Population growth and the transfer paradox in an overlapping generations model

• Author: Tsuyoshi Shinozaki,Kojun Hamada,Mitsuyoshi Yanagihara
• Published date: 01 February 2019
• DOI: http://doi.org/10.1111/rode.12541
• Date: 01 February 2019

REGULAR ARTICLE

Population growth and the transfer paradox in an

overlapping generations model

Kojun Hamada

1

|

Tsuyoshi Shinozaki

2

|

Mitsuyoshi Yanagihara

3

1

Faculty of Economics, Niigata

University, 8050 Ikarashi 2-no-cho,

Nishi-ku, Niigata, Niigata, Japan

2

Faculty of Economics, Tohoku Gakuin

University, 1-3-1 Tsuchitoi, Aoba-ku,

Sendai, Miyagi, Japan

3

Graduate School of Economics, Nagoya

University, Furo-cho, Chikusa-ku,

Nagoya, Aichi, Japan

Correspondence

Kojun Hamada, Faculty of Economics,

Niigata University, 8050 Ikarashi

2-no-cho, Nishi-ku, Niigata, Niigata,

950-2181, Japan.

Email: khamada@econ.niigata-u.ac.jp

Funding information

JSPS KAKENHI, Grant/Award Number:

16K03615, 16H03612, 26380360,

17K03762, 15K03449

Abstract

This study investigates whether the transfer paradox

(donor enrichment and/or recipient impoverishment)

occurs when a donor and a recipient have different popu-

lation growth rates by using a one-sector, two-country

overlapping generations model. We show that if the popu-

lation growth rates differ, neither donor enrichment nor

recipient impoverishment occurs in the steady state under

dynamic efficiency. This result is in stark contrast to the

existing results that the transfer paradox might occur

when a donor and a recipient country have different mar-

ginal propensities to save, assuming that both have the

same population growth rate. Furthermore, we present the

condition for the transfer problem to occur on the transi-

tion path and show that the transfer paradox is less likely

to occur as the economy converges to the steady state.

Our result shows that the prevailing finding that the trans-

fer paradox can occur in an overlapping generations

model is limited to the special case of countries having

the same population growth rate.

1

|

INTRODUCTION

In this study, we demonstrate that the transfer paradox never occurs when a donor and a recipient

have a different population growth rate in a one-sector, two-country overlapping generations

(OLG) model. The transfer paradox refers to a situation in which a transfer from a donor to a

recipient paradoxically increases the donor's welfare and/or decreases the recipient's welfare, that

is, enriches a donor and/or impoverishes a recipient. In particular, Galor and Polemarchakis (1987)

DOI: 10.1111/rode.12541

Rev Dev Econ. 2019;23:331–347. wileyonlinelibrary.com/journal/rode © 2018 John Wiley & Sons Ltd

|

331

were the first to show that the transfer paradox occurs in an OLG setting. However, all of the

existing literature on the transfer paradox in an OLG model assumes for brevity that a donor and a

recipient have the same population growth rate. We extend the model to include different popula-

tion growth rates and find that the existing result on the occurrence of the transfer paradox is lim-

ited to the special case in which the population of a donor and a recipient grows at the same rate.

In a static general equilibrium framework, ever since the seminal papers of Samuelson (1952,

1954), it has generally been established that in a two-country model, the transfer paradox can

never occur if the equilibrium is Walrasian stable and there are no trade distortions. For the trans-

fer paradox to arise in a static model, there must be Walrasian instability or distortions such as

trade barriers and administrative transfer costs that restrict free trade.

1

By contrast, in a dynamic

framework, existing studies have shown that the transfer paradox can arise even without any dis-

tortions in a two-country model. Galor and Polemarchakis (1987) pointed out that a permanent

lump-sum transfer can bring about the transfer paradox in the steady-state equilibrium by using an

OLG model. Haaparanta (1989) showed that a temporary transfer accompanied by an issue of gov-

ernment bonds might cause the transfer paradox in an OLG model. Cremers and Sen (2008)

showed that the results obtained by Galor and Polemarchakis (1987) also apply not only in the

steady state, but also on the transitional path. Overall, in the OLG framework, the existing

literature has demonstrated that the transfer paradox can arise even if the market equilibrium is

stable because the change in the interest rate caused by a transfer intertemporally affects capital

accumulation.

However, all studies that have investigated the transfer paradox in a dynamic setting assume

that the donor country and the recipient country have the same population growth rate.

2

Although

this simplifying assumption undoubtedly improves the tractability of the transfer problem in a

dynamic framework, it sacrifices generality and does not coincide with the real situation. Typically,

a donor country has a different population growth rate to that of a recipient, and developed coun-

tries as donors tend to have lower population growth rates than developing countries.

3

For exam-

ple, the top four countries that provided official development assistance (ODA) in 2013 were the

United States, the United Kingdom, Germany, and Japan, and the top four countries that received

ODA in 2009–2010 were Afghanistan, Indonesia, India, and China.

4

Based on UN population pro-

jections (United Nations, 2013), Figure 1 illustrates the changes in the population growth rates of

the top three countries excluding Afghanistan, indicating that they differ significantly even within

donor and recipient countries.

5

Nevertheless, virtually all existing studies of the transfer paradox based on the OLG model

assume that donor and recipient countries share the same population growth rate. Therefore, in this

study, we consider a more generalized situation by explicitly allowing population growth rates to

differ between a donor and a recipient, thereby presenting a novel result. We investigate whether

and how the difference in population growth rates between a donor and a recipient affects the pos-

sibility of the transfer paradox and shed new light on the conditions for the transfer paradox to

arise not only in the steady state, but also on the transitional path.

It is also valuable that the transfer problem should be tackled in the area of development eco-

nomics. Indeed, whether a transfer improves economic welfare or accelerates economic growth in

recipient countries has gained much attention both in theoretical and in empirical studies. Empiri-

cally, on the one hand, since Burnside and Dollar (2000) showed that financial aid increases the

economic growth rates of recipient countries by using cross-country data, several works have sup-

ported the positive relationship between aid and economic growth. On the other hand, Easterly,

Levine, and Roodman (2004) reexamined the analysis of Burnside and Dollar (2000) and found no

significant relationship between foreign aid and economic growth. However, the empirical

332

|

HAMADA ET AL.