Population Aging, Technology, and the North-South Trade M ... · 1 Population Aging, Technology,...
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Population Aging, Technology, and the North-South Trade
M. Aykut Attar Dept. of Economics, Hacettepe University
06800 Cankaya/Ankara-TURKEY
Phone: +90-312-7805705
E-mail: [email protected]
Serdar Sayan Dept. of Economics, TOBB University of Economics & Technology
06560 Cankaya/Ankara-TURKEY
Phone: +90-312-2924285
E-mail: [email protected]
Abstract
Developed countries in Europe, Asia and North America have markedly different demographic and technological
characteristics than those of less developed ones in the “South.” They have significantly older populations and
lower population growth rates, particularly in Europe and Asia. Currently, a significant fraction of global North-
South trade appears to be explained by diverging demographics, which lead to differences in age compositions of
populations and hence, relative factor endowments through their effects on relative sizes of workforces and savings
(and capital formation).
The surge in the North-South trade following the 1980s has led to a marked growth in the literature on North-South
trade flows. Recent studies focus on differences in production technologies, as well as relative factor endowments
of trading nations that diverge due to demographic differences across these regions.
In this paper, we develop a dynamic general equilibrium model of North-South trade with hybrid Ricardo-
Heckscher-Ohlin features and study the evolution of demographic and technological differences over time and
their effects on comparative advantages, inequality, economic growth, and welfare. Our model features two regions
populated by two overlapping generations (OLG) of agents in each period where two goods are produced using
two factors of production.
Our quantitative analysis builds upon numerical solutions of the model’s perfect foresight equilibrium. In the
benchmark scenario, we feed the model with the UN population projections and assume that current differences in
technology (and hence productivity) persist in the long run. Our simulation exercises against this benchmark yield
the following results: First, both demographic and technological differences affect the total volume of trade and
inequality. However, we find that population differences create larger effects on inequality as compared to
productivity. Conversely, productivity differences turn out to be more important for the total volume of trade.
Second, there exist strong Stolper-Samuelson effects, hurting the scarce factor in the absence of a compensation
scheme. Third, the South’s advance in the capital-intensive sector and the North’s defensive innovation weaken
the Stolper-Samuelson effects considerably. Finally, immigration from the South to the North, if allowed, improves
the lifetime welfare in both regions without lowering the volume of trade. These results significantly extend our
understanding of the nature and consequences of the North-South trade that is expected to continue into a
considerably distant future.
Keywords. North-South trade, Welfare, Inequality, Growth, OLG model, General equilibrium,
Computational simulations, Numerical solutions
J.E.L. Codes. C63, D91, F11, J10
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1. Introduction
Economists use the term North-South trade to identify international trade occurring between
more developed (or advanced/richer) economies which, as a group, are called the North, and
less developed (or poorer) ones called the South. Productive activities in the North are typically
carried out by using superior production technologies that are perpetually improved upon
through continuous innovation. This keeps per worker productivity levels in the North visibly
higher than in the South. Partially offsetting this productivity advantage is a markedly slower
population growth that countries in the North experience due to their earlier entry into the
demographic transition process, characterized by declining fertility rates.1
Given the differences in (aggregate and sectoral) productivity levels, as well as shares of
working-age populations and capital stocks per capita between the North and the South, both
the Ricardian and the Heckscher-Ohlin streams of the old trade theory provide useful
frameworks in understanding the direction of comparative advantages and patterns of
international trade in a world economy consisting of a more developed North and a less
developed South.
Ricardo’s (1817) famous theory of comparative advantage focuses on productivity differences
in (labor) productivity across trading economies. In a world with two trading economies and
two goods produced only with labor, an economy specializes and exports the good for which it
has a relative productivity (and hence, cost) advantage. In the famous textbook example of
‘England versus Portugal,’ England produces both cloth and wine less costly than Portugal, but
the cost advantage due to higher productivity is more pronounced in cloth. England thus
specializes in cloth by devoting more resources to cloth production and exports part of the
increased cloth output to Portugal. Portugal, in turn, specializes in wine production and exports
part of the resulting wine output to England, her trading partner.
The factor proportions theory building upon Heckscher’s (1919) and Ohlin’s (1933) early work
and later formalized by Samuelson (1948) also considers two regions and two goods that are
produced by employing (not one but) two factors of production, usually taken to be capital and
labor. The regions have identical preferences and use identical technologies in the production
of each good but differ in relative abundance of factors that go into the production of goods
they commonly produce. While each region produces the same good by employing the same
technology, production of each good requires a differing relative intensity of factors. Under the
assumptions of perfectly competitive commodity and factor markets, constant-returns-to-scale
production technologies, zero transportation costs, and immobility of factors across regions,
four key results emerge: First, a region becomes a net exporter of the good whose production
uses its abundant factor more intensively; this is known as the Heckscher-Ohlin theorem.
Second, the Factor Price Equalization (FPE) theorem dictates that free trade equalizes not only
the relative prices of goods but also the prices of factors, despite immobility of factors across
regions. Third, Stolper and Samuelson’s (1941) theorem proves that a ceteris paribus increase
1 There exists a sizable and growing literature on this so-called Great Divergence, i.e., on why the Northern and
Southern paths of economic development exhibit such remarkable differences with respect to population and
technology. Galor and Mountford (2008: 1143) lists the plausible causes proposed by various scholars as
“geographical and institutional factors, human capital formation, ethnic, linguistic and religious fractionalization,
colonialism, and globalization.”
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in the relative price of a good leads to an increase in the relative return to the factor used more
intensively in the production of that good. Finally, according to Rybczynski’s (1955) theorem,
other things being equal, an increase in the supply of a factor leads to an increase in the output
of the good that uses this factor more intensively.
The North-South trade literature traditionally characterizes the North as the exporter of
manufactured products, and the South as the exporter of primary goods. This characterization
has its roots going back to the 19th century when sharp drops in transportation costs led to a
remarkable expansion in intercontinental trade and commodity price convergence between
relatively land-abundant non-industrialized countries serving as net exporters of food and raw
materials to land-scarce European countries that act as net exporters of manufactured products
(O’Rourke and Williamson, 2002; Findlay and O’Rourke, 2003; Galor and Mountford, 2008).
In the words of O’Rourke and Williamson (2002: 434), the historically distinct episode from
1820s to 1913, or from the end of the Napoleonic Wars to World War I is clearly a classic
Heckscher-Ohlin century.
Then came the 20th century and things began to change. International trade data for this century,
especially for the second half, revealed an increasing tendency for developed country exports
to be delivered to other developed countries with relatively similar technological and
demographic features. In other words, starting from the mid-20th century, a growing portion of
world (merchandise) trade has become of the North-North type, eventually leading to the
emergence and development of a new trade theory that primarily aims to explain comparative
advantage and the patterns of trade via increasing returns and imperfect competition (Krugman,
1979; Lancaster, 1980; Helpman, 1981).2
Even though most of the global trade now occurs between similar countries and is therefore of
North-North or South-South type, the North-South trade has made up the most rapidly growing
portion of global trade in the last three decades (see, e.g., Zymek, 2015). Its total volume
represents 40% of global trade in 2013 according to UNCTAD (2013). This second round
expansion in the North-South trade is facilitated by
export-oriented trade reforms in newly industrializing and (unskilled-)labor-abundant
countries of the South such as China, India, and Mexico,
international trade agreements, and
reductions in transportation costs.
With the growth of (unskilled-)labor-intensive merchandise production in less developed
economies of the South, the movement of manufactured goods from the South to the North has
become increasingly commonplace, triggering renewed interest in North-South trade among
trade economists. Noticeably large differences in relative factor endowments and productivity
levels across these two groups of countries have once again been boosting the popularity of the
traditional models of Ricardian and Heckscher-Ohlin mechanisms. This reemerging literature
on the North-South trade has largely focused on the effects of increasing volumes of
merchandise trade on wages, employment, welfare, and skilled/unskilled wage inequality in the
North from 1990s to the present (Wood, 1994, 1995, 1998; Richardson, 1995; Freeman, 1995;
Krugman, 2008; Chusseau et al., 2008; Harrison et al., 2011; Autor et al., 2016; Helpman,
2 See Helpman and Krugman (1985) and Krugman (1995) for detailed treatments of the new trade theory.
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2017). An increasing volume of North-South trade is typically associated with resource
reallocation toward capital- and skill-intensive sectors, decreasing relative demand for unskilled
labor, growing wage inequality, and/or increasing unemployment of unskilled workers in the
North after 1980s. But skill-biased technological change (SBTC) is another plausible
mechanism that may have been inducing these outcomes. An overall message from this
literature, emphasized in both early and recent reviews, is that both the North-South trade and
SBTC do matter for such labor market effects in the North.3
The purpose of this paper is to contribute to literature by exploring the (relative) roles of
Ricardian and Heckscher-Ohlin type mechanisms underlying the recent growth of North-South
trade. We are particularly interested in the effects of differences in population growth rates and
differential speeds of aging, on the one hand, and technology-induced productivity differences,
on the other, on comparative advantages, inequality, economic growth, and welfare in the North
and the South.
For this purpose, we follow Sayan (2005) and construct a dynamic, general equilibrium,
overlapping generations (OLG) model with two regions (the North and the South); two factors
of production (labor and physical capital); two goods (one labor-intensive and one capital-
intensive) and two generations (the working young and the retired elderly). In this 2×2×2×2
model, the good whose production is relatively more labor-intensive is used only for
consumption purposes, whereas the capital-intensive good serves both as a consumption and an
investment good. Individuals work and save when they are young, and they finance
consumption in the old-age using principal and interest income on their savings. Savings of the
young generation in each period finance investment which forms the capital stock of the next
period.
The model features both Ricardian and Heckscher-Ohlin type elements. Differences in
population growth rates and, hence, the shares of working-age populations across regions create
à la Heckscher-Ohlin differences in relative factor endowments, whereas diverging total factor
productivities (TFP) by sectors provide Ricardian motives for trade. Together they contribute
to autarky differences in relative prices across two regions.
In our numerical exercises, we use the United Nations’ (UN) canonical projections of working-
age population levels for the decades ahead by letting the UN’s classification of ‘more
developed’ regions make up the North, while the South is encompassing ‘less developed’
regions.4
For the sectoral TFP differences, we use Fadinger and Fleiss’ (2011) estimates to come up with
3 US and China are two exemplary countries given China’s rise as a major exporter of (unskilled-)labor-intensive
products and alleged labor market effects of increasing volume of imports from China on skill- and capital-
abundant US. The average tariff rate in China has decreased by about 18% points from 1980 to 2008 (Zymek,
2015), and Chinese trade balance to GDP ratio in manufactured goods rose from –5% to +10% since 1985 (Autor
et al., 2016). Parallel to these developments, the bilateral US trade deficit to GDP ratio in goods with China
increased about 56-fold from 1986 to 2015. Besides, Morrow (2010: 137) notes that US and China exhibit
specialization patterns fitting well with the Heckscher-Ohlin theorem. In 2000, US and China respectively supply
35% and %0.1 of global aircraft exports, and 2.4% and 25.8% of global apparel and clothing exports. 4 The working-age populations of the North and South in our benchmark calibration are the respective projected
levels reported under the medium-fertility scenarios.
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plausible boundaries for the ratios of TFPs across sectors. Empirically, the more developed
economies have absolute advantage, in Adam Smith’s words, in the production of many
products often including several labor-intensive goods due to their distinctly higher productivity
levels. Yet, their comparative productivity advantage lies in capital- and skill-intensive products
as recognized by parameter values we choose for our computational simulation exercises.
In the benchmark scenario, population and productivity differences described above lead to
significant differences in relative autarky prices across regions, leading to the expected pattern
of trade. Under free trade, the North and the South are net exporters of relatively more capital-
intensive and relatively more labor-intensive goods, respectively. Implementing a number of
different demographic and technological scenarios relative to this benchmark, we obtain the
following results:5
Both demographic and technological differences affect the total volume of North-South
trade. But a larger fraction of trade volume is explained by differences in productivity
levels. Inequality, on the other hand, is determined mainly by demographic differences
with a smaller fraction of changes explained by productivity differences across regions.
Our counterfactual scenarios where we mute population or productivity differences
result in lower volumes of trade relative to the benchmark. In these scenarios, the North
enjoys relatively larger levels of lifetime welfare and real GDP per capita, while facing
a lower level of rental-to-wage ratio. Thus, workers in the North lose relatively less with
weaker Stolper-Samuelson effects when the volume of trade is relatively lower. Results
also show that North’s technological superiority dominates the adverse output and
welfare effects of trading with a younger, labor-abundant South.
Two scenarios leading to qualitatively similar results are faster capital-biased
productivity growth in the South and faster labor-biased productivity growth in the
North, i.e., the defensive innovation in Wood’s (1994) terminology. In these scenarios,
comparative advantages stemming from population differences become less pronounced
over time, the total volume of trade decreases relative to the benchmark, and the scarce
factor in each region loses relatively less.
Two other counterfactuals that weaken Stolper-Samuelson effects without implying a
decrease in the total volume of trade are immigration of workers from the South to the
North and faster population growth in the North. In fact, when we calibrate the faster
growth rate of population in the North to exactly match the flow of workers joining the
labor force in the case of immigration, lifetime welfare and real GDP per capita are
larger in the immigration scenario.
These results extend our understanding of a future when the North and the South are expected
to exhibit considerable demographic and technological differences. First, since the North’s
output and welfare gains from its technological superiority dominates the losses originating
from trading with the labor-abundant South, the North’s ability to compensate for adverse
Stolper-Samueson effects is crucial for the North-South trade to continue in the long run.
Second, demographic differences partially explain the volume of North-South trade, trade will
continue even if the South completely transfers the Northern technology, a possibility more
likely than establishing identical demographic structures in the North and the South. Third,
5 In all cases, we focus on the free trade equilibrium without taxes and transfers that in general need to be
implemented to compensate for the adverse Stolper-Samuelson effects.
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defensive innovations that result in plausibly-sized productivity changes and weaken the
Stolper-Samuelson effects achieve the desired ends without altering the pattern of trade, i.e.,
without a switch in the goods of regions are the net exporters. Industrial policies that incentivize
product and process innovations in sectors facing serious import competition receive strong
theoretical support. Finally, among all of the scenarios with different policy implications,
immigration from the South to the North is the most preferable scenario both for the North and
for the South and without a decreasing volume of trade. This result complements studies finding
large gains from international labor market integration, e.g., Klein and Ventura (2009) and
Kennan (2003), and policies fostering immigration of workers from younger countries of the
South to the older ones in the North would increase global welfare in a world of continuing
North-South trade.
The outline of the paper is as follows: In the next section, we present a review of related
literatures. In Section 3, we summarize the main patterns and regularities of demographic and
technological differences between the North and the South. We introduce the model economy
in Section 4 and characterize the model’s dynamic general equilibrium under free trade. In
Section 5, we describe the quantitative analyses and introduce our benchmark scenario. We
describe counterfactual scenarios and present the results in Section 6, followed by a discussion
of policy messages and concluding remarks collected in Section 7. For interested readers, we
outline the solution algorithm in the technical appendix.
2. Related Literature
This paper is related with different strands of literature. First, the paper is centrally related with
the literature on dynamic Heckscher-Ohlin models. Second, there is a literature on extending
the Heckscher-Ohlin model with technological differences across trading parties, e.g., with
Ricardian productivity differences across countries. Finally, the welfare effect of free trade
relative to autarky has been an issue of interest because the existence of net gains from free
trade may not always hold in dynamic Heckscher-Ohlin models with overlapping generations
under the absence of compensation schemes.
Dynamic Heckscher-Ohlin Models
Numerous papers in the literature propose dynamic extensions of the Heckscher-Ohlin model
as reviewed by Bajona and Kehoe (2014).6 One useful classification suggested by these authors
is to group the papers into those developing infinite-horizon models versus OLG models. But
regardless of the way in which time and demographics are introduced into the static Heckscher-
Ohlin setup, each and every model focuses on at least one aspect where the trading partners
differ from each other, and the existence of two sectors that produce two distinct tradeable goods
is a common approach.7
6 For an older but illuminating review of North-South trade and growth models, see Chui et al. (2002). 7 One-sector models are not suitable for analyzing the long-run commodity composition of trade. Deardorff (1987)
builds an example of such a model and focuses on the question of how relative factor endowments change over
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The leading papers that construct infinite-horizon models are those of Oniki and Uzawa (1965),
Bardhan (1965), and Findlay (1970). These models feature two sectors, of investment and
consumption goods, and population growth and saving rates are fixed, reflecting Solow’s
(1956) influence. Stiglitz (1970) introduced intertemporal choice where discount rates differ
across countries. Unlike these papers, Deardorff and Hanson (1978) focus not on the
equalization of factor prices but the Heckscher-Ohlin theorem itself, demonstrating that it holds
in the long run regardless of how the saving function is specified. Chen (1992) proposes another
change in perspective and shows that trade continues to occur in the long run if initial factor
endowments differ in a model with identical preferences including the discount rate.8 Ventura
(1997) extends the model with more than two countries and shows that imposing sufficiently
specific structure that ensures factor price equalization implies conditional convergence across
trading economies. Deardorff’s (2001) model with endogenous saving rates lead to multiple
long-run equilibria and poverty traps under free trade. Bond et al. (2003) develops a model with
physical and human capital accumulation where factor price equalization implies
indeterminacy. Cuñat and Maffezzoli’s (2004) analysis shows that a multi-country Heckscher-
Ohlin model does not feature convergence in income per capita levels under free trade. Bajona
and Kehoe (2010) generalizes Ventura’s (1997) model to show that Ventura’s (1997)
convergence results vanish if factor price equalization is not imposed. Bond et al. (2011) work
with non-homothetic preferences and show that a steady-state version of the Heckscher-Ohlin
theorem holds if countries do not differ in labor productivity levels.
OLG models in the literature usually build upon Galor’s (1992) two-sector model. Parallel to
the early models featuring infinite lives, Galor and Lin (1997) focuses on two countries that
differ in time preference rates but are otherwise identical. Mountford (1998), also stressing time
preference differences, show that static implications the Heckscher-Ohlin model do not need to
hold in a dynamic universe. Mountford (1999) introduces endogenous growth via learning by
doing and shows that divergence in world income distribution is centrally related with
international trade. Sayan’s (2005) 2×2×2×2 model differentiates countries with respect to
population growth rates and demonstrates numerically that static Heckscher-Ohlin results do
not necessarily generalize in the dynamic general equilibrium under free trade. Galor and
Mountford (2006, 2008) construct two-country models and show that international trade has
first-order effects on demographic transition since trade affects factor returns differently for
economies at different stages of economic development. Naito and Zhao (2009) and Yakita
(2012) largely follow Sayan’s (2005) model and extend it respectively with compensation
schemes and life expectancy changes. Georges et al. (2013) construct a multi-regional OLG
model that builds upon the Armington model and show that the aging North can benefit from
expanding trade with the South.
We closely follow Sayan (2005) in building the hybrid Ricardo-Heckscher-Ohlin model with
standard preferences and technologies. Our contribution to this literature is twofold: First, we
motivate our benchmark scenario with plausible demographic and technological prospects for
the 21st century. Second, the model realistically features a world economy where growth paths
of more developed and less developed economies diverge. These are not trivial points since the
time as population in one of the countries grows at a higher rate than in the other. Fried (1980) constructs a one-
sector overlapping-generations model and studies the welfare effects of labor-saving technological progress. 8 Understanding long-run comparative advantage via differences in time preference across countries is not
satisfactory in a Heckscher-Ohlin model that originally emphasizes relative factor endowment differences.
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evolution of comparative advantage critically depends on all of these elements in general
equilibrium.
Ricardian Elements within the Heckscher-Ohlin Framework
Leontief’s (1953) paradox, analyzed rigorously by later authors such as Leamer (1980) and
Maskus (1985), has raised a serious challenge to the Heckscher-Ohlin model by showing that
US exports in 1947 were relatively more labor-intensive than US imports. The foremost
explanation for the paradox is that countries do not possess identical technological structures.
Unifying the Heckscher-Ohlin and the Ricardian streams of the old trade theory has therefore
been a viable alternative (Findlay and Grubert, 1959; Minhas, 1962; Bhagwati, 1964).
Empirical tests of the Heckscher-Ohlin-Vanek (HOV) model of the factor content of trade
indeed indicate that Ricardian elements increase the explanatory power of the HOV model (e.g.,
Bowen et al., 1987).9 Trefler (1993, 1995) show that productivity differences play an important
role in partially determining the factor content of trade. Harrigan (1997), Davis and Weinstein
(2001), and Hakura (2001) obtain similar results on the complementariness of the two
explanations using different methods and samples.10 More recent papers such as those of
Morrow (2010), Egger et al. (2011), Fisher (2011), Nishioka (2012), and Levchenko and Zhang
(2014) also indicate that both the relative factor abundance and the relative productivity
differences are significant in correctly determining the direction of comparative advantages
across nations.
There is no consensus in the literature on how productivity differences should be introduced
into an otherwise standard or demographically extended dynamic Heckscher-Ohlin model. We
here use production technologies that feature exogenous Harrod-neutral technological progress
with four distinct productivity parameters, i.e., productivity terms for two sectors in each of the
two regions. This leads to a hybrid Ricardo-Heckscher-Ohlin model with a well-defined steady-
state where variables exhibiting perpetual growth are proportional to productivity in the long-
run.
Welfare Gains and Losses
That free trade is Pareto superior to autarky is one of the main results in international trade
theory (Samuelson, 1962; Kemp, 1962). Three classic papers written by Grandmont and
McFadden (1972), Kemp and Wan (1972), and Chipman and Moore (1972) prove that lump-
sum transfers can be used to redistribute aggregate gains under free trade from winners to losers.
On the grounds that lump-sum transfers are subject to incentive compatibility problems, Dixit
and Norman (1980, 1986) show that commodity taxes/subsidies and poll grants/taxes, not being
individual specific, are better alternatives in ensuring that free trade is Pareto superior to
autarky.11
9 See Leamer (1995), Leamer and Levinsohn (1995), and Feenstra (2015) for reviews of this literature. 10 Debaere (2003) tests a specification of the HOV model that is not very sensitive to productivity differences and
finds a strong support for the role of relative factor abundance. Romalis’ (2004) results also indicate that, in a
multi-country model with transportation costs and monopolistic competition as in Krugman (1980), the Heckscher-
Ohlin and Rybczynski theorems are empirically valid. 11 Authors contributing to the welfare analysis of free trade versus autarky include Fried (1980), Brecher and
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That free trade is Pareto superior to autarky, however, does not necessarily hold in dynamic
environments (with overlapping generations). Kemp and Long (1979), Binh (1985, 1986) and
Serra (1991) are early studies exemplifying the pessimistic outcome as cited by Kemp and
Wong (1995). Besides, as demonstrated by Willmann (2004), Pareto superiority of free trade
with lump-sum transfers vanishes under policy commitment and time inconsistency problems.
Sayan’s (2005) results indicate that free trade (without redistribution) is not mutually beneficial
in the sense of Pareto. Yakita’s (2012) model also shows that free trade creates winners and
losers. There exist, on the other hand, some compensation schemes to make free trade a better
outcome for everyone. Kemp and Wong (1995) and Wong (1995) show that various policy tools
are effective in redistributing welfare gains from winners to losers in order to achieve Pareto
improvements. Naito and Zhao’s (2009) compensation scheme, for instance, achieves this
target.
In this paper, we analyze only the free trade equilibria of the model, and we construct these free
trade equilibria without any form of compensation that redistributes the welfare gains from
winners to losers. We compare different free trade scenarios, and we should emphasize that our
results on welfare effects are relative to the benchmark scenario and not to the case of autarky.
3. North-South Differences in Demography and Technology
The purpose of this section is to discuss how the North and the South have differed in the past
and are highly likely to differ in the future with respect to population dynamics and
technological characteristics. More developed and less developed economies exhibit significant
differences in several dimensions of social, political, and economic development. Demographic
and technological differences can be seen both among the causes and among the outcomes of
the process of development in the long run.12
Fertility and Working-Age Population
Agricultural societies are typically characterized with high mortality and high fertility. These
societies are poor in modern standards and subject to Malthusian pressures. In these societies,
resource constraints allow for only a miniscule rate of population growth if any, and increasing
living standards lead to higher fertility (i.e., child quantity) but not to investments in health and
education (i.e., child quality). Western Europe before the Industrial Revolution, most of today’s
developing economies before mid-1900s, and several countries in Sub-Saharan Africa today,
for instance, are historical examples of this high mortality-high fertility situation (Kirk, 1996;
Wilson, 2001; Lee, 2003).
Choudhri (1994), Feenstra and Lewis (1994), Hammond and Sempere (1995), and Facchini and Willmann (1999). 12 The unified growth literature after Galor and Weil (2000) and Galor (2005, 2011), for instance, has extended our
understanding of complex interactions among population, technology, and resources.
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The demographic transition is a continuous process by which a society that initially has high
mortality and high fertility rates and a young population realizes secular declines in mortality
and fertility rates and gets older on average (Kirk, 1996: 361). Most typically, mortality decline
precedes fertility decline, and the associated difference between the two leads to increasing
Figure 1: Population and Fertility Differences
Source: United Nations Population Division (2015)
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population growth rates at the early stages of the transition. In time, after realizing a peak level,
population growth decreases as both mortality and fertility stabilize at low levels at the
advanced stages of the transition.13
Demographic variables exhibit considerable variation both across countries at any given period
after the Industrial Revolution and across time for any given country. Differences mainly reflect
the differential starting dates and differential speeds of demographic transition. Today, many
economies have total fertility rates below the replacement level of approximately 2.1 children
per woman, i.e., the number of births per woman that would imply a constant population from
one generation to the next. The lowest fertility rates are generally recorded in former Eastern
Bloc countries of Europe and Mediterranean countries such as Portugal, Spain, and Greece.
Some of the low fertility economies are the ones that experienced major declines in fertility
from late 19th to early 20th centuries. Early industrializers such as England and France and
Western Offshoots are among these forerunners. Nordic countries of Europe including Finland,
Norway, and Denmark also have low fertility rates below but closer to the replacement level.
A much larger set of poorer economies at different stages of demographic transition have higher
fertility rates. Roughly grouped and ranked from highest to lower levels of fertility, Sub-Saharan
Africa, the Middle East and North Africa (MENA) region, relatively poor economies of Asia
and Latin American countries are in this set.
Figure 1 pictures the evolution of total fertility rate for selected countries and working-age
population levels for more developed and less developed country groups. The data source for
both variables is the United Nations Population Division’s (2015) World Population Prospects.
This source collects and publishes actual demographic data and several projections of key
demographic variables for a large set of countries, and researchers generally take this source as
the most reliable one for demographic projections.
In the top panel of Figure 1, the data for Italy, Japan, France, and the US exemplify the fertility
patterns in developed economies. The other set includes India, China, Bangladesh, Pakistan,
Indonesia, Mexico, Turkey, and Brazil, representing developing economies that have been
integrated with the global economy in recent decades through increased labor-intensive exports.
There exists a noticeable difference between the fertility levels of these two groups of
economies as expected. More developed economies enter the final stage of their demographic
transition in 1970s throughout which fertility remains below the replacement level. In the same
historical episode, less developed economies experience an earlier stage of their transitions with
the secular decline of fertility.
The bottom panel of Figure 1 pictures an inevitable consequence of the differential timing of
demographic transitions in more developed and less developed economies. In World Population
Prospects, the group of more developed economies includes Japan, New Zealand, Australia, and
13 There exists a very large literature on demographic transition. Chesnais (1992) presents an influential
longitudinal analysis of demographic transition for 67 countries. Lee (2003) provides a broad historical outline of
main patterns and regularities, focusing on both causes and consequences. Guinnane (2011) reviews the literature
on the causes of fertility decline with an emphasis on the historical experiences of today’s developed economies.
A collected volume edited by Lee and Reher (2011) specializes in the consequences of demographic transition.
Lehr (2009) and Strulik and Vollmer (2015) provide empirical assessments focusing on the determinants of fertility
decline.
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countries in Europe and North America, and the rest of the countries are included in the group
of less developed ones. Under this grouping, which we take as a fairly plausible representation
of the North-South separation, the levels of working-age populations markedly differ, and there
exist both level and growth differences. In 1950, the level difference is about 2-fold but the
growth difference throughout the period from 1950 to 2015 increases this to some level larger
than 4-fold. Furthermore, fertility differences projected to persist until the end of the 21st
century imply that the South-to-North ratio of working-age populations will be larger than 6-
fold.
Productivity Differences
Large and persistent differences in total factor productivity lead to large and persistent cross-
country income differences. Since Solow’s (1957) growth accounting work on the US economy,
this is a common view in the development accounting literature, and several studies attribute a
large role to TFP differences (Klenow and Rodriguez-Clare, 1997; Hall and Jones, 1999;
Parente and Prescott, 2000; Hendricks, 2002; Caselli, 2005; Hsieh and Klenow, 2010).14
Figure 2: TFP Differences
Source: UNIDO
TFP differences have first-order implications for the North-South trade. In a world of two
regions producing two goods with differing levels of sectoral productivities, the Ricardian
14 Some more recent studies find that the role of human capital differences is larger than previously suggested.
These include Erosa et al. (2010), Hanushek and Woessmann (2012), Jones (2014), Manuelli and Seshadri (2014),
and Hendricks and Schoellman (2016).
13
theory predicts that regions have an incentive to trade with each other.
The Penn World Tables of Feenstra et al. (2015) provide the most frequently used and detailed
TFP measurements for the postwar period and for a large number of countries.15 Figure 2
pictures the evolution of relative TFP levels for selected economies from 1960 to 2000 where
the TFP of the US economy is equal to unity for all years. Relative TFPs exhibit a high degree
of variation even for a small number of economies. Italy, Japan, and France show some limited
success in closing the TFP gap with the US, but India, China, Bangladesh, Pakistan, and
Indonesia represent failures as the TFP gaps for these countries remains large.
4. A Ricardo-Heckscher-Ohlin Model
The model we describe in this section is a synthesized dynamic general equilibrium model of
international trade. The model features both Ricardian productivity differences and factor
endowment differentials as in the original Heckscher-Ohlin model. Throughout the analysis, we
assume that productivity variables and population levels evolve exogenously. While this
assumption prevents us from analyzing some interesting issues such as how trade affects
technological progress, it allows us to analyze the isolated effects of demographic and
technological differences in a transparent way.
We consider a world economy with two regions, i.e., the North and the South. Both are endowed
with two primary factors, i.e., labor and capital. These factors are perfectly mobile within a
region but immobile across regions. Two goods are produced in the North and the South by
perfectly competitive firms, and the goods differ in factor intensity. We take Good 1 as the
consumption-investment good and normalize its price to unity, and we assume that Good 2 is
relatively more labor-intensive. We denote the relative price of Good 2 in trade equilibrium by
𝑝𝑡.
The North and the South differ both in relative factor endowments and in relative productivities.
These differences cause autarky prices to be different in two regions. Therefore, regions have
incentives to trade goods and specialize more in the production of the good in which they have
a comparative advantage.
We denote the model time by 𝑡 ∈ {0,1, … }. There exist overlapping generations of young and
old individuals in each region, and 𝑡 serves as an index variable for generations as well. The
mass of young individuals in region 𝑖 ∈ {𝑛, 𝑠} at period 𝑡 is denoted by 𝑁𝑡𝑖 and grows from 𝑡 to
𝑡 + 1 at the rate 𝑛𝑡𝑖 ≥ 0.
The young individuals, each endowed with a unit of labor, supply labor services in a perfectly
competitive labor market for the real wage 𝑤𝑡𝑖 and save for their old age given the real rental
rate 𝑟𝑡+1𝑖 . Their savings form the next generation’s aggregate capital stock denoted by 𝐾𝑡+1
𝑖 .
15 TFP is not directly observed and can only be inferred as a residual within a model with assumed production
functions and market structures.
14
While the trade equilibrium features a unique level of relative price 𝑝𝑡 by definition, the Factor
Price Equalization (FPE) do not hold in general because of productivity differences across
regions. We shall therefore keep indexing factor prices by superscript 𝑖.
Preferences
Individuals derive utility from the consumption of both goods in both ages. The lifetime utility
function of a young individual at period 𝑡 is of Cobb-Douglas form and satisfies
𝑢𝑡𝑖 ≡ [(𝑐1,𝑦,𝑡
𝑖 )𝜃
(𝑐2,𝑦,𝑡𝑖 )
1−𝜃]
𝜇
[(𝑐1,𝑜,𝑡+1𝑖 )
𝜃(𝑐2,𝑜,𝑡+1
𝑖 )1−𝜃
]1−𝜇
(1)
where 𝑐𝑗,𝑔,𝜏𝑖 ≥ 0 denotes the consumption of good 𝑗 ∈ {1,2} by an individual of age 𝑔 ∈ {𝑦, 𝑜}
at period 𝜏 ∈ {𝑡, 𝑡 + 1} in region 𝑖 ∈ {𝑛, 𝑠}. The preference parameters 𝜃 and 𝜇 satisfy 𝜃, 𝜇 ∈(0,1).
The representative young individual has 𝑤𝑡𝑖 as young-age income and obtains gross interest
income of (1 + 𝑟𝑡+1𝑖 ) per unit of saving in the old-age.
Technologies
Goods differ in factor intensities, and regions differ in relative productivities. We postulate
constant returns to scale Cobb-Douglas functions that satisfy these assumptions with Harrod-
neutral productivity terms as in
𝑌1,𝑡𝑖 = (𝐾1,𝑡
𝑖 )𝛼
(𝐴1,𝑡𝑖 𝐿1,𝑡
𝑖 )1−𝛼
and 𝑌2,𝑡𝑖 = (𝐾2,𝑡
𝑖 )𝛽
(𝐴2,𝑡𝑖 𝐿2,𝑡
𝑖 )1−𝛽
(2)
where elasticity parameters 𝛼, 𝛽 ∈ (0,1) satisfy 𝛼 > 𝛽 so that Good 2 is relatively more labor-
intensive. That productivities enter the model as Harrod-neutral terms ensures that the model
has a well-behaved steady-state with positive long-run growth rates in both regions.
We also assume that 𝛼 − 𝛽 is sufficiently large to imply a sufficiently large cone of
diversification. This is to ensure that both regions produce both goods in trade equilibrium.
Since we divide the world economy into two regions, that both regions produce both goods is a
realistic assumption at this level of abstraction. Finally, for notational convenience, we define
relative productivity term 𝑎𝑡𝑖 for region 𝑖 and period 𝑡 as in 𝑎𝑡
𝑖 ≡ 𝐴1,𝑡𝑖 /𝐴2,𝑡
𝑖 . The growth rate of
𝐴2,𝑡𝑖 from 𝑡 to 𝑡 + 1 is denoted by 𝑔𝑡
𝑖 > 0.
Equilibrium
We are mainly interested in the dynamic general equilibrium of this model under incomplete
specialization and free trade of both goods. In this equilibrium, all young individuals maximize
their lifetime utility, all firms maximize their profits, and all markets clear. Obviously, the good
markets clear with the global demand for good 𝑗 being equal to the global supply of it for each
𝑗 ∈ {1,2}.
15
Both the utility and the profit maximization problems have unique solutions. The former
solution implies that young individuals save a constant fraction of their wage income for the
old age. Specifically, for region 𝑖 ∈ {𝑛, 𝑠}, we have like
𝐾𝑡+1𝑖 = (1 − 𝜇)𝑤𝑡
𝑖𝑁𝑡𝑖 (3)
where the solution of the profit maximization problem determines 𝑤𝑡𝑖 as a function of relative
price 𝑝𝑡 and relative productivity 𝑎𝑡𝑖 . Then, capital stock per worker in region 𝑖 ∈ {𝑛, 𝑠} satisfies
𝑘𝑡+1𝑖 =
(1−𝜇)(1−𝛼)𝜖𝛼𝑝𝑡
𝛼𝛼−𝛽
(𝑎𝑡𝑖 )
𝛽(1−𝛼)𝛼−𝛽 (1+𝑔𝑡
𝑖)(1+𝑛𝑡𝑖 )
(4)
To define the trade equilibrium, we lastly impose the market clearing conditions. Since Walras’
Law holds, we only need to clear one of the markets, and it is simpler to work with Good 2
since this good is used only for consumption purposes:
𝑌2,𝑡𝑛 + 𝑌2,𝑡
𝑠 = (𝑁𝑡𝑛𝑐2,𝑦,𝑡
𝑛 + 𝑁𝑡−1𝑛 𝑐2,𝑜,𝑡
𝑛 ) + (𝑁𝑡𝑠𝑐2,𝑦,𝑡
𝑠 + 𝑁𝑡−1𝑠 𝑐2,𝑜,𝑡
𝑠 ) (5)
After making arrangements that use the solutions to the optimization problems, we arrive at a
forward-looking equation that describes the evolution of 𝑝𝑡:
𝑝𝑡 = 𝑓(𝑝𝑡+1, 𝑥𝑡 , 𝑧𝑡+1) (6)
The function 𝑓(𝑝𝑡+1, 𝑥𝑡, 𝑧𝑡+1) solves for the current relative price 𝑝𝑡 given the perfectly
foreseen future relative price 𝑝𝑡+1 and two auxiliary vectors 𝑥𝑡 and 𝑧𝑡+1 of exogenous variables.
The former includes two population variables (𝑁𝑡𝑛, 𝑁𝑡
𝑠) and four productivity variables
(𝐴1,𝑡𝑛 , 𝐴1,𝑡
𝑠 , 𝐴2,𝑡𝑛 , 𝐴2,𝑡
𝑠 ), and 𝑧𝑡+1 collects two forward-looking relative productivity terms
(𝑎𝑡+1𝑛 , 𝑎𝑡+1
𝑠 ).
It is highly intuitive that 𝑝𝑡, the key endogenous variable of the model, is determined through
all of the exogenous variables that include productivity and population levels.
5. Quantitative Analysis
The dynamic general equilibrium of the model under free trade is unique, but achieving explicit
analytical solutions is not feasible. For this reason, our quantitative results follow from
numerical solutions of the model.16
We take the length of a period as 20 years as it is usual for OLG models and simulate the model
for 14 periods starting at 1980 and ending at 2220. We study several different scenarios of
16 We present brief discussions of the positive properties of equilibrium and the numerical solution of the model in
the technical appendix.
16
demographic and technological differences across regions (see below).
Initial Capital Stocks
Two model inputs, the initial values of capital stock per worker denoted by 𝑘0𝑛 and 𝑘0
𝑠, remain
same in all scenarios. We obtain representative values for these initial levels using the Penn
World Tables data of Feenstra et al. (2015). Specifically, we divide the set of countries for which
data is available into two groups of 23 more developed economies of the North and 117 less
developed economies of the South. We then calculate, for each country, the level of physical
capital per worker by dividing capital stock at constant national prices (million 2011 US dollars)
with the number of persons engaged, i.e., employment. Taking the group-wise averages of the
resulting values roughly indicate that, in the year 1980, capital stock per worker in the North is
about 2.6 times larger than the level calculated for the South.17
Balanced Growth Paths
Both the North and the South have well-behaved balanced growth paths where long-run growth
of real GDP per capita in both economies is driven by exogenous productivity growth. In all of
the scenarios including the benchmark, we specify long-run growth rates and fixed or time-
varying wedges between two sectoral productivity levels for both economies. To set realistic
growth rates, we use the Maddison Project's database of real GDP per capita levels estimated
for the period of 1950-2008. After dividing countries into two groups of more developed and
less developed economies, we calculate average annual growth rates of real GDP per capita for
all economies in each group and then end up with two group averages. These averages are
respectively equal to 2.7% for the North and 1.6% for the South. Converted to 20-year growth
rates per generation, these rates are roughly equal to 70% and 37%, respectively.
Structural Parameters
The numerical values assigned to structural parameters of the model are also common to all
simulated scenarios and also common to both the North and the South. These parameters are
two preference parameters, 𝜃, 𝜇 ∈ (0,1), and two technology parameters, 𝛼, 𝛽 ∈ (0,1). Recall
that 𝛼 > 𝛽 implies that Good 1 is relatively more capital-intensive.
We follow Sayan (2005) in determining the values for 𝜃, 𝜇, and 𝛼, but we also enlarge the cone
of diversification for incomplete specialization in both economies and at all periods through a
smaller value for 𝛽, i.e., by making relatively more labor-intensive good slightly less capital-
intensive compared to Sayan’s (2005) setup. Table 1 shows the assigned values.
17 If one excludes 10 major oil exporting countries from the group of less developed economies, this difference
would rise from 2.6 to 4.3. Our results, on the other hand, are not sensitive to the inclusion of oil exporting
economies.
17
Table 1: Structural Parameters
𝜃 𝜇 𝛼 𝛽
0.40 0.75 0.60 0.10
The Benchmark Scenario
Before proceeding to the specification of alternative scenarios and results, it is essential to
describe the benchmark scenario with some detail. This benchmark of population and
technology, after all, is what we think as the most representative and plausible present and future
scenario for the North-South trade when we divide the world economy into two aggregate
economies with differing characteristics.
For the evolution of working-age populations, we feed the model directly with the United
Nations Population Division’s data for more developed and less developed economies pictured
in Figure 1 above.
For technology, the task is to determine the initial values (𝐴1,0𝑛 , 𝐴1,0
𝑠 , 𝐴2,0𝑛 , 𝐴2,0
𝑠 ) of four
productivity variables as the balanced growth rates are set as discussed above. In other words,
once we determine the initial values, we would impose a particular pattern of productivity-based
comparative advantage that persists in the long run such that 𝑎𝑡𝑖 = 𝐴1,𝑡
𝑖 𝐴2,𝑡𝑖⁄ for each 𝑖 ∈ {𝑛, 𝑠}
and 𝑎𝑡𝑛 𝑎𝑡
𝑠⁄ remain fixed at their initial levels.
The empirical foundation of the values we use is Fadinger and Fleiss’ (2011) estimates
originating from a Ricardo-Heckscher-Ohlin model. In this multi-sectoral model, 24
manufacturing industries in more than 60 countries with available data are described by cross-
sectoral probability distributions of associated TFP levels filtered out through bilateral trade
data. Closely inspecting estimates for sectors with lowest and highest TFP levels after grouping
countries into the North and the South once again, we proceed as follows: We choose Food as
the representative labor-intensive sector to ease inference since the TFP of the US economy in
this sector is normalized to unity. We then calculate the average TFP in Food for the countries
of the South whose highest TFP is recorded for Food. When Argentina as an outlier is included,
this average reads 0.804 for 10 countries, and excluding Argentina results in an average of 0.679
for 9 countries. We therefore take an intermediate value of 0.75 and set 𝐴2,𝑡𝑛 𝐴2,𝑡
𝑠⁄ = 1/0.75 =
1. 3̅ as the benchmark value. For the capital-intensive sector, it is not feasible to choose a
representative one. However, four capital-intensive sectors are commonly recorded for highest
and lowest TFP sectors respectively by the North and the South countries according to our
grouping. These are Beverages, Transport, Machinery, and Other Non-Metallic sectors, and
𝐴1,𝑡𝑛 𝐴1,𝑡
𝑠⁄ values implied by averaging are respectively equal to 2.00, 11.25, 11.81, and 3.11.
The average of these four values is around 7.00, and we choose a slightly parsimonious
benchmark of 𝐴1,𝑡𝑛 𝐴1,𝑡
𝑠⁄ = 6. 6̅.
18
6. Results
We document our results in three subsections. We focus exclusively on the North, and the results
follow from quantitative analyses of the model under different scenarios of demographic change
and technological progress. For each scenario, we analyze the evolution of four variables; these
are the volume of trade measured by the net import of the labor-intensive good by the North,
lifetime welfare, real GDP per capita, and, finally, the rental rate to wage ratio, i.e., a measure
of within-country inequality that worsens the relative condition of labor suppliers if it increases.
We visualize the values of these four variables under the experimented scenario divided by the
values they are equal to under the benchmark scenario. Thus, the level of unity in the vertical
axes of the following figures signifies the level above which the experimented scenario results
in a larger level compared to the benchmark. Table 2 located at the end of this section presents
a summary of the long-run effects.
Population versus Productivity Differences
The first four scenarios study the relative importance of demographic versus technological
differences on the North-South trade, and Figure 3 presents the results. Recall that the
benchmark scenario features (i) large and persistent differences in relative productivities and
(ii) large differences in working-age population levels as projected by the UN Population
Division. We contrast this benchmark with the following:
Scenario 1: No population differences but high productivity differences as in the benchmark
Scenario 2: No population differences but low productivity differences
Scenario 3: UN population differences as in the benchmark but low productivity differences
Scenario 4: UN population differences as in the benchmark but no productivity differences
Scenarios 1 and 4 respectively isolate the effects of population and (large) productivity
differences by shutting down either one of these. The top left panel of Figure 3 indicates that
both the Heckscher-Ohlin and the Ricardian channels are important in explaining the volume
of the North-South trade. Without any demographic difference in Scenario 1, net import of
relatively more labor-intensive good from the South decreases by more than 50% relative to the
benchmark in 2000 (circles). But the decrease in Scenario 4 without productivity differences is
larger with a decrease slightly less than 70% (dashes).18
18 In Scenario 4 where the difference in population growth rates decreases and is equal to zero at 2220, regions
become identical with equal autarky prices. As a result, the North-South trade does not take place in and after 2220.
19
Regarding the Stolper-Samuelson effects, the bottom left panel of the figure shows that
population clearly dominates productivity in determining inequality. The rental rate to wage
ratio decreases by about 20% in 2000 when productivity differences are shut down, but the
decrease associated with population differences is larger than 50%. Thus, while it is productivity
that mainly affects the volume of trade, inequality is determined to the largest extent by
population differences.19
Figure 3 also pictures the effects of population and productivity on the North’s lifetime welfare
and real GDP per capita. Focusing first on Scenario 4, we see that welfare and output are lower
than their respective benchmark levels for all horizons when the South has access to the North’s
technology entirely (dashes). This follows because FPE holds strictly at all horizons under free
19 In fact, when population growth rate difference decreases sufficiently in Scenario 4, inequality exceeds the
benchmark level at 2140.
Figure 3: Population vs. Productivity Differences
20
trade when regions are technologically identical with identical productivity growth rates in both
sectors. This implies that the South determines the terms of trade as the largest region given its
large population size, and this results in the North’s convergence to the South’s autarkic
equilibrium exactly as in Sayan (2005). Since the South is poorer than the North because of
population level differences, Scenario 4 indicates welfare and output losses for the North under
free trade. Put differently, in a world of sizable and continuing demographic differences between
the North and the South, the North’s technological superiority is essential for the region to
sustain its welfare and growth under free trade.
For Scenario 1, the similar forces of comparative advantage, specialization, and scale effects
operate through technological differences. The North in this scenario remains the
technologically superior economy with faster productivity growth and persistent differences in
sectoral productivities, but regions are demographically identical with exactly same levels of
fıxed population. The North in this case determines the terms of trade as the “largest” region,
and there exist gains in lifetime welfare and real GDP per capita where FPE does not hold.
Defensive Innovation
Given that the model’s benchmark scenario returns strong Stolper-Samuelson effects where the
relatively scarce factor worse off in both countries under free trade, a question of interest is how
defensive innovation that increases the relative productivity of the scarce factor does affect
trade, welfare, inequality, and growth.
Defensive innovation weakens comparative advantages originating from productivity
differences and makes the regions technologically more similar in time relative to the
benchmark scenario. In the two scenarios that investigate the role of defensive innovation, we
alter the productivity growth rates in such a way that capital-biased productivity growth is faster
than the benchmark in the South and labor-biased productivity growth is faster than the
benchmark in the North.
Scenario 5: Labor-Biased Productivity Growth in the North
Scenario 6: Capital-Biased Productivity Growth in the South
More specifically, in Scenario 5, we increase the percentage growth rate of the unit productivity
of labor in the production of relatively more labor-intensive good, 𝐴2,𝑡𝑛 , above its benchmark
value by 1.1-fold starting from 2000 onwards. In average annual terms, this translates into an
increase from 2.75% in the benchmark scenario to 2.96% in Scenario 5.
Scenario 6 changes the percentage growth rate of the unit productivity of labor in the production
of relatively more capital-intensive good, 𝐴1,𝑡𝑠 , once again by 1.1-fold and from 2000 onwards.
The annual growth rate of this productivity term increases from its benchmark value of 1.6% to
1.73% starting with the 2000-2020 period.
Figure 4 pictures how defensive innovation in the North (circles) and the South (squares) affects
trade, inequality, welfare, and growth in the North. Both types of defensive innovation result in
decreases in the volume of trade (top left panel) and in inequality (bottom left panel) as
expected. For defensive innovation in the North and for all horizons, decreases in inequality
relative to the benchmark scenario are larger in percentage terms than decreases in the volume
21
of trade.20
Figure 4: Defensive Innovation
The North’s defensive innovation leads to sizable increases in lifetime welfare and real GDP
per capita as shown in top right and bottom right panels. For both variables, there is a direct
effect associated with higher labor-biased productivity growth, but there also exist indirect
effects associated with endogenous reactions of specialization and trade. Specifically, the share
of labor increasingly allocated to relatively more capital-intensive good remains lower than its
benchmark level under defensive innovation.
Contrary to these findings, the South’s defensive innovation does not significantly affect
lifetime welfare and real GDP per capita in the North. For most of the 21st century, effects are
very close to zero and do not exceed 5% increase in the long run. This is simply because the
South’s defensive innovation does not have a direct effect on the North’s output and the
experimented increase in the growth rate is lower than that of the North’s defensive innovation.
20 The evolution of inequality exhibits an overturn in 2180 when population growth rate differences are sufficiently
small so that defensive innovation that makes the regions more similar starts dominating.
22
Immigration and Fertility
In the two sets of experiments discussed above, increases in real GDP per capita and lifetime
welfare and decreases in inequality are associated with decreases in the volume of trade. In two
other scenarios, on the other hand, we obtain similar results for real GDP per capita, lifetime
welfare, and inequality without decreases in the volume of trade. In Scenario 7 on immigration,
we allow for the flow of workers from the South to the North for each generation, and Scenario
8 increases fertility in the North in such a way that the number of workers increases for each
generation.
Scenario 7: Immigration from the South to the North
Scenario 8: Increasing Fertility Levels in the North
Figure 5: Immigration and Fertility
More specifically, Scenario 7 basically dictates that 5% of the South’s workers migrate to and
work in the North for each generation. In 2000 where counterfactual migration flow in the
model starts, this total is roughly equal to 130 million workers, and this is a plausible value
given that the total numbers of immigrants living in Northern America and Europe are
respectively equal to 54 million and 76 million in 2015 (United Nations, 2016: 1). Clearly,
(adult) population growth rates change in both regions under this counterfactual scenario. In the
23
South, it decreases from the benchmark rate of 2.41% to 2.15% per annum for the 2000-2020
period. Conversely, in the North, it increases from 0.6% to 1.4% per annum for the 2000-2020
period, and from 0.06% to 0.35% per annum for the next 20 years.
In Scenario 8, we increase fertility and (adult) population growth rates in the North in such a
way that the increase in the number of workers for each generation exactly matches the increase
experimented in Scenario 7, but we do not implement any change for the South. The resulting
numbers, for instance, indicate that (adult) population growth rate from 2000 to 2020 is 0.8%
points larger than its benchmark value in the North, but it is equal to its benchmark value of
2.41% in the South.
Scenarios 7 and 8 have similar effects, but effects change in time at different horizons as
pictured in Figure 5. The generation whose working years coincide with the first generation of
immigrants in 2000 realizes a decrease in the volume of trade relative to the benchmark (top
left panel). Inequality on the other hand increases to worsen the relative position of workers in
2000 (bottom left panel). Since the number of workers increases in the North under both
Scenarios 7 and 8, and the number of workers decreases in the South under Scenario 7, these
results for 2000 are not surprising.
But effects are reversed after 2020; the total volume of trade is larger and inequality is lower.
Why? For trade, the reason lies behind the counteracting effect of the population level against
the role of population growth rate. In both Scenarios 7 and 8, the (positive) South-minus-North
difference in population growth rates decreases relative to the benchmark, and this should
decrease the volume of trade per worker. However, starting with 2020 and in both scenarios,
the level of adult population in the North becomes large enough to increase the total volume of
trade relative to the benchmark. For instance, the total volume of trade is about 2.5% larger than
the benchmark in 2020 in Scenario 7, but it is about 19% lower in per worker terms.
For inequality after 2020, the reversal can best be understood via specialization. Relative to the
benchmark, increasingly more capital stock per worker is now allocated to the relatively more
labor-intensive good in the North, and this decreases the rental rate to wage ratio relative to the
benchmark.
The right panels of Figure 5 indicate that the effects on real GDP per capita and lifetime welfare
are slightly more dramatic for the first couple of generations. Under the immigration scenario,
lifetime welfare is lower than the benchmark level only in 2000, but real GDP per capita remains
below the benchmark level for 2000, 2020, and 2040. For the increasing fertility scenario,
adverse effects are stronger, and it takes one more generation for these variables to exceed their
benchmark levels.
Important messages originating from these two experiments are the following: First,
immigration and fertility scenarios are the only ones where Stolper-Samuelson effects are
weakened in the long run without a decrease in the volume of trade. Second, immigration
scenario leads to higher lifetime welfare, higher real GDP per capita, and lower inequality in
comparison with fertility scenario that implies the same level of increase in the number of
workers in the North.
24
Table 2: Long-Run Effects on the North Scenario Trade Inequality Welfare RGDP pc
1: Same Population (High Prod.) − − + +
2: Same Population (Low Prod.) − − + +
3: UN Population (Low Prod.) − − + +
4: UN Population (Same Prod.) − + − −
5: Defensive Innovation in North − − + +
6: Defensive Innovation in South − − + +
7: South to North Immigration + − + +
8: Fertility Increase in North + − + +
7. Conclusion
The hybrid Ricardo-Heckscher-Ohlin model studied in this paper has two driving forces,
population and productivity. The model rests on the notion that the North and the South have
exhibited sizable demographic and technological differences in the past, and these differences
are going to persist in the upcoming decades of the 21st century. The South has higher fertility
levels and a younger and larger population, but the North has the superior technology in both
capital-intensive and labor-intensive products with a sizable comparative advantage in the
former.
To analyze the effects of different demographic and technological scenarios with incomplete
specialization under free trade, we first calibrate the model’s structural parameters and initial
values for a benchmark scenario. In this benchmark, population and fertility levels are borrowed
from the United Nations Population Division that group countries into two sets of more
developed and less developed countries. For productivity differences, we inspect Fadinger and
Fleiss’ (2011) TFP estimates following from a multi-sector, multi-country Ricardo-Heckscher-
Ohlin model and calibrate the TFP ratios across goods and regions accordingly. Finally, we
construct the benchmark scenario as the one where both regions are located at well-behaved
balanced growth paths in the long run.
A summary of our results is now in order: First of all, both demography and technology do
matter in explaining the volume of trade and the size of within-region inequality. For the volume
of North-South trade, productivity differences play a slightly larger role than population
differences. But the reverse is true for inequality since population differences clearly dominate
productivity differences in explaining the rental rate to wage ratio.
The second noteworthy result is that North’s technological superiority dominates the adverse
output and welfare effects of trading with a younger, labor-abundant South. Thus, the North’s
ability to compensate for adverse Stolper-Samueson effects is crucial for the continuation of
North-South trade.
Two scenarios also concerned with the Stolper-Samuelson effects study the role of defensive
innovation (Wood, 1994). Defensive innovation protects the owners of the scarce factor under
free trade by altering productivity growth rates. For instance, defensive innovation by the North
25
features a larger growth rate of TFP in the labor-intensive sector. Our numerical results show
that North’s defensive innovation is indeed effective in decreasing the rental rate to wage ratio
in the North but at the cost of a lower volume of North-South trade.
We finally look at the effects of two demographic scenarios, immigration from the South to the
North and fertility increases in the North. These scenarios increase the number of workers in
the North, adversely affecting trade volume and inequality for the early generations that
welcome immigrants and baby boomers. But, in the longer run, scale effects and specialization
patterns cause increases in the total volume of trade and decreases in inequality. Most
importantly, immigration is the most preferred scenario that is welfare-improving in the long-
run without decreasing the total volume of trade.
It is important to note that our simple Ricardo-Heckscher-Ohlin model assumes away within-
region redistribution schemes that may be needed to compensate for the adverse Stolper-
Samuelson effects in OLG models of international trade. Thus, counterfactual scenarios are
compared with the benchmark scenario in this paper, and we do not calculate the minimum
amount of lump-sum transfers or capital income tax rates that would ensure that free trade with
a younger, labor abundant South is Pareto-superior to autarky for the older, capital-abundant
North. We leave this analysis to future research.
26
References
To be added
27
Technical Appendix
Existence, Uniqueness, Stability, and Determinacy
The model economy’s dynamic general equilibrium under free trade is fully described by a path
of relative price 𝑝𝑡 satisfying (6) for 𝑡 ∈ {0,1, … } given initial values 𝑘0𝑛 > 0 and 𝑘0
𝑠 > 0. Since
the limits 𝑥∗ ≡ lim𝑡→+∞ 𝑥𝑡 and 𝑧∗ ≡ lim𝑡→+∞ 𝑧𝑡 exist, a steady-state 𝑝∗ > 0 is defined by 𝑝∗ =𝑓(𝑝∗, 𝑥∗, 𝑧∗), and there exists a unique 𝑝∗ > 0 that can be solved numerically. This unique
steady-state is asymptotically (locally) stable since 𝑓𝑝(𝑝∗, 𝑥𝑡, 𝑧𝑡+1) > 1 for all 𝑡. Furthermore,
our numerical work demonstrates that, for any given pair of initial values 𝑘0𝑛 > 0 and 𝑘0
𝑠 > 0,
the equilibrium path converges to 𝑝∗. This however does not ensure that the equilibrium path is
determinate under free trade. Unlike in the case of autarky where the equilibrium paths feature
initial jumps of 𝑝𝑡𝑛 and 𝑝𝑡
𝑠 to the levels 𝑝0𝑛 and 𝑝0
𝑠 respectively consistent with 𝑘0𝑛 and 𝑘0
𝑠, the
relative price 𝑝𝑡 can in general jump to any initial level 𝑝0 ∈ [𝑝0𝑠, 𝑝0
𝑛] under free trade. Thus,
there exist an inifite number of dynamic equlibrium paths all converging to 𝑝∗. Galor (1992)
and Kemp and Wong (1995) provide extensive discussions of equilibrium properties of two-
sector OLG models.
The Numerical Solution of the Model
Since the path of 𝑝𝑡 converges to 𝑝∗ for any given pair (𝑘0𝑛, 𝑘0
𝑠) of initial values, the model can
be solved via forward recursion using (6). To this end, one must first solve for 𝑝0 > 0 to initiate
the simulation but this initial level must satisfy (6) for 𝑡 = −1 as in 𝑝−1 = 𝑓(𝑝0, 𝑥−1, 𝑧0) under
the assumption that (𝑝−1, 𝑝0, 𝑝1, … ) are all perfect foresight equilibrium prices under free trade.
Then, 𝑝−1 must be consistent with initial values (𝑘0𝑛, 𝑘0
𝑠) through (4) evaluated for 𝑡 = −1
simply because 𝑝−1 determines the real wage 𝑤−1𝑖 on the supply side, and 𝑤−1
𝑖 then determines
𝑘0𝑖 through savings. Because of indeterminacy, on the other hand, the relative price 𝑝−1 can
jump to any initial level within the interval [𝑝−1𝑠 , 𝑝−1
𝑛 ] under free trade. For this reason, we
simply choose the midpoint value between autarky prices 𝑝−1𝑠 and 𝑝−1
𝑛 to set the free trade price
𝑝−1.