Full text of Working Papers (Federal Reserve Bank of Richmond) : Industrial Development and the Convergence Question, Working Paper 99-01

View original document

The full text on this page is automatically extracted from the file linked above and may contain errors and inconsistencies.

Working Paper Series

Industrial Development and the
Convergence Question

WP 99-1
(originally WP 98-10)

Marvin Goodfriend
Federal Reserve Bank of Richmond
John McDermott
University of South Carolina

This paper can be downloaded without charge from:
http://www.richmondfed.org/publications/economic_
research/working_papers/index.cfm

Industrial Development and the Convergence Question*

Marvin Goodfriend and John McDermott**

December 1998

Federal Reserve Bank of Richmond Working Paper No. 98-10

ABSTRACT: The paper studies endogenous world balanced growth equilibria
in which national learning productivity differentials govern relative per capita products.
Learning productivities depend on the national share of world specialized-goods
production, national and world scale, and familiarity with the foreign economy.
Familiarity indexes the extent to which imported specialized goods enhance learning
productivity. We find that mutual familiarization causes per capita products to
converge. Unfamiliar economies diverge substantially and persistently. Unilateral
familiarization of a less-developed country (LDC) with the leading economy causes the
LDC to catch up to, and even overtake, the leader.
JEL Nos. F12, F43, N1, O11.
Keywords: growth, convergence, trade, technology, familiarity, human capital.

The paper appears in the December 1998 American Economic Review. We are grateful to seminar
participants at the 1994 American Economics Association Meetings, Arizona State University, the
Bank of Japan, the Federal Reserve Board, the Institute for International Economic Studies at
Stockholm University, the International Monetary Fund, Miami University of Ohio, the 1993 NBER
Summer Institute, New York University, Princeton University, the University of Florida, The
University of Virginia, Virginia Polytechnic Institute, and the World Bank for perceptive comments.
McDermott acknowledges a grant from the College of Business, University of South Carolina. The
views expressed are not necessarily those of the Federal Reserve Bank of Richmond or the Federal
Reserve System.
**

Goodfriend: Research Dept., Federal Reserve Bank of Richmond, P.O. Box 27622, Richmond, VA
23261; McDermott: Economics Dept., University of South Carolina, Columbia, SC 29208.

On the eve of the Industrial Revolution the variation in national living standards
around the world was relatively small by today’s standards. Per capita products
diverged substantially during the nineteenth century as industrialization spread across
Europe and North America. Only toward the end of the century did forces making for
convergence among the leaders once again begin to assert themselves [William J.
Baumol and Edward N. Wolff (1988), J. Bradford DeLong (1988), and Angus
Maddison (1982)]. By 1900 a succession of 22 countries had achieved “ turning
points” marked by a significant, sustained jump in per capita product growth, and 12
more achieved turning points after that [Lloyd G. Reynolds (1983)]. Industrialization
was limited, however, and by the middle of the century it became clear that a large and
persistent productivity gap had opened between industrial leaders and less-developed
countries [Stephen L. Parente and Edward C. Prescott (1993), World Bank (1991)].
Lant Pritchett (1997) estimates that between 1870 and 1985 the proportional per
capita income gap between the richest and poorest countries grew five-fold, increasing
from 9 to 45.
Industrial development has seen numerous shifts in relative standing among
individual countries. Most famous perhaps is the overtaking of Great Britain by the
United States at the end of the last century. Using Maddison's data for the period 1870
to 1979, Moses Abramovitz (1986) notes that Switzerland fell by 8 places and Britain
by 10 in per capita product, while the United States and Germany both rose by 4, and
Norway, Sweden, and France rose by 5, 7, and 8 places, respectively. Japan achieved
the most remarkable record of overtaking in the last hundred years, but the postWorld War II growth miracles of the newly industrialized nations of the Pacific Rim
also constitute spectacular and unexpected cases of less-developed countries rising
rapidly into the ranks of the developed world [World Bank (1993)].
This paper presents a model designed to interpret the record of divergence,
convergence, and overtaking of per capita products that has accompanied industrial

development. We think that by modeling sweeping observations from economic
history we can uncover clues about economic development not as apparent in data
from specific countries and shorter time periods. Our model embodies three basic
ideas. First, there must be a form of localized increasing returns that induces
geographically concentrated industrialization. Such localized elements are the basis for
divergence in the model. Second, it must be possible for know-how developed in the
industrial leaders to flow to the followers. This creates the potential for convergence.
Finally, the model turns crucially on the idea that there is an important form of
jointness in production--one analogous to the jointness in production emphasized in
learning by doing models. Local production of certain goods enhances local production
of human capital.
Many models that have looked at learning by doing alone predict divergence.
Early leaders never lose their advantage. The combination of all three elements in our
model shows how this prediction can go wrong. This possibility comes from the mix of
localized elements in learning and the international flow of knowledge. These are
mediated by a combination of trade in goods and a process that we summarize with a

“ familiarity” parameter.
Growth rates converge in our model, but national per capita products generally
do not. If a lagging economy is unfamiliar with the leader, then the location of
specialized-good production matters a great deal. A growing share of specialized-good
production attracted to the leader reinforces its learning productivity advantage. And
the world converges to a balanced growth equilibrium with a wide gap in living
standards. On the other hand, when countries are broadly familiar with each other the
location of specialized-good production matters little for learning productivity. Per
capita products tend to converge because world scale exercises a more favorable effect
on growth in the lagging than in the leading economy. In the limit, when familiarity is
complete, so is the convergence of living standards.

Our notion of familiarity builds on the work of Luis A. Rivera-Batiz and Paul M.
Romer (1991), who emphasize the importance of the international flow of ideas for
growth. They study the effect on growth rates of integrating two identical economies,
however, while we explore the implications of familiarity for relative per capita
products. Our model is also reminiscent of one in Robert Tamura (1991), in which
knowledge spillovers in the investment sector of an endogenous growth model cause
incomes to converge. We, however, show how limited familiarity can account for
incomplete convergence, and how familiarization of the lagging economy with the
industrial leader makes overtaking possible.
The plan of the paper is as follows. World goods production is characterized in
Section I. Section II motivates and describes the learning technology. World balanced
growth is characterized in Section III. The model is employed in Section IV to interpret
the history of industrial development. First, we use it to understand the divergence of
national per capita products following the Industrial Revolution and the convergence
among leading industrial economies thereafter. Then, we show why a large and
persistent productivity gap can arise between a leading economy and a less-developed
follower, and why it is so difficult to close. Finally, we analyze growth miracles
— catching up and overtaking — by building on our analysis of the productivity gap.
Section V concludes with a brief summary of our results.
I. World Goods Production
The world contains two countries each of which produces an identical,
nonstorable final good with two inputs: human-capital augmented (effective) labor and
nonstorable specialized intermediate inputs. Intermediate goods are produced with
effective labor alone on a continuum over the range M = M A + M B, where M A are
produced in Country A and M B in Country B. Through trade each country uses the full
range of the world’s specialized goods to produce the final good. The appendix contains

the formal specification of the goods-producing technology and the market structure,
as well as the relevant derived equilibrium conditions. Each intermediate good is
produced in identical fixed supply by a single firm in equilibrium. Moreover, the
equilibrium world range of intermediate-good production, M, is proportional to world
scale as measured by the global effective labor supply, E.
National labor forces are immobile, but trade in goods equalizes the cost of
comparably skilled labor across countries. This means that the cross-country wage
differential is proportional to the difference in national per capita human capital. Since
effective labor is the only factor of production, national per capita final-good output
equals the product of the world base (unskilled) wage, national human capital per
capita, and national work effort per person. The common worldwide base wage rises
with world scale, E, due to increasing returns to specialization in the manner of Romer
(1987).
We assume a small shipping cost so that intermediate-good firms choose to
locate in the country with the greatest demand for intermediate goods.1 Intermediategood firms will exist in both countries if and only if sales in each market are the same.
Hence, we determine the share SM of intermediate-good firms located in Country A
under the condition of equal intermediate input use in the two countries:
S M = 1 + 2S – 1 ,
2
2α

(1)

where SM ≡ M A /M, S ≡ E A /E is the share of world effective labor in Country A, and
0 < α < 1.2 Since SM must lie between 0 and 1, equation (1) is valid only for
1 – α < S < 1 + α . Above this range, S = 1 and Country A produces all the
M
2
2

world’s intermediate goods; below it, SM = 0 and all intermediate-good production is
located in Country B.
Equilibrium condition (1) says that a country's share of world specialized-good
production depends positively on its share of world effective labor. The dependence

works as follows. An increase in the share of world effective labor in one country
relative to the other raises the relative marginal product of intermediate inputs in the
former, and so raises relative demand there, too. Specialized-good producers react by
moving to the larger market in sufficient number to eliminate the incipient inequality in
market size, unless the larger economy already produces all the world's specialized
inputs.
II. National Learning Technologies
Individuals can devote time to learning in order to accumulate human capital.
We identify three key elements that govern the productivity of the representative
individual’s learning time: own human capital, worldwide specialization, and familiarity
with the foreign economy. We combine these in the following learning technology for
the representative individual in Country i:
(2)

h = eL h

i 1–γ

i γ

M
ni

where eL is the fraction of time allocated to learning as opposed to working (eL ≡ 1 —
eW ), h is per capita human capital, n is city population, and 0 < γ < 1. The functional
form and exponent restrictions in (2) are chosen so that the model supports
endogenous world balanced growth.

^
The argument M captures the effect of specialization on the learning
productivity of a resident of Country i. Exposure and routine access to specialized
goods enhances the productivity of time spent learning for two reasons. First,
innovation involves problem solving which is facilitated by access to specialized tools
and techniques. Second, specialized goods embody technical knowledge that helps
point the way to future advances in technical know-how.

^
The variable M is a weighted average of the specialized intermediate goods
produced domestically and globally. For Country A this is:
(3)

M = (1 – κ A)M A + κ A M

.
5

The parameter κA, which lies between 0 and 1, governs the extent to which the
representative resident of Country A is familiar with Country B.
A value of κ near 1 indicates a familiarity with the foreign economy so great that
the importation of specialized goods hardly involves a learning disadvantage. In this
case, domestic residents understand well, through written material and personal
experience, how imported goods work and how they are made. Among other things,
geographical proximity, active commercial relations, and a common language and
culture facilitate indirect acquisition of technical understanding. A value of κ near 0, on
the other hand, indicates that technical knowledge from abroad flows poorly, so that
hands-on domestic production of specialized goods greatly facilitates learning.3 Lack of
familiarity acts as a brake on the international flow of ideas. In effect, our familiarity
parameter governs the extent to which technological spillovers are geographically
concentrated.4

^ by n so that the model supports a balanced growth path in the
We divide M
presence of a growing population. Each country is allowed to have multiple cities
because otherwise relative national per capita products would vary inversely with
relative population size.5 The distinction between intensive population (people per city)
and extensive population (number of cities) enables the model to explain the
convergence of national per capita products in countries with widely different
populations.6
From (2) the rate of growth of per capita human capital in Country i can be
compactly expressed as:
(4)

where:

h
h

= LP i e L i ,

LP i ≡

M
ni hi

Using (1), (3), (A4), and the definition of SM, we can express the LP — learning

productivity — coefficients in (4) as follows:7
(5)
(6)

LP A ≡ e W A v A
LP B ≡ e W B v B

a (1 –κ A) + b (κ A – κ) 1
S

a (1 – κ B ) + b (κ B – κ)

1
1–S

,
γ

where, as noted above, S is Country A’s share of the world effective supply of labor:
S ≡ E A/E , E ≡ E A + E B, and E i ≡ eW i h i n i v i. 8 The parameter vi represents the
number of cities in Country i, so that v i n i is national population.
As will be seen in Section IV, the essence of our model is embodied in
expressions (5) and (6). In particular, the three arguments, v i, κi, and S will be central to
our characterization of balanced growth. They influence the respective national
learning productivities as follows:
First, a parametric increase in the number of a country’s cities v i raises its
learning productivity through a national scale effect that raises the range of specialized
goods available locally.
Second, as long as a country imports some specialized inputs, a parametric rise
in its familiarity with the foreign economy (higher κ i ) raises its learning productivity
due to a familiarity effect.9
Third, a change in S has conflicting effects on learning productivity. From the
perspective of Country B, for instance, an increase in Country A’s share, S, of world
effective labor raises B’s learning productivity by increasing the range of specialized
goods available through trade. But the increase in S also causes some intermediate
goods production to relocate to Country A. The world scale effect raises B’s learning
productivity and the relocation effect reduces it. The scale effect dominates if Country
~
B is sufficiently familiar with Country A that κ B > κ . Then, Country B’s learning
productivity rises with S. On the other hand, when Country B is insufficiently familiar
with Country A, so that κ B < ~
κ , the relocation effect dominates and a rise in S reduces
Country B’s learning productivity.

III. World Balanced Growth
Our goal in this section is to characterize world balanced growth equilibria in the
model using the expressions for national learning productivity derived in Section II. In
particular, we seek to determine the stationary value of Country A’s share of world
effective labor, S *, that supports world balanced growth. Assuming that the world is
populated by infinitely-lived, utility-maximizing households, it is straightforward to
show that the model economy converges to a balanced path along which effort
allocations are constant and national per capita products grow at a common, constant
rate.10
Since effort allocations are constant in balanced growth, and we take the number
of cities v in a country as a fixed parameter, S is stationary if and only if h n grows at
the same rate in the two countries. If we assume further that national population
growth rates are the same, then the stationarity of S requires that per capita human
capital grow at the same rate. Time allocated to learning depends positively and
identically on the respective national learning productivity coefficients, LP i. Hence,
according to (4), S* is the value that equates the national learning productivities,
LP A and LP B. 11
We characterize balanced growth diagrammatically because it is more
convenient for our purposes than working with the analytical solution for S*. The
balanced-growth equilibrium is illustrated in Figure 1 for two countries sufficiently
~
familiar with each other that both κA and κB exceed κ . The solid locus represents LP A
and the dashed locus LP B. In the interior, where specialized inputs are produced in
both countries, the loci are representations of (5) and (6), respectively. The segments of
the loci in the corners (where intermediate inputs are produced only in one country)
are representations from (B1) and (B2) in the appendix.12 Familiarity with the foreign
economy is irrelevant for a country that imports no intermediate inputs. A country’s
learning productivity locus is anchored along the vertical axis by its value in autarky.13

LP: Learning
Productivity
~

LP B (κ B > κ~ )

LP A (κ A > κ )

LP*

F
LPAaut

D
LPBaut

Inputs
Produced
Only in B

S*
S : Country A's Share of World Effective Labor

Inputs
Produced
Only in A

FIGURE 1. WORLD BALANCED GROWTH

The stationary value S* and the common learning productivity coefficient LP*
are determined by the intersection of the learning productivity loci at point E in Figure
1. The common balanced growth rate of national per capita products in the model is
the sum of human capital growth and a term reflecting the scale effects of a growing
world effective supply of labor. The latter term grows, in turn, with the sum of human
capital and population growth. Hence, by differentiating (A5) in the appendix and
substituting from (4) the balanced growth rate of per capita product can be expressed
as:
y
* *
y = 2 – α LP e L + (1 – α)η ,

(7)

where η is a common national population growth rate. Effort allocated to learning
depends positively on learning productivity, so world per capita product growth varies
directly with learning productivity.14
Although growth rates converge in our model, national per capita products can
vary widely along a balanced path. We shall see why this is the case below, when we use
the model to interpret the history of industrial development in Section IV. However,
we note here that the ratio of Country A's to Country B's per capita product in
balanced growth can be expressed as:15
yA

(8)

S*
vB nB
vA nA 1 – S *

Given the vi and ni that index relative national scale, expression (8) indicates that the
ratio of the per capita product of Country A to Country B varies directly with Country
A's share, S, of the world effective supply of labor. We use (8) extensively in the
analysis that follows.
To illustrate the mechanics of the model, consider what would happen if the two
countries became more familiar with each other, rotating the two LP curves in Figure 1
upward so as to keep S* unchanged. According to (8), relative per capita product
would stay the same. Mutual familiarization, however, would increase LP* and raise the
9

world growth rate by (7) as knowledge flowed more easily in both directions. If only
one nation increased its familiarity with the other, world growth would still increase but,
since S* would change in this case, the nation that increased its familiarity with the
other would experience a relative rise in its living standard.
IV. Interpreting the History of Industrial Development
Prior to the Industrial Revolution, the variation in living standards around the
world appears to have been due to differences in regional market size and proximity to
international trade routes. In Europe, for instance, the fact that some regions were not
well integrated with the rest — the Iberian peninsula and Eastern Europe — while others
such as the Netherlands profited greatly from trade, meant that there could be
substantial variation in incomes. For those portions of Europe linked by trade,
however, the variation in living standards was probably smaller on the eve of the
Industrial Revolution than it was to be for the next 150 years.
The potential profit from commerce encouraged an ongoing effort to reduce
transport costs that steadily expanded trade in the centuries before the Industrial
Revolution [Daniel Boorstin (1983), Carlo M. Cipolla (1985)]. Along with the rising tide
of commerce came rising living standards based on ever-greater specialization made
possible by increasing market size. Goodfriend and McDermott (1995) argue that trade
and population growth increased specialization and eventually raised learning
productivity enough to initiate the self-sustaining technological progress that gives rise
to modern industrial growth.16
A. The Divergence and Subsequent Convergence of National Per Capita Products
Our model provides a natural interpretation of the tendency for industrialization
to cause national per capita products to diverge initially and to converge again over
time. The interpretation flows from the fact that the model implies that two very
different mechanisms determine equilibrium relative per capita products in the pre-

industrial and post-industrial eras.
In terms of the model, we interpret the pre-industrial era as the period prior to
the activation of national learning technologies, that is, prior to the period of
fundamental technological progress marked by the accumulation of human capital. In
the pre-industrial interpretation of the model, per capita product differentials are
governed by the fact that trade equalizes the cost of comparably-skilled labor across
countries. Thus, national per capita products are tied to differences in know-how
indexed by human capital per person. By all accounts, know-how did not differ widely
across countries tightly linked by trade on the eve of the Industrial Revolution. Hence,
our model leads one to expect that differences in standards of living would not be very
large either.
In marked contrast, human capital accumulation is the engine of modern
industrial growth in our model. The per capita product differential between two
industrial economies is governed by forces pushing them toward balanced growth
according to Figure 1. In particular, relative national standing is determined by relative
national learning productivities, which in turn depend on familiarity and national scale.
Other things the same, the country more familiar with its trading partner achieves
higher per capita product; and the country with more cities ultimately does better. Our
model suggests that industrialization caused national per capita products to diverge
initially because of differences among nations in scale and familiarity with foreign
economies.
Although familiarity is a parameter in our model, it is easy to see that familiarity
would grow over time with the economy. Nations become more familiar with each
other as technological progress lowers transport and communication costs, trade
increases, and business and cultural contacts multiply. The limit to mutual
familiarization in our model occurs when κ A = κ B = 1. The equilibrium that results from
such complete or perfect familiarity is shown as point G in Figure 2. There is no longer

LP: Learning
Productivity

LP A (κ A = 1)

LP B (κ B = 1)

LP max
~
LP A (κ A < κ )

~
LP B (κ B < κ )

F
H
K

LPAaut

LP Baut

Inputs
Produced
Only in B

vA
v A + vB

S : Country A's Share of World Effective Labor

Inputs
Produced
Only in A

FIGURE 2. ANALYSIS OF BALANCED GROWTH EQUILIBRIA

any learning productivity advantage to the domestic production of specialized goods.
The common learning productivity goes to LP max and according to (7) world growth
reaches its maximum. Mutual familiarization also moves S* to v A / (v A + v B ) so that
according to (8) per capita products converge absolutely if national city sizes (ni ) are
equal.17 To the extent that national scale is associated with number of cities rather than
average city size, our model identifies in mutual familiarization a powerful force causing
the per capita products of industrialized countries to converge over time.
B. The Great Productivity Gap
One of the most disturbing outcomes in the history of industrial development
has been the emergence and persistence of a large gap in living standards between the
leading industrial economies and less-developed countries (LDCs). Our model locates
the problem in an LDC's extreme lack of familiarity with the leading economy due to
such barriers as distance, language, and culture, or deliberate impediments to
commercial intercourse.18

that κ

To illustrate the point, suppose that Country B is so unfamiliar with Country A
~ and Country B's learning productivity locus looks like KDLJ in
B is less than κ

Figure 2. Lack of Country B familiarity with Country A causes the relocation effect of
an increase in S to dominate the scale effect, so that the LP B locus slopes downward
between points D and L. Thus, the LP B locus passes below the LP A locus until the
former comes up to intersect the latter from below at point J. The extreme lack of
familiarity of Country B with Country A puts the balanced-growth equilibrium at point
J far to the right and leaves Country A with a very large fraction, S*, of the world’s
effective labor supply. According to (8), a value of S* near unity makes Country A's
per capita product enormously greater than that of Country B.
Even though wages for comparably skilled workers are the same in the two
countries, the typical worker in Country A has accumulated far more human capital in
balanced growth than his counterpart in Country B. The differential in human capital

per capita sustains the huge productivity gap that supports the large difference in living
standards. Nevertheless, S* is large enough in balanced growth that the national
learning productivity coefficients are the same and the two countries grow at the same
rate.
The wide productivity gap develops because the lagging economy’s lack of
familiarity with the leader makes the relocation effect dominate the scale effect. The
growing share of specialized goods production attracted to the leading country
reinforces its initial learning productivity advantage. The leader grows faster, and the
follower grows more slowly, until the leader has attracted all of the world’s specializedgood production.19 Thereafter, the relocation effect ceases to operate and the leader’s
learning productivity begins to fall toward its level in autarky. Simultaneously, the
follower’s learning productivity begins to rise as the lagging economy benefits
increasingly from the growing relative size of the leader. National learning
productivities converge gradually as the world asymptotically approaches balanced
growth.
Our model suggests that an enormous productivity gap is hard to close because
it inhibits the kind of commercial interaction that promotes familiarization. In the
model, the LDC produces no specialized goods for export to the leader and imports
very little.20 Thus the model reproduces a pattern that has become well established and
is likely to continue for some time: most developed and less-developed countries
continue to grow at similar rates, but with staggering differences in income levels.21
C. Growth Miracles: Catching Up and Overtaking
History has recorded extraordinary examples of catching up and overtaking of
per capita products of leading economies by less-developed countries. Much has been
written about growth miracles in an effort to isolate the secret of their success.22 Our
model identifies the familiarization of the less-developed country with the leading
economy as the source of growth miracles. Familiarization not only explains catching

up, but also the more puzzling phenomena of overtaking.
We understand growth miracles in our model by building on the analysis of the
productivity gap. To begin, suppose that Countries A and B are so unfamiliar with each
other that both κA and κB fall short of ~
κ . Take the LP A locus in Figure 2 to be HIFJ
and the LP B locus to be KDLJ so that a unique balanced growth equilibrium exists
initially at point J, where as before Country A is the leading economy and County B
lags far behind.
To see what happens when Country B familiarizes itself with Country A consider
a parametric increase in κ B. We justify holding κ A fixed by the fact that Country A
produces all the world's specialized goods and would have little interest in the lessdeveloped economy. As κ B increases, the LP B locus rotates counter-clockwise around
point D, moving the balanced growth equilibrium first to F and eventually all the way
to I if Country B completely familiarizes itself with Country A.
Familiarization raises Country B's LP schedule because it better enables the lessdeveloped country to learn from imported specialized goods. As a result, Country B
begins to accumulate technological know-how (human capital) more rapidly than
Country A and Country A's share of world effective labor, S, falls as the world
converges to the new balanced growth equilibrium.
If city sizes are the same in the two countries, we see from (8) that Country B
catches up, i.e., achieves equality, with Country A in per capita product if S falls to v A /
(v A + vB). Overtaking of per capita products occurs if Country B familiarizes itself
sufficiently with Country A to push S below v A / (v A + v B ). The room for overtaking is
greater the less familiar the initial leader remains with the surging economy. In fact,
Figure 2 makes clear that if Country A were to completely familiarize itself with the
rising economy, the best the latter could do would be to achieve equality of per capita
products at point G (again, assuming city sizes to be the same).
Figure 2 reveals a possible side effect of catching up: in this case catching up is

only good for world growth up to a point. Country B's familiarization with A raises the
common world growth rate only until point F is reached. Once the equilibrium has
moved to the left of F, however, increases in B’s familiarity cause specialized-good
firms to leave A. If A is sufficiently unfamiliar with B that the relocation effect
dominates the scale effect, as assumed here, then the common balanced growth rate
actually falls as B continues to catch up with A. Thus, world growth could fall over
some range because Country B experiences a growth miracle.23
This suggests that the world productivity slowdown since the 1970s [e.g.,
Parente and Prescott (1993)] may have been due, in part, to the Asian growth miracles.
Catching up, accomplished by familiarization with the West, has led to a surge in the
number of specialized goods produced in the East. According to our model, the
relocation is potentially harmful to growth in the West, and may reduce growth
worldwide if Western nations remain unfamiliar with the rising nations of the Pacific.24
By the same token, world growth will ultimately increase as Western nations familiarize
themselves with the East.
Our view that catching up reflects a familiarization with industrial leaders on the
part of less-developed countries appears to be consistent with the evidence. The
Japanese growth miracle, for example, seems closely tied to increasing familiarity with
the West. It began in 1868 with deliberate steps following the Meiji Restoration to
adopt Western ways [William Lockwood (1954), Chapter 6]. The significant US
presence in Japan immediately following World War II and during the Korean and
Vietnam Wars further familiarized Japan with developments outside of Asia. Our
model suggests that the protracted US involvement in the Far East, especially in Japan
and South Korea, may have helped lay the groundwork for the post-War growth
miracles of the Pacific Rim by familiarizing people in those nations with the United
States.

The model predicts that anything building a “familiarity bridge” from less-

developed countries to industrial leaders helps the former to catch up. In this view, the
first wave of developed nations on the Pacific Rim may be serving as a bridge for a
second wave of Asian nations. China’s rapidly growing coastal provinces have
benefited greatly from the nearby Chinese-speaking economies of Hong Kong and
Taiwan [Economist (1992)]. One might even imagine that the westernmost nations of the
old Soviet bloc might re-industrialize first and then serve as a familiarity bridge for the
regions of the old Soviet Union itself.26
V. Conclusion
We began by summarizing the diverse patterns of convergence, divergence, and
overtaking that have characterized industrial development. Although such phenomena
would appear to fit together awkwardly, we presented a model of endogenous growth
capable of delivering the wide range of outcomes that we have observed.
We endowed two countries with identical goods-producing technologies and,
through trade, gave each access to the full world range of specialized intermediate
goods. Goods productivity differentials arose because of differences in national knowhow as indexed by per capita human capital. At the heart of our model was the idea
that national learning productivities would differ depending on how well technical
knowledge could be absorbed without the hands-on experience that comes with
domestic production. Familiarity with the foreign economy raised a country’s learning
productivity by enabling it to better understand the design and manufacture of
imported specialized goods. Learning productivity differentials did not lead to
permanent growth differentials, however, but rather determined relative international
standing in world balanced growth.
The major theme of our paper is that the efficiency with which knowledge can
be acquired is a primary determinant of relative per capita products in the long run.
Countries that promote openness and familiarity with others find it easier to acquire

know-how and will eventually catch up to or even overtake the per capita product
levels of more advanced trading partners. Less-developed countries that cannot
increase their familiarity with the developed world will persistently lag world leaders,
perhaps by staggering amounts. On the other hand, countries that now lead cannot
afford to be complacent — a refusal to keep in touch with the know-how being
developed abroad may force them to surrender their lead.

Appendix A: Goods-Market Equilibrium
Two countries, A and B, each produce an identical final good, Y, with the same
technology. Output is generated by perfectly competitive firms within Country i (i = A,
B) using the following production function:
i

(A1)

Y = eY h N

i 1–α

x Ai

dτ+

x Bi τ
M

dτ ,

where 0 < α < 1. The labor force numbers N i individuals, each possessing human
capital hi , and working a fraction eY i of time in the final-goods sector. Effective labor,
eYi h i N i, cooperates with intermediate input goods (indexed by τ) that are produced in
both countries. Inputs produced in Country A, called x Ai, exist on a continuum over
the range M A, while those from Country B, x Bi , are produced on the range M B = M –
M A. This production function exhibits constant returns to scale given M A and M B, but it
also captures the notion that specialization raises worker productivity.
Intermediate-good inputs that originate in Country i are produced with effective
labor alone by M i different monopolistically competitive firms. The labor cost of
producing the quantity x of any input in either country is given by C (x) / h, where
C ´(x) > 0 and C ´´ (x) > 0.
Each individual in Country i splits his total work effort eW i between final
production and intermediate production:
(A2)

eW i = eY i + eI i .

The total demand for labor to produce intermediates must equal the available supply:
(A3)

C (x i )
= eI i N i .
hi

In equilibrium, each input is produced by a single monopolistic competitor in
fixed supply ~
x . Global specialization, M, is proportional to the world effective labor
supply, E :
(A4)

M = α E .
C (x)

Per capita output of Country i is proportional to h and eW , and increases with E:
y i = β E 1 – α h i eW i ,

(A5)

α (1 – α)1 – α x α
, and βE
where β ≡
C (x )

1–α

is the common worldwide base wage, or the

wage of a worker with one unit of human capital.
Intermediate good uses in the two countries are as follows:
(A6)

x A = θ (S – α S M ) ,

(A7)

x B = θ [(1 – S ) – α (1 – S M )] ,

where: S M ≡

MA
, θ≡ x
, and S ≡ E A /E is Country A’s share of the world’s
M
1–α

effective labor supply.
The interior solution for SM given in equation (1) in the text is found by equating
(A6) and (A7). To see that the value of SM in (1) is indeed an equilibrium, consider an
arbitrary relocation of intermediate-good firms between the two countries. The
positive perturbation of SM shifts labor from the final- to intermediate-good sector in
Country A and does the reverse in Country B. By (A6) and (A7) this decreases the
demand for intermediate inputs in A and increases it in B, causing intermediate-good
producers to relocate to B until the initial perturbation is reversed.
Appendix B: Learning Productivity in the Corners
According to (1), Country A produces all of the intermediate inputs (SM = 1)
when S ≥ (1 + α) / 2. In this case, the national learning productivity coefficients are
given by:
(B1)
where φ i ≡

LP A = φ A v A
α eW i
C (x)

1
S

LP B = φ B v B

κB
1–S

On the other hand, when S ≤ (1 – α) / 2 Country B produces all of the intermediate

inputs (SM = 0) and we have:
(B2)

LP A = φ A v A

κA
S

LP B = φ B v B

1
1–S

Footnotes

In general, both final- and intermediate-goods are traded, but since final-good firms produce a

homogeneous good and are price takers, they are indifferent to location in equilibrium.
2

S M in (1) is found by equating (A6) and (A7) from the appendix.

De Long (1992) and Nathan Rosenberg (1976) present evidence that locally produced specialized

goods used in production generate ideas for improving productivity more readily than less-wellunderstood imports.
4

See Romer (1986, example 3), and Gene Grossman and Elhanan Helpman (1991, Chapter 8).

Cities within a country are entirely symmetric except that each produces a different subset of the

range of the specialized goods produced nationally. Through trade each city acquires the full range of
world specialized goods for use in final goods production. Our characterization of goods market
equilibrium is unaffected by the distinction between extensive and intensive population.
6

See the related discussion in Lucas (1993), p. 263.
Duncan Black and Vernon Henderson (1997) present a model in which growth occurs in an

economy with a stable relative size distribution of cities. Individual cities grow with human capital
accumulation; and cities grow in number if national population growth is high enough.
7

In terms of the underlying goods-producing technology described in the appendix, the constants are

~
~
~
as follows: a ≡ 1 / C (x ), b ≡ (1 + α) / 2C (x ), and κ ≡ (1 – α) / (1 + α).
8

Expressions (5) and (6) only determine the national LP coefficients when 0 < S M < 1. When S M = 1,

the LP coefficients are given by (B1) in the appendix; when SM = 0, they are given by (B2). We make
use of the corner cases in Section IV.
9

Formally, this follows from the definitions of a and b in footnote 7, and the expression for the

interior range of S that appears after (1).
10

The wealth and substitution effects of human capital per capita are offsetting in balanced growth, so

that effort allocations are independent of h.

Equality of LP A and LP B supports balanced growth when national population growth rates (η),

pure rates of time preference (ρ), and γ in (2) are the same for Country A and Country B. In this case,
the national effort allocations are identical. Using a procedure that parallels the one in Marvin
Goodfriend and John McDermott (1995) we can show that work effort is given by

eW * =

1 γ + ρ – η , where ρ > η. Learning effort is then e * = 1 – e * .
L
W
1+γ
LP *

If the parameters above are not the same across countries, the values of LP A and LP B that
support a stationary share of effective labor, S*, differ from each other, as do the national effort
allocations.
12

To restrict the relevant LP loci to reflect balanced growth we require that eW = eW * as given in

footnote 11. Notice that the direct effect of a change in κ i or S on LP A or LP B is attenuated somewhat
by an indirect negative effect of LP i working through eW * .
13

The respective national learning productivities in autarky are given by φauti (v i ) , where

φaut
14

α eW i *
≡
C (x)

ρ–η

The balanced-growth allocation of effort to learning is given by e L * = 1 – 1
γ+
1+γ
LP *

Equation (8) is easily derived using (A5) together with the definitions of E i and S .

The idea that trade assisted the growth of knowledge is an old one. It is found, for example in the

work of David Landes (1969) and Walt W. Rostow (1975).
17

To see that complete familiarity drives S* to v A / (v A + v B ), set κ A = κB = 1 in (5) and (6), equate the

two, and solve for S.
18

Parente and Prescott (1994) study the effect on relative living standards of deliberate barriers to

technology adoption.
19

The force making for divergence in our model is reminiscent of that in Alwyn Young (1991). In his

model, trade creates a divergence in growth rates by shifting the composition of output in the follower

to older industries for which learning by doing has been nearly exhausted, and does the reverse in the
leader.
20

See (A6) and (A7), recognizing that x A and x B differ from each other in a corner where S M equals 0

or 1.
21

It is worth pointing out that multiple equilibria are possible in our model when mutual national

familiarity is low enough. If Country A's familiarity with Country B were even lower than that shown
in Figure 2, the LP A locus could end up crossing the LP B locus three times. Another stable balanced
growth equilibrium could exist to the left of point D and there would be an unstable balanced growth
equilibrium in the interior.
22

For a recent example, see Lucas (1993).

Point I could be higher or lower than J, so ultimately B’s growth miracle could be either good or

bad for world growth.
24

What we have in mind here, for example, is the idea that Japanese firms have become increasingly

familiar with the chip-making techniques developed originally in the US. On the other hand, the US
has been slower to learn about Japanese technology for making LCD screens. Thus, firms in the US
that once had direct access to the latest technology, are now unable to access parts that are being
developed in Japan.
25

The source of growth miracles remains controversial. Young (1995), for instance, shows that much

of Singapore’s growth was due to rising labor force participation rates and physical capital, not
technical change.
26

The beneficial effects of a familiarity bridge would be offset to the extent that familiarization gives

rise to an out-migration of the sort commonly referred to as a brain drain.

References
Abramovitz, Moses. “Catching Up, Forging Ahead, and Falling Behind.” Journal of
Economic History June 1986, 46 (2), pp. 385 – 406.
Baumol, William J. and Wolff, Edward N. “Productivity Growth, Convergence, and
Welfare: Reply.” American Economic Review December 1988 78 (5), pp. 1155 –
59.
Black, Duncan and Henderson, Vernon. “Urban Growth.” National Bureau of
Economic Research (Cambridge, MA) Working Paper No. 6008, April 1997.
Boorstin, Daniel. The Discoverers. New York: Random House, 1983.
Cipolla, Carlo M. Guns, Sails, and Empires: Technological Innovation and the Early Phases of
European Expansion 1400-1700. Kansas: Sunflower University Press, 1985.
De Long, J. Bradford. “Productivity Growth, Convergence, and Welfare: Comment.”
American Economic Review December 1988 78 (5), pp. 1138 – 54.
___________. “Productivity and Machinery Investment: A Long-Run Look 18701980. Journal of Economic History June 1992 52 (2), pp. 307 – 424.
Economist. “The Economist Survey of China.” Vol, 325, No. 7787, November 28,
1992, pp. 1 – 22.
Goodfriend, Marvin and McDermott, John. “Early Development.” American Economic
Review March 1995 85 (1), pp. 116 – 33.
Grossman, Gene and Helpman, Elhanan. Innovation and Growth in the Global Economy.
Cambridge: MIT Press, 1991.
Landes, David. The Unbound Prometheus: Technological Change and Industrial Development in
Western Europe from 1750 to the Present. London: Cambridge University Press,
1969.
Lockwood, William. The Economic Development of Japan. Princeton: Princeton U. Press,
1954.
Lucas, Robert E. “Making a Miracle.” Econometrica March 199316 (2), pp. 251 – 72.
24

Maddison, Angus. Phases of Capitalist Development. New York: Oxford University Press,
1982.
Parente, Stephen L. and Prescott, Edward C. “Changes in the Wealth of Nations.”
Quarterly Review, Federal Reserve Bank of Minneapolis, Spring 1993, 17 (2), pp. 3

– 16.
____________________. “Barriers to Technology Adoption and Development.” Journal of
Political Economy April 1994102 (2), pp. 298 – 321.
Pritchett, Lant. “Divergence, Big Time.” Journal of Economic Perspectives Summer 1997
11 (3), pp. 3 – 17.
Reynolds, Lloyd G. “The Spread of Economic Growth to the Third World.” Journal of
Economic Literature September 1983 21 (3), pp. 941 – 80.
Rivera-Batiz, Luis A. and Romer, Paul M. “Economic Integration and Endogenous
Growth.” Quarterly Journal of Economics May 1991 106 (2), pp. 531 – 56.
Romer, Paul M. “Increasing Returns and Long-Run Growth.” Journal of Political
Economy October 1986 94 (5), pp. 1002-37.
________. “Growth Based on Increasing Returns Due to Specialization”. American
Economic Review May 1987 77 (2), pp. 56-62.
Rosenberg, Nathan. Perspectives on Technology. New York: Cambridge University Press,
1976.
Rostow, Walt. W. How It All Began: Origins of the Modern Economy. London: Methuen and
Co., Ltd., 1975.
Tamura, Robert. “Income Convergence in an Endogenous Growth Model.” Journal of
Political Economy June 1991 99 (3), pp. 522 – 41.
World Bank. World Development Report 1991: The Challenge of Development. New York:
Oxford University Press, 1991.
______________ . The East Asian Miracle. New York: Oxford University Press, 1993.
Young, Alwyn. “Learning By Doing and the Dynamic Effects of International Trade.”

Quarterly Journal of Economics May 1991 106 (2), pp. 369 – 406.
____________ .”The Tyranny of Numbers: Confronting the Statistical Realities of the
East Asian Growth Experience.” Quarterly Journal of Economics August 1995 110
(3), pp. 641 – 80.

Full text of Working Papers (Federal Reserve Bank of Richmond) : Industrial Development and the Convergence Question, Working Paper 99-01

FRASER