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1 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

Transcript of 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).

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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.

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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}.

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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.

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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.

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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.

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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.

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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

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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

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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.

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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

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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.

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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

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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.

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References

To be added

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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.