Externalities, Productivity and Sustained Growth

• Published date: 01 August 2014
• Date: 01 August 2014
• DOI: http://doi.org/10.1111/rode.12102
• Author: Xiaopeng Yin

Externalities, Productivity and Sustained Growth

Xiaopeng Yin*

Abstract

This paper shows that the existence of endogenous growth, in the closed-form solution, in a single sector

economy with a convex technology in an overlapping generations (OLG) framework, which attempts to fill

the current gap in endogenous growth theory. It finds there is an unbounded growth when trade, in the

form of knowledge spillover, affects labor productivity through the formation of human capital with self-

education that is not an independent sector but builds the human capital here. This conclusion holds even

though there is the “limited income” expressed as the “non-increasing wage/investment ratio” for each gen-

eration. Moreover, it shows the convergence of growth rates for each country, which is unique and con-

stant, while the growth rate per capita negatively relates with each country’s population growth rate. Also,

there is no “poverty trap” with the introduction of externalities that is different from existing literature.

1. Introduction

Unbounded growth in economies that are characterized by standard classical assump-

tions, i.e. capital accumulation under perfect competition and constant returns to

scale technologies, is always a question in economic growth, and is still a question for

endogenous growth theory.1For the infinite lived agent framework, it appeared to

have been solved in the late 1980s and the early 1990s in a one-sector model (Romer,

1986; Xie, 1991, among others) and in a two-sector model (Lucas, 1988; Romer, 1990,

among others). However, for the overlapping generations (OLG) framework of

finitely lived households, it is still a question, at least in a one-sector model.

Generally, the simplest possible way to get endogenous growth in an OLG

economy with a convex technology is either to have at least two sectors (a consump-

tion good sector and an investment good sector) with specific assumptions on the pro-

duction technologies and on the allocation of labor between the two sectors2or to

have the one sector in the economy with externalities. The former approach has been

done by Fisher (1992). He argues that only the economy with at least two sectors can

possess the unbounded growth in an OLG model.

For the one-sector economies, Boldrin (1992) and Jones and Manuelli (1992) have

shown that unbounded growth is not possible in a simple one-sector growth model

within an overlapping generations framework. The intuition behind this result is

simple. In an OLG framework with a convex technology wages cannot raise at a rate

greater than or equal to that of the capital stocks, so that the young generation could

not afford to buy all the capital stocks from the old if the capital stocks would grow

without bound. Hence, the limited growth rate of the economy must be zero. We call

this argument a “limited income argument”. This argument is broken down in the

* Yin: No. 10, Huixin Street East, School of International Trade and Economics, University of Interna-

tional Business and Economics, P.O. Box 119, Beijing, China, 100029. Telephone: +86-10-6449-3689; Fax.

+86-10-6449-3042; E-mail: xyin_ca@yahoo.com. The author wishes to express great appreciation to Ngo

Van Long, Rodolfo Manuelli, Yuntong Wang and an anonymous referee for their helpful comments.

Funding from University of International Business and Economics is gratefully acknowledged. The author

remains responsible for any errors.

Review of Development Economics, 18(3), 543–563, 2014

DOI:10.1111/rode.12102

© 2014 John Wiley & Sons Ltd

case of an infinitely lived representative consumer who does not need to buy the

capital stocks from the old generation and unbounded equilibrium growth is indeed

possible in this setting (Jones and Manuelli, 1990). Therefore, it seems helpful to

introduce externalities into a one-sector model to find the possible unbounded

growth.3

The approach to introduce externalities in endogenous growth theory was first used

by Romer (1986). He studies a model with increasing returns to scale that are internal

to the economy but external to the firm. This model is able to explain positive equilib-

rium growth rates although every firm is facing a convex technology in an infinite-

lived agent model. In the context of one-sector OLG models, Boldrin (1992) on the

one hand, explores some properties of externalities and their roles in generating

endogenous growth. He does not, however, provide any explicit solution for the one-

sector growth rate. On the other hand, he also recognizes the key of unbounded

growth in an OLG model as the “limited income argument” discussed above. That is,

he mentions the increasing wage/investment ratio is one of “the necessary and suffi-

cient requisites” (1992) to allow the unbounded growth. It is, however, impossible for

the economy with a convex technology. Therefore, the question for the existence of

unbounded growth in a one-sector economy with an OLG model still exists, which

leaves a gap needed to be filled in endogenous growth theory in an OLG economy.

This is our first purpose to find out the explicit solution for of existence of sustainable

endogenous growth in the one-sector OLG economy with convex technology. Pre-

cisely we show that the closed form of endogenous growth rate with the externalities

results from self-financed education and international trade.

More importantly, most existing results including Jones and Manuelli’s (1990,

1992), Boldrin’s (1992) and Fisher’s (1992), regardless of having or not having endog-

enous growth, are based on the “limited income argument”. That is, they all agree

that the “limited income”, compared with rapidly growing capital stocks, is the key

burden for unbounded growth in an OLG model. Another purpose of this paper is to

show that “limited income” is not a constraint for unbounded growth in an OLG

economy with a convex technology. With such “limited income” there still exists an

equilibrium growth rate. Therefore our paper could be viewed as one paper, together

with Boldrin’s (1992), Fisher’s (1992) and corresponding with Jones and Manuelli’s

(1990, 1992) papers, to fill in the gap of endogenous growth in an OLG economy. This

paper could also be treated as the first paper to break the “limited income argument”

to have endogenous growth in an OLG economy.

The understanding of endogenous growth has been gradually focused on the role of

the consumers in the growth process since the 1990s (Alvarez-Cuadrado et al., 2004;

Boldrin, 1992; Jones and Manuelli, 1992; Liu and Turnovsky, 2002; Michel, 1993,

among others). For example, Michel (1993) analyzes endogenous growth in a one-

sector OLG model with education. He assumes that households live for three periods.

In the first period they borrow from the older generation in order to finance their

education which determines the productivity of their labor. In the second period they

work, consume, pay back their debts, and save. In the third period they consume only.

Moreover, the productivity of labor depends not only on the amount of education in

the current period but also on that of the past period. This assumption introduces an

externality in this model and can be given the following interpretation. Productivity of

the young generation does not only depend on the amount spent for education but

also on the competence of their teachers.

In this paper we adopt Michel’s (1993) basic framework (but without the aforemen-

tioned externality) to explore unbounded growth through studying the relationship

544 Xiaopeng Yin

© 2014 John Wiley & Sons Ltd