Dynamic two‐country Heckscher–Ohlin model with externality

• Author: Kazuo Nishimura,Kazumichi Iwasa
• DOI: http://doi.org/10.1111/ijet.12027
• Date: 01 March 2014
• Published date: 01 March 2014

doi: 10.1111/ijet.12027

Dynamic two-country Heckscher–Ohlin model

with externality

Kazumichi Iwasa∗and Kazuo Nishimura†

We extend a dynamic Heckscher–Ohlin model with production externality presented in recent

work by Nishimura and Shimomura by assuming a consumable capital good. Following work

by Bond, Iwasa, and Nishimura, we define a steady-stateexcess demand function and derive the

locus of home and foreign capital stocks that are consistentw ith a steady-stateequilibrium under

free trade. Also, we examine the relationship between externality and local dynamics in autarky

or under free trade, which includes a phase diagram analysis. Then we show that opening trade

can generate expectation-driven fluctuations in a world trade market.

Key wor ds two-country model, Heckscher–Ohlin, externality,indeterminacy

JEL classification E13, E32, F11, F43

Accepted 30 October 2013

1 Introduction

While market integration and globalization are often seen to be beneficial to growth, it is still a

question whether opening trade has stabilizing or destabilizing effects on the world trade market.

This study investigates the dynamic behavior of multiple countries’economic activities in a two-

good, two-factor model in which factorsare internationally immobile and the countries’ technologies

are subject to sector-specific external effects.

It has been demonstrated that in a perfect foresight model with many consumers, a competitive

equilibrium path behaves like an optimal growth path; see Becker (1980), Bewley (1982), Yano

(1983), and Epstein (1987). Building on this property,Nishimura and Yano (1993a,b) and Nishimura

et al. (2006, 2013) have shown that a country’s business cycles (i.e., two-period cycles) can spread

throughout the world once trade opens.

Atkeson and Kehoe(2000) applied a large-country Heckscher–Ohlin (H-O) model to the analysis

of development patterns. Bond et al. (2003) characterized an integrated world equilibrium path in a

dynamic H-O model. Chiglino and Olszak-Duquenne (2001) investigated economic fluctuations in

a two-country dynamic general equilibrium model.

The recent macroeconomics literature has shown that local indeterminacy of equilibria and

sunspot fluctuations may arise in closed-economy or small open-economy two-sector models with

sector-specificexternalities. See, for instance, Benhabib and Nishimura (1998), and Meng and Velasco

∗Institute of Economic Research,Kyoto University, Kyoto, Japan.

†Research Institute for Economicsand Business Administration, Kobe University, Kobe, Japan.

Email: nishimura@rieb.kobe-u.ac.jp

Wethank an anonymous referee and Yunfang Hu for constructive comments on the paper.

International Journal of Economic Theory 10 (2014) 53–74 © IAET 53

International Journal of Economic Theory

Dynamic H-O model with externality Kazumichi Iwasa and Kazuo Nishimura

(2003). They showed that in multisector models, local indeterminacy can arise with constant social

returns to scale if there is a small wedge between private and social returns. As has been well known

since Woodford(1986), local indeterminacy of equilibria, derived for instance from external effects in

production, is a sufficient condition for the occurrence of sunspot fluctuations. Thus,indeterminacy

provides a possible explanation of business cycle fluctuations. Macroeconomicinstabilit y indeed can

be based on multiple equilibria and volatility of expectations.

Nishimura and Shimomura (2002) studied a large-country H-O model where there are two

goods, one of which is a pure consumption good and the other is a capital good, and their production

is subject to sector-specific externalities. They obtained the conditions for the indeterminacy under

constant social returns to scale.

In the present study, we extend the Nishimura–Shimomura model by assuming that the capital

good is also consumable. Wecompare two types of stationar y capital allocations, a closed-economy

allocation and a free-trade allocation. In the former, each country produces, in the long run, the

amount of capital precisely necessary to produceboth goods; in the latter, one country is characterized

by net exports in the consumable capital good and net imports in the pure consumption good, while

the other country is characterized by net imports in the consumable capital good and net exports in

the pure consumption good.

Following Bond et al. (2012), we derive steady-state excess demand functions by combining the

curves of the steady-state Rybczynski line, the income expansion path evaluated at the steady-state

prices, and the steady-state resource constraints. Usingthese excess demand functions, we can derive

the locus of home and foreign capital stocks that is consistentw ith a steady-stateequilibr ium with free

trade. The diagrammatic analysis in Bond et al. (2012) can be extended to the case with production

externality.

We then examine the local behavior of the autarkic steady state and the free-trade steady states.

In previous studies on indeterminacy with production externality (e.g., Nishimura and Shimomura

2002), felicity functions are assumed to be linear (or close to linear) in consumption. We show

that this assumption is needed to guarantee excess demand for the pure consumption good that is

decreasing in its price.1Wealso show that as long as the excess demand is decreasing, indeterminacy

also arises under general preferences.

We also show that opening trade enhances expectation-driven fluctuations in the sense that

under free trade, the world economy consisting of two symmetrical economies, each of which has

saddle-point stability in autarky, will have multiple equilibrium paths in some cases.2In particular,

we demonstrate that indeterminacy can arise under free trade even when households’ intertemporal

elasticity of substitution is low enough (close to 1), which excludes the possibility of indeterminacy

in autarky.

In Section 2 we present the dynamic H-O model in a continuous-time model with factor-

generated externalities. In Section 3 we derive autarkic steady states and a continuum of free-trade

steady states. In Section 4 we examine local stability of free-trade steady states as well as the autarkic

steadystate. In Section 5, assuming a standard felicity function with a constant intertemporal elasticit y

1In the previous studies, it is also necessary for indeterminacy to arise that the pure consumption good is labor intensive

from the social perspective, but capital intensivefrom the private one. Assuming the capital good is also consumable, one

can see the possibility of indeterminacy even when its factor intensity ranking is reversed.

2Sim and Ho (2007) show that indeterminacy could be eliminated byopening tr ade between twoasy mmetric economies,

where indeterminacy arises in one country but the other has saddle-point stability before opening trade. Hu and Mino

(2013) discuss whether opening trade enhances the possibility of indeterminacy or not, and they conclude trade structure

matters for the result.

54 International Journal of Economic Theory 10 (2014) 53–74 © IAET