International trade and capital accumulation in an overlapping generations model with a public intermediate good

• Published date: 01 August 2019
• Date: 01 August 2019
• DOI: http://doi.org/10.1111/roie.12396
• Author: Mitsuyoshi Yanagihara,Tsuyoshi Shinozaki,Makoto Tawada

Rev Int Econ. 2019;27:765–785. wileyonlinelibrary.com/journal/roie

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765

© 2019 John Wiley & Sons Ltd

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INTRODUCTION

Why do developed countries trade with developing countries? At first glance, both intend to gain

from international trade. In fact, acceleration of economic growth in both developed and developing

countries has been accompanied by an increase in trade volume. World Bank data over the 40 years

from 1971 to 2010 show that average economic growth rates of those the OECD classifies as mid-

dle‐ and low‐income countries were 2.81% and 4.65%, respectively, while their share of exports of

goods and services in GDP increased by 0.94% and 2.01%, respectively.1

During those years, capital

accumulation in developed countries preceded this growth; the total growth rate of productive capital

stock of OECD countries was respectively 4.1% and 3.3% in 1990–1999 and 2000–2009.2

Therefore,

Received: 12 June 2017

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Revised: 28 September 2018

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Accepted: 24 December 2018

DOI: 10.1111/roie.12396

ORIGINAL ARTICLE

International trade and capital accumulation in

an overlapping generations model with a public

intermediate good

TsuyoshiShinozaki1

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MakotoTawada2

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MitsuyoshiYanagihara3

1Faculty of Economics,Tohoku‐Gakuin

University, Sendai, Japan

2Faculty of Economics,Aichi Gakuin

University, Nagoya, Japan

3Graduate School of Economics,Nagoya

University, Nagoya, Japan

Correspondence

Mitsuyoshi Yanagihara, Graduate School of

Economics, Nagoya University, Furo‐cho,

Chikusa‐ku, Nagoya, Aichi 464‐8601,

Japan.

Email: yanagi@soec.nagoya-u.ac.jp

Funding information

Japan Society for the Promotion of

Science, Grant/Award Number: 15K03449,

17K03730 and 17K03762

Abstract

We investigate the effects of a public intermediate good on

trade patterns, capital accumulation, and the gains from

trade in a two‐country, three‐sector overlapping generations

model. A public intermediate good affects not only the pro-

ductivity of private production but capital accumulation;

thus, the results differ from those obtained in previous stud-

ies. First, opening to trade may accelerate capital accumula-

tion in the higher‐savings country. Additionally, the country

producing a public intermediate good more (which is labor‐

intensive) may be the importer of the investment good

(which is the most capital‐intensive). Finally, the lower‐sav-

ings country may have lower steady‐state welfare under

trade.

JEL CLASSIFICATION

E20, F41, F43, H41

766

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SHINOZAKI et Al.

international trade can be perceived as one of the important elements of the engine of economic

growth via capital accumulation.

It is, however, not easy to theoretically explain how trade affects, and/or is affected by, economic

growth and capital accumulation. Buiter (1981)—a seminal work investigating the effect of interna-

tional capital movement in a dynamic, one‐good, two‐country model—shows that when international

capital movement is permitted, the capital level of a country with a high savings rate falls. In con-

trast, that of a country with a low savings rate rises. Mazumdar (1996)—another pioneering work

that attempts to show the relationship between trade and growth—proves that, on the one hand, the

economic growth rate of a country with low savings accelerates, while on the other hand, one with

high savings does not change in a small‐open, infinitely lived agent model. This is because the latter

country exports capital goods, which does not affect the marginal product of capital and the rate of

capital accumulation, and the former imports them, which leads to an increased rate of accumulation

of capital after trade opens.3

Cremers (2005) produces similar findings in a two‐sector, overlapping

generations model. Thus, many dynamic models have pointed out that trade lowers economic growth

of high‐savings countries (e.g., a developed country), by decreasing the growth of capital stock. This

cannot, however, explain why such developed countries are motivated to trade.4

The objective of this paper is, therefore, to construct a dynamic framework for explaining how

international trade can promote capital accumulation in developed countries. We introduce one spe-

cific factor, public intermediate goods, into a two‐sector, overlapping generations model developed

by Galor (1992).5

In reality, the supply of public intermediate goods is a key element in formulation of industrial

structure and economic growth in a country. Accordingly, this will greatly influence the country’s

trade patterns. For example, Rodrik (1998), Alesina and Wacziarg (1998), and Romp and de Haan

(2007) showed a difference in the level of public intermediate goods strongly influences the pattern

and volume of international trade and the economic growth rate; therefore, it becomes a source of

income disparities among countries engaging in international trade with each other.

Our results exhibit stark differences from previous studies, such as Mountford (1998) and Cremers

(2005), in trade patterns and the gains from trade. This is caused by our introduction of a public

intermediate good. First and foremost, opening to trade can accelerate capital accumulation in the

developed country and decelerate that in the developing country, which partly indicates the benefit of

international trade to the developed country. Second, regarding trade patterns, we show the possibility

of a country with a higher level of a public intermediate good assumed to be most labor‐intensive

importing the investment good assumed to be most capital‐intensive. Regarding gains from trade,

we restrict attention to comparison of steady‐state welfare and, thus, do not account for the gains or

losses incurred by the old generation in the first period when countries begin to open to trade. We

find a country with a lower (higher) level of capital accumulation may become better (worse) off in

terms of steady‐state welfare because of this opening.6

We derive these results because a public inter-

mediate good determines comparative advantage not only through the change in productivity of the

private goods production sectors, but also through the change in capital accumulation in the long run.

Notably, as a public intermediate good affects not only on a demand side but also a supply side, the

introduction of a public intermediate good changes the capital accumulation path and, moreover, the

trade pattern. Thus, our model provides a comprehensive framework for the two‐country, overlapping

generations model for investigating international trade.

The rest of this paper is as follows. Section 2 presents the one‐country, three‐sector, overlapping

generations model with a public intermediate good. Section 3 describes its equilibrium. Section 4

extends the model to a two‐country economy. Section 5 investigates trade patterns and the gains from

trade. Section 6 provides the conclusion.