
KL = NL Pl'p L and KH = NH P^ZH, we obtain:
B( J,
NL NH
,
)
[Kl^lP]
B(J,NL Nh)
,
x [KH l -P
is
-ii-j
(ZHf
as defined in equation (19).
(Part l)Recall that technology parameters, Nl and Nh,
Nr
n
= Jm as
economies. Then, equation (15) implies that J — N +N
Proof of Proposition
same
f logi^di
~\L/J)^
where integration estabhshes that
are the
BGP
3:
.
3.
Therefore,
TFP
is
maximized, along BGP, in the North.
s
Since
jj < j-, Proposition 2 - and, in particular, equation (16) - implies that J > N£fN
Applying again Lemma 3 estabhshes that TFP in the South is strictly less than TFP in
the North.
38
(Part 2)With the alternative definition of
also
an inverse U-shaped function with a
maximum
we have
(19),
Jm
at
that
B(J,NL ,NH
)
is
where:
(NH \wi
./'"'
I
TFP,
Jm
V
N1L
- J n )/Jn = ZHn /L n > (1 - J n )/Jn = Z^J{H n /L n (H /L s ).
This implies that NH < NL i.e. ZH n < L, is sufficient to guarantee B(J n ,NL ,NH >
B(J S NL NH ). So if ZH n < L, the desired result is established.
From
(15),
we have
s
(1
)
)
,
,
,
> NL
Let
S
A = (H /L )/(H
< 1. Then, 3A < lsuch that if A < A, then B(J ,NL ,NH >
B(J S NL NH ). This follows immediately by observing that if A = 0, then B(J S NL NH =
minj B( J, NL NH ) = NL and B( J, NL NH is continuous in J. QED.
Next,
s
the
n
n
/L
consider
s
ZH n >
where
case
L",
so
Nh
that
.
)
,
)
,
Proof of Proposition
4: First, trade ensures that
are equalized. Equation (9) in Section
are
now
II.
C
still
commodity
J
determines
when the
prices,
Pj and P^
in each country given prices.
the same in the North and the South, so
Next, observe that
)
)
,
,
Pl and Ph
,
,
J7^ — JTn
(unanticipated) trade opening occurs,
= JT
.
Nh/Nl
is
given
This implies - given equations (8)-(9)-(12) - that immediately after
(predetermined).
trade opening (PH /PL )
n
< (Ph /Pl)1 <
(Ph/Pl)",
n
Jn < Jl < J s and (w H /w L ) <
(wH /wL )Jo < (wH /wL y
After the impact effect of trade opening, the state variables
now
BGP
the
condition, (23),
when (Ph/Pl)
71
'h
>
7T
'l-
T
=
no longer
is
(Ph/Pl)" Since
This condition
satisfied.
after trade
Nh
opening (Ph /Pl)
T
will
>
d
ai
be
NL
change, as
satisfied again
(Ph/Pl)", we have
Transitory dynamics can be characterized by an argument identical to that
of Proposition
In particular, (31) applies exactly except that the second differential
1.
equation has a different "zero". Therefore, our previous argument immediately implies
that after trade opening x H
As Nh/Nl
world
increases, the
Proof of Proposition
to
GDP
in the
South
> x^
5:
until
skill
(L n fl 2
+ (^-ZH n l^
(L«)i/2 + (ZjlzH*)*/ 2
s
strictly increasing in
(from Proposition
4),
increases,
GDP in the North
is:
Y
is
premium
(NH /NL ) T as given by (24).
and Ph/Pl and J decline. QED
converges to
Equation (11) implies that the ratio of
Yn
which
Nh/Nl
so
it
increases
Proof of Proposition
A(l NL
,
Nh/Nl
l
since
)
Hn /Ln
>
(32)
H /L
s
s
Trade increases
.
Nh/Nl
Yn /Y QED
s
.
6: Recall that
NH =
2
)
TFPl
-J
[NLJ NH
(1
39
-
is:
J)-
(w) J- J
f
•
exp[-l]
(33)
Since
J s = J n with
TFP
trade,
argument applies to TFP2, B(J,
Proof of Proposition
of property rights reduces
convergence.
8:
North and the South are equalized The same
in the
NL NH QED
).
,
Once again
Nh/Nl
(see
GDPs
relative
Lemma 4
in
are given by (32). Enforcement
Appendix B), and hence
leads to
GDP
QED
Proof of Proposition
9:
As
before, equilibrium in the
North can be characterized
without reference to the South, since there are no property rights or commodity trade.
Equation (15)
premium
skill
the
BGP
still
in the
North
with (26)
this
is still
Given
in the North.
combining
R&D
determines equilibrium
equal to Z. Combining this with (26), for c
NH and NL
for c
=
choices for given relative supplies.
s gives
,
(12) gives the skill
the
BGP
skill
premium
premium and
=
The
n, gives
in the South,
and
relative supplies in
the South.
Finally, to analyze the local
a differential equation in £
H
/Ln
Recall that
.
we only need
economy continues to be block
equilibrium (the world
North's equilibrium
=
dynamics, augment the dynamic system in (31) with
n
first,
to describe North's
recursive, so
we can
solve the
without reference to the South). Around the North's BGP, we
have:
j
_
6{
U
H»m /* = g| - g = „r. «M)
[in
/ (r
+v-
,)] I
IT -
[l-r4nWK)/(r+o-j)]]/i"
Using a first-order Taylor approximation, we write:
c
=4
n
n
-
[wH /w L
n
[w H /wl)
SS
]
[n- n ss
-d 2
where
d\
>
and d2
>
0,
(34)
]
c
and the superscript SS denotes steady-state.
equations (8) and (12) from the text,
we can
system of linear
which applies around the BGP:
differential equations
replace relative wages and end-up with the
n
- =
-Oi(/C-l)
I -
-M«-»
n
—
xh
£
ss
)
(n-n ss )+c2 (x H -x sHs
=
Cl
=
-(d 1 /2
)
+ d2 )((-( ss + d (n-n ss )/2
)
40
Then, using
1
The second equation
generally depends on relative skill supplies in the North, £
= H n /L n
,
but this dependence disappears in the neighborhood of the BGP. Therefore, the system
ss we have
continues to be block-recursive, so starting from n < n
xh > x L n = Nh/Nl
,
,
increases to its
BGP value.
Similarly,
if
H
n
towards that value. Given the behavior of
South also converges to
its
BGP
/L
n
is less
than
its
BGP value,
it
also increases
NH /NL determined in the North, H
level following
41
equation (34).
QED
s
/L s
in the
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44
Inequality:
Changing Fortunes in a
Appendix
A (Continued)
Table
A
Country
B|CR
Bhj
A
B
B2
H/L
(H/L) 2
J
Algeria
0.996
0.841
0.858
0.673
0.814
0.024
0.067
0.834
Benin
0.559
0.442
0.780
0.530
0.596
0.006
0.012
0.908
Botswana
0.778
0.309
0.788
0.543
0.767
0.007
0.048
0.902
Cameroon
0.702
0.422
0.788
0.543
0.710
0.007
0.031
0.902
Central African Republic
0.410
0.293
0.760
0.498
0.531
0.004
0.006
0.924
Congo
0.915
0.533
0.876
0.708
0.770
0.031
0.049
0.814
0.800
0.905
0.768
Egypt
0.048
0.778
Gambia
0.487
0.417
0.709
0.419
0.573
0.001
0.010
0.961
Ghana
0.509
0.362
0.795
0.556
0.632
0.008
0.017
0.896
Kenya
0.451
0.301
0.788
0.543
0.597
0.007
0.012
0.902
Lesotho
0.487
0.333
0.771
0.515
0.624
0.005
0.016
0.916
Liberia
0.487
0.839
0.636
0.586
0.017
0.011
0.854
Malawi
0.380
0.218
0.760
0.498
0.529
0.004
0.006
0.924
Mali
0.463
0.337
0.748
0.478
0.541
0.003
0.007
0.934
Mauritius
0.801
0.846
0.878
0.713
0.807
0.032
0.064
0.812
Mozambique
0.529
0.469
0.709
0.419
0.582
0.001
0.011
0.961
Niger
0.380
0.255
0.732
0.453
0.494
0.002
0.004
0.945
Rwanda
0.539
0.435
0.748
0.478
0.612
0.003
0.014
0.934
Senegal
0.577
0.507
0.827
0.613
0.642
0.014
0.018
0.866
0.696
0.771
0.515
0.596
0.858
0.673
0.812
0.024
0.066
0.834
0.379
0.795
0.556
.
0.008
.
0.896
Sierra
Leone
South Africa
0.790
Sudan
0.005
0.916
Swaziland
0.688
0.575
0.827
0.613
0.728
0.014
0.036
0.866
Togo
0.410
0.234
0.831
0.621
0.536
0.015
0.007
0.862
Tunisia
0.915
0.776
0.871
0.699
0.788
0.029
0.056
0.820
Uganda
0.475
0.369
0.748
0.478
0.591
0.003
0.012
0.934
Zaire
0.438
0.295
0.780
0.530
0.558
0.006
0.008
0.908
Zambia
0.410
0.184
0.788
0.543
0.596
0.007
0.012
0.902
Zimbabwe
0.568
0.307
0.807
0.577
0.649
0.010
0.019
0.885
Barbados
0.861
0.830
0.917
0.794
0.911
0.058
0.141
0.762
Canada
1.021
1.023
0.988
0.964
0.994
0.239
0.397
0.612
Costa Rica
0.829
0.635
0.963
0.902
0.837
0.131
0.080
0.680
Dominican Rep.
0.778
0.610
0.927
0.817
0.785
0.068
0.054
0.747
El Salvador
0.735
0.631
0.884
0.725
0.748
0.035
0.041
0.804
Hf
Bkr
Bhj
A
B
B2
H/L
(H/L) 2
J
Guatemala
0.818
0.828
0.886
0.730
0.758
0.036
0.045
0.802
Haiti
0.529
0.410
0.788
0.543
0.594
0.007
0.012
0.902
Honduras
0.666
0.507
0.882
0.721
0.716
0.034
0.033
0.807
Jamaica
0.586
0.378
0.871
0.699
0.694
0.029
0.028
0.820
Mexico
1.113
0.950
0.935
0.836
0.905
0.079
0.135
0.733
Nicaragua
0.728
0.429
0.937
0.840
0.745
0.081
0.041
0.730
Panama
0.807
0.487
0.961
0.896
0.861
0.125
0.095
0.686
1.202
0.851
0.882
0.721
0.969
0.034
0.255
0.807
USA
1.000
1.000
1.000
1.000
1.000
0.508
0.508
0.520
Argentina
0.829
0.749
0.943
0.853
0.885
0.089
0.114
0.721
Bolivia
0.643
0.453
0.937
0.840
0.730
0.081
0.036
0.730
Brazil
0.896
0.831
0.927
0.817
0.810
0.068
0.065
0.747
Chile
0.728
0.546
0.943
0.855
0.835
0.091
0.078
0.719
Colombia
0.850
0.706
0.919
0.800
0.820
0.060
0.070
0.758
Ecuador
0.795
0.530
0.972
0.923
0.830
0.157
0.075
0.660
Guyana
0.475
0.277
0.849
0.656
0.951
0.020
0.207
0.844
Paraguay
0.747
0.524
0.903
0.765
0.782
0.047
0.053
0.780
Peru
0.728
0.551
0.965
0.907
0.812
0.136
0.066
0.676
Uruguay
0.702
0.695
0.942
0.851
0.826
0.088
0.073
0.722
Venezuela
1.029
0.890
0.955
0.882
0.905
0.111
0.134
0.698
Bangladesh
0.778
0.893
0.839
0.636
0.722
0.017
0.034
0.854
Burma
0.438
0.255
0.846
0.649
0.561
0.019
0.009
0.847
.
0.224
0.813
0.587
Hong Kong
0.948
1.075
0.939
0.844
0.940
0.083
0.184
0.727
India
0.509
0.415
0.890
0.737
0.623
0.038
0.015
0.797
Indonesia
0.620
0.388
0.780
0.530
0.703
0.006
0.030
0.908
Iran
0.987
0.744
0.866
0.689
0.840
0.027
0.081
0.825
Iraq
1.102
.
0.909
0.778
0.865
0.052
0.098
0.773
Israel
0.929
0.874
0.995
0.984
0.971
0.316
0.261
0.578
Japan
0.824
0.757
0.980
0.943
0.932
0.190
0.171
0.639
Jordan
1.148
0.999
0.960
0.895
0.912
0.124
0.143
0.687
Korea
0.772
0.695
0.964
0.903
0.891
0.133
0.120
0.679
Malaysia
0.824
0.587
0.849
0.656
0.839
0.020
0.080
0.844
Nepal
0.577
0.831
0.621
0.608
0.015
0.014
0.862
Pakistan
0.681
0.684
0.849
0.656
0.681
0.020
0.025
0.844
Philippines
0.568
0.368
0.985
0.956
0.755
0.217
0.044
0.624
Singapore
1.012
1.051
0.900
0.759
0.881
0.045
0.110
0.784
Country
Trinidad
& T.
China
Y"
0.880
0.011
MIT LIBRARIES
3 9080 01444 0736
Bkr
Bhj
A
B
B2
H/L
(H/L) 2
J
0.715
0.537
0.827
0.613
0.798
0.014
0.060
0.866
Syria
1.192
1.032
0.939
0.844
0.914
0.083
0.145
0.727
Taiwan
0.886
0.844
0.960
0.895
0.911
0.124
0.141
0.687
Thailand
0.628
0.514
0.910
0.780
0.740
0.053
0.039
0.771
Austria
0.948
0.986
0.919
0.800
0.927
0.060
0.162
0.758
Belgium
0.929
0.985
0.959
0.891
0.972
0.120
0.264
0.690
Cyprus
0.795
0.747
0.974
0.927
0.883
0.163
0.113
0.656
Denmark
0.840
0.792
0.987
0.960
0.972
0.229
0.263
0.617
Finland
0.834
0.809
0.973
0.925
0.954
0.160
0.213
0.658
France
1.017
1.082
0.958
0.888
0.939
0.117
0.183
0.692
Germany
0.906
0.940
0.939
0.844
0.956
0.083
0.218
0.727
Greece
0.834
0.769
0.946
0.862
0.893
0.095
0.122
0.714
0.441
0.939
0.844
Country
Sri
Lanka
Hungary
0.083
0.727
Iceland
0.961
0.955
0.951
0.871
0.951
0.103
0.207
0.707
Ireland
0.886
0.795
0.952
0.876
0.937
0.106
0.180
0.703
Italy
1.017
1.134
0.930
0.823
0.935
0.072
0.175
0.742
Malta
0.861
0.820
0.884
0.725
0.902
0.035
0.131
0.804
Netherlands
0.992
0.964
0.973
0.925
0.972
0.160
0.264
0.658
Norway
0.906
0.788
0.972
0.922
...984
0.156
0.315
0.661
0.381
0.937
0.840
Poland
0.730
0.081
Portugal
0.807
0.829
0.903
0.765
0.796
0.047
0.059
0.780
Spain
0.970
1.070
0.933
0.830
0.905
0.075
0.134
0.738
Sweden
0.896
0.983
0.950
0.970
0.203
0.258
0.631
Switzerland
0.911
0.920
0.964
0.904
0.966
0.134
0.246
0.678
Turkey
0.735
0.632
0.897
0.752
0.741
0.043
0.039
0.789
United Kingdom
0.906
1.007
0.969
0.915
0.957
0.147
0.221
0.668
Yugoslavia
0.688
0.487
0.947
0.863
0.843
0.096
0.083
0.713
Australia
0.934
0.902
0.992
0.976
0.985
0.279
0.323
0.594
Fiji
0.766
0.574
0.903
0.765
0.854
0.047
0.090
0.780
New Zealand
0.850
0.736
0.999
0.997
0.991
0.435
0.368
0.539
Papua N. G.
0.539
0.362
0.771
0.515
0.606
0.005
0.013
0.916
Reunion
.
0.645
0.827
0.613
.
0.014
Czechoslovakia
.
0.387
0.936
0.838
.
0.080
-
0.732
Romania
.
0.319
0.923
0.807
.
0.064
.
0.753
0.603
0.960
0.894
Soviet Union
See next page for notes.
i1
0.122
0.866
0.688
Variable Definitions:
Bkr:
TFP measure
calculated by Bils and
Klenow (1998) and Klenow and Rodriguez
(1997). See
text.
Bhj:
TFP measure
calculated
by Hall and Jones (1998). See
A: Predicted TFP1, see equation (18) in the
text.
Calculated with
text.
H/L from Barro-Lee (column
6).
B: Predicted TFP2, see equation (20) in the
text.
Calculated with
H/L from Barro-Lee (column
6).
B2: Predicted TFP2. Calculated with
H/L from Klenow and Rodriguez (column
7).
H/L: Fraction of the population aged over 25 with higher education divided by fraction without
in 1985.
(H/L)2:
From
Barro-Lee.
Human
capital
by worker calculated by Klenow and Rodriguez (1997). U.S. value
noramlized to 0.508, same as H/L from column
J:
6.
Threshold sector from the model, used in calibration. See equation (15) in the
[1
R7q
r
5
</r
text.