Macroeconomic volatility and trade in OLG economies

• Date: 01 December 2017
• DOI: http://doi.org/10.1111/ijet.12134
• Published date: 01 December 2017
• Author: Antoine Le Riche

doi: 10.1111/ijet.12134

Macroeconomic volatility and trade in OLG economies

Antoine Le Riche∗†

This paper analyzes the effect of free-trade integration on the dynamical properties of economies.

Weformulate a two-country, two-good, two-factor overlapping generations model where coun-

tries only differ with respect to their discount rate. The main contribution of this paper is to show

that opening up to international trade may have a destabilizing effect. In particular, we prove

that, under perfect mobility of labor and capital between countries, sunspot cycles can occur in

the trade regime although one country is characterized by saddle-point stability in the autarky

regime.

Key wor ds two-sector OLG model, two-country, local indeterminacy, endogenous fluctua-

tion, dynamic efficiency

JEL classification C62, E32, F11, F43, O41

Accepted 29 November2016

1 Introduction

The phenomenon of globalization has expanded rapidly in recent decades. One particular feature

of globalization is the increasing development of international trade. For example, in the past three

decades the value of the share of trade in the gross domestic product has increased by a factor of 2

for the main OECD countries (OECD 2010). Along with this globalization, the global crisis since

2008 has evidenced that business cycles in countries are increasingly interlinked. Recent empirical

studies, using industry-level data to estimate the link between macroeconomic volatility and trade

openness, show that countries more exposed to trade are more volatile (Koseet al. 2003). A g rowing

interest has thus emerged in understanding the effect of international trade on the instability of

trading economies.

How can trade affect the business cycles of trading countries? In this paper we attempt to address

this question by analyzing the co-movementof cycles between countries in a two-good (consumption

and investment), two-factor (capital and labor), two-sector model in which the two factors are

∗School of Economics, Sichuan University,Chengdu, China. Email: antoineleriche@scu.edu.cn

†University of Maine (GAINS-TEPP, IRA) CAC-IXXI,Complex Systems Institute, France.

I would like to warmly thank the Associate Editor and two anonymous referees for their precious suggestions and

comments. I wish to thank my advisors, Carine Nourry and Alain Venditti,for having introduced me to the OLG model,

for their invaluable advice and continued support, together with Sebastian Bervoets, Raouf Boucekkine, Stefano Bosi,

H´

el`

ene Latzer, Paul Maarek, Francesco Magris, Kazuo Nishimura and Thomas Seegmuller for useful comments and

suggestions. This paper benefited from presentations at the European DoctoralGroup in Economics Jamboree, Munich,

Germany, September 2012, at the 17th Theories and Methods in Macroeconomics Conference, Lyon, France, March

2013, at the Overlapping Generations Days, Clermont-Ferrand, France, May 2013, at the PhD seminar of G.R.E.Q.A.M.,

Marseille, France, June 2013, and at the 12th Journ´

ees Louis-Andr´

eG

´

erard-Varet, Aix-en-Provence, France, June 2013.

Any remaining errors are our own.

International Journal of Economic Theory 13 (2017) 401–425 © IAET 401

Macroeconomic volatility and trade Antoine Le Riche

internationally mobile and countries differ only with respect to their discount rate. In particular,

our aim is to study the dynamic behavior of two countries through the occurrence of endogenous

fluctuations. A large proportion of the literature considers that endogenous cycles occur through

sunspot equilibria and are driven by changes in expectations about fundamentals. This change

in expectations is based on the concept of sunspot equilibria defined in Shell (1977). As shown

by Woodford (1986), the existence of sunspot equilibria is related to the indeterminacy of the

equilibrium under perfect foresight, that is, the existence of a continuum of equilibrium paths

converging towards one steady statefrom the same initial value of the state variable.

The literature demonstrates that opening up to international trade may have different impacts

on the stability properties of trading countries. They may be classified into two subsets. In the first we

find the contributions based on a two-country version of Benhabib and Nishimura (1998) who study

the existence of local indeterminacy in a closed two-sector (consumption and investment)infinitely

lived agent model with sector-specific externalities and social constant returns with international

immobility of factors.1Nishimura and Shimomura (2002) consider a model where countries only

differ with respect to their initial factor endowments. They show that international trade has no

effect on the stability properties of the two countries.2By contrast, Sim and Ho (2007) consider that

the technologies are different across countries.3They prove that the world economyis characterized

by saddle-point stability even if before trade one country exhibits sunspot fluctuations. Finally,

Hu and Mino (2013) consider different trade structures with lending and borrowing, and show

that international trade produces endogenous cycles in both countries, even if before trade sunspot

cycles do not emerge in the two countries. The second subset of models contains the contributions

which deal with international capital mobility and international labor immobility. Nishimura et al.

(2010) consider an infinitely lived agent model with asymmetric technologies across countries and

sector-specific externalities. They show that trade creates a contagion of sunspot cycles from one

country to another. In a subsequent paper,Nishimura et al. (2014) consider an infinitely lived agent

model with asymmetric technologies across countries and Cobb–Douglas decreasing returns to scale

technologies. They analyze the existence of flip bifurcation and deterministic cycles and prove that

the destabilizing effect of international trade and international capital mobility arises under certain

parameter configurations. In other words, the opening up of trade may create persistent endogenous

fluctuations at the world level while the closed-economy equilibrium in each country is saddle-point

stable.

This literature focuses on the infinitely lived agent model. In this framework, local indetermi-

nacy necessarily requires the presence of market imperfection such as sector-specificexternalities. It

implies that any equilibrium is Pareto inefficient. By contrast, local indeterminacy together with dy-

namic efficiency can arise in overlapping generations (OLG)models without any market imperfection

(Nourry and Venditti2011). In OLG models, Pareto efficiency is associated with under-accumulation

of capital stock with respect to the golden rule. Reichlin (1986) shows how the coexistenceof Pareto

efficiency and local indeterminacy in OLG models is an important question in terms of stabilization

policies. If sunspot fluctuations occur under dynamic efficiency, a fiscal policy can simultaneously

stabilize the economy and reach the Paretooptimal steady state.

1They show that sunspot fluctuations arise provided that the investment good sector is more capital intensive than the

consumption good sector from the social perspective and less capital intensivefrom the private perspective, and that the

elasticity of intertemporal substitution in consumption is large enough.

2Iwasaand Nishimura (2014) extend Nishimura and Shimomura (2002) by introducing a consumption capital good. They

show that international trade can create sunspot fluctuations in the world economy.

3One country is characterized by sector-specific externality and the other country is not.

402 International Journal of Economic Theory 13 (2017) 401–425 © IAET