Capital Mobility in Open OLG Models of Neoclassical Growth

• DOI: http://doi.org/10.1111/1467-9361.00119
• Published date: 01 June 2001
• Date: 01 June 2001
• Author: Emily T. Cremers

Capital Mobility in Open OLG Models of

Neoclassical Growth

Emily T. Cremers*

Abstract

This paper explores whether the international mobility of physical and/or financial capital is essential for

productive efficiency in each of three open OLG models of neoclassical growth that vary in terms of dimen-

sional attributes.A tradeoff between capital mobility requirements and dimension has previously been estab-

lished by example where, ceteris paribus,neither form of capital mobility is required with three productive

sectors, only physical capital mobility is required with two sectors, and both forms of mobility are required

with a single sector.This paper reconsiders that tradeoff using a generalization of the production and utility

functions which introduces the potential for specialization along the transition path—an event which would

imply inconsistent capital mobility requirements along the growth path for models with fixed dimension.

Conditions are established under which the tradeoff between capital mobility requirements and dimension

remains valid.

1. Introduction

Is international capital mobility essential to the efficient utilization of world resources?

Even in simple deterministic settings theory has provided opposing answers to this

fundamental question. On the macroeconomic front, two-country versions of the neo-

classical growth model are often used to demonstrate that, in the general case, capital

mobility is essential to efficiency. Indeed, this viewpoint is often represented in the

growth literature by the question: why doesn’t capital flow from rich countries to poor?

From trade theoretic literature,however, one of the seminal contributions (namely,the

factor price equalization theorem) includes a demonstration that capital immobility

does not necessarily represent a departure from efficient outcomes. The discrepancy

between these conclusions is highlighted by the common neoclassical grounding of

both approaches as well as by their consequential positioning as a benchmark view-

point for the respective fields of growth and trade. The disparity between these views

cannot, however, be attributed either to the usual vagaries associated with the term

“capital mobility” (which may refer equally to trade in physical capital goods or factors,

trade in financial assets,or all of the above) or to obvious differences between dynamic

and static environments. Rather, both perspectives can be represented in a common,

dynamic framework which incorporates all forms of capital mobility.A point not yet

well-recognized by either field, but apparent in such a framework, is that the substan-

tive difference in perspectives is accounted for by a single fact: dimensionality alone

has a priori implications regarding overall market sufficiency.The role of capital mobil-

ity is merely integral to this larger concern.

In this vein, Ethier and Svensson (1986) have argued that international markets

are sufficient for productive efficiency in static trade models when they are equal

* Cremers: National University of Singapore, Singapore 117570. Tel: (65) 874-6832; Fax: (65) 775-2646;

E-mail: cremers@nus.edu.The author thanks Mick Devereux and Jeongwen Chiang for helpful suggestions.

Review of Development Economics, 5(2), 211–226, 2001

© Blackwell Publishers Ltd 2001, 108 Cowley Road,Oxford OX4 1JF, UK and 350 Main Street, Malden,MA 02148, USA

in number to the factors of production, and regardless of their type (e.g., markets

for goods or factors). Even for these models,where capital is regarded only as a factor

of production, this market sufficiency argument alone does not yield unambiguous

conclusions regarding the necessity of capital mobility. That is, if together there

are enough traded goods and noncapital factors (as in the standard setting with two

traded consumption goods and two nontraded factors), capital mobility is unnecessary,

but if the total number of these combined markets are too few, the conclusion is

reversed.

The relationship between market sufficiency conditions and capital mobility is more

relevant in dynamic environments, where capital serves not only as a factor of pro-

duction, but is also a produced good and an asset. Capital immobility may then imply

that neither capital inputs nor outputs (physical capital), nor claims of ownership

(financial capital) are internationally exchanged. Cremers (1997) explores this issue in

the context of three overlapping generations (OLG) models with neoclassical growth

that differ only with regard to dimension. It demonstrates, using Cobb–Douglas tech-

nologies and log utility functions, that the Ethier and Svensson finding can survive the

introduction of capital accumulation. Successive increases in the number of produced

consumption goods,while holding the number of assets fixed and both the number and

type of factors of production constant at the standard two (labor and reproducible

physical capital), leave unchanged the number of markets required to achieve the

efficient equilibrium path and steady state of an integrated world economy; in each

instance only two international markets are required.

However, with regard to the composition of these markets a contrast arises between

low- and high-dimensional models. In models with low dimension the set of markets

comprising the sufficient set is inflexible—a fact that has immediate implications

for the role of capital mobility. More particularly, market sufficiency in a one-sector

growth model requires the international mobility of both physical and financial capital,

whereas the two-sector model requires only physical capital mobility and the three-

sector model does not require capital mobility of any sort. Each increase in dimension

represents the introduction of a market which can replace those for either physical or

financial capital in the sufficient set.1Because the number of traded consumption goods

increases with dimension and reaches a maximum of two in the three-sector setting, it

is clear that capital mobility is necesary only when the economy is short on markets

for consumption goods relative to the number of factors of production, and otherwise

represents a market redundancy.Thus,the one-sector growth model favored by macro-

economists and the multisector models often used by trade theorists are separated only

by their positioning relative to this criterion.

This paper reaffirms that the explicit tradeoff between dimension and capital mobil-

ity requirements in neoclassical growth models is robust to an extension of the model

to more general preferences and technologies. The extreme reliance on international

capital mobility in the one-sector model reflects the familiar but stringent efficiency

requirement of a common capital–labor ratio in all countries at all dates.Both the two-

and three-sector variants allow for indirect channels of arbitrage for the interest rate

as well as the price and rental of capital. Specifically, both utilize a dynamic version of

the factor price equalization theorem (which permits efficiency despite differences in

capital–labor ratios across countries) to establish the redundancy of capital markets,2

and differ only in that the lower dimensional model requires newly produced physical

capital to be traded to initiate the theorem. With three sectors, two traded consump-

212 Emily T. Cremers

© Blackwell Publishers Ltd 2001