A relative answer to the growth–saving puzzle

• Published date: 01 August 2023
• Author: Noam Gruber
• Date: 01 August 2023
• DOI: http://doi.org/10.1111/infi.12426

Received: 14 October 2021

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Accepted: 6 October 2022

DOI: 10.1111/infi.12426

ORIGINAL ARTICLE

A relative answer to the growth–saving puzzle

Noam Gruber

China Center for Economic Research,

National School of Development, Peking

University, Beijing, China

Correspondence

Noam Gruber, China Center for

Economic Research, National School of

Development, Peking University, Beijing,

China.

Email: noam.gruber@gmail.com and

noam.gruber@nsd.pku.edu.cn

Abstract

Prolonged rapid growth, that is, the ‘catching‐up’

process through which countries close the gap to the

development frontier, is known to be accompanied by

high rates of household saving. This phenomenon is

central in explaining the direction of international

capital flows and trade imbalances in the past several

decades, yet it is very much in contradiction to

prevailing macroeconomic theory. This paper finds

that a standard life‐cycle model, even when integrated

with uncertainty about future growth and with credit

constraints, is completely unable to replicate the

relations between growth and saving, represented by

three stylized facts gleaned from the empirical

literature. However, adding utility from relative con-

sumption to the model allows for the full replication

of these relations.

KEYWORDS

allocation puzzle, household saving, life cycle, life cycle models

and saving, Lucas paradox, open economy growth, relative

income hypothesis, saving growth

JEL CLASSIFICATION

D91, E21, F43, O11

1|INTRODUCTION

The phenomenon of high saving rates accompanying rapid growth is well‐known in the

economic literature. Modigliani (1970) notes it with relation to post world‐war II Europe. More

recently it is usually identified with the rapidly growing Asian economies, most notably

China. Deaton and Paxson (2000) state, based on cross‐country evidence, that a 1% increase in

per‐capita growth is accompanied by a 2% increase in the saving rate.

International Finance. 2023;26:139–171. wileyonlinelibrary.com/journal/infi © 2022 John Wiley & Sons Ltd.

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However, standard infinite‐horizon representative agent models predict the opposite—the

higher the expected growth, the more the agent borrows. In the international context, this

means that a relatively poor but rapidly developing country is supposed to run trade deficits,

essentially borrowing from slow‐growing rich countries at the expense of its future wealth.

Reality is often the complete opposite. Lucas (1990) discusses the ‘Lucas paradox’of capital not

flowing from rich to poor countries,

1

while Gourinchas and Jeanne (2013) further define the

‘allocation puzzle’, according to which productivity growth is negatively correlated with foreign

investment. The latter paper rightfully concludes that the key factor in creating the ‘allocation

puzzle’is the positive relation between growth and saving. While the ‘allocation puzzle’

revolves around the question of why developing countries with rapid productivity growth are

receiving less foreign investment, it does not directly deal with an even greater conundrum:

how can rapid growth in developing countries raise the saving rates there so much that the net

flow of capital into them becomes negative, that is, so that it is the rich countries that are

borrowing from the poor ones?

It has been suggested that it is a higher propensity to save that is causing higher growth.

However, as Carroll and Weil (1994), Andersson (1999) and Kumar et al. (2020) show, causality

runs from growth to saving and not the other way around. While a positive causality from

saving to growth cannot be completely ruled out,

2

clearly the saving decision must be optimal

given growth expectations. Since much of the greater saving‐to‐GDP ratio is attributed to higher

household saving rates,

3

the question of saving‐rate optimality should be discussed from the

household's perspective, rather than from some central planner's.

Another sometimes‐suggested explanation is that both saving and growth are attributable to

cultural characteristics. For example, the rapid growth and high saving rates in East Asia can be

the result of Confucian values shared by many countries in that region. This line of argument

fails, however, to account for several facts. First, high saving rates have historically

accompanied prolonged rapid growth (a ‘catching‐up’process) in many countries across the

world. While much of the current discussion is about China, this phenomenon has been seen in

post‐world‐war II Europe, in Japan, the four tigers (Korea, Taiwan, Hong‐Kong and Singapore),

in Ireland, in Chile, and more recently in Vietnam and India. Second, as discussed above,

saving increases following a rise in growth. Why then have Confucian values not made

households save in high rates all along? Finally, Carroll et al. (1994,1999) look at the effect of

cultural background on saving behaviour among immigrants, and do not find a correlation with

the saving rates in the countries of origin. Therefore, it seems appropriate to investigate the

growth–saving correlation in generality, and not to explain it away by reference to local cultural

attributes.

Modigliani (1966) attempts to explain the causality from growth to saving using a life‐cycle

model. The intuition behind this explanation is simple; since it is the young that save (toward

retirement) and the old that dissave (being retired), growth, making the young richer compared

to the old, should raise the saving rate. However, as Tobin (1967) and Carroll and Summers

(1991) note, this explanation requires that growth increases income from cohort (age group) to

cohort, but not within a cohort (i.e., it requires that growth does not affect an existing agent's

lifetime income, but rather increases the lifetime income of a ‘newborn’agent with respect to

the previous‐generation agent), otherwise the young, expecting higher future income, would

lose their motivation to save. Carroll and Summers (1991) bring evidence to refute this

assumption, showing that growth increases the income of people of all ages, and argue that

this invalidates Modigliani's life‐cycle explanation completely. Another attempt to explain this

direction of causality is made by Carroll and Weil (1994) and Carroll et al. (2000), using a

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habit‐formation mechanism.

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While habit‐formation may indeed create a positive relation

between growth and saving, by shifting consumption to the future (where the agent is more

‘spoiled’), Chamon and Prasad (2010), examining Chinese data, find no evidence of it.

In addition to its effect on the saving rate, rapid growth seems to have two more effects,

closely related to each other: In Carroll and Summers (1991), the authors find that households

in rapidly growing countries experience a higher rate of increase in their consumption

expenditure compared to their peers in lower‐growth countries. This phenomenon, also

observed in Lee et al. (2014), which Carroll et al. (2000) seek to explain with habit‐formation, is

inconsistent with the standard Permanent Income Hypothesis (PIH) and life‐cycle models. A

second related phenomenon observed in Carroll and Summers (1991), is that the cross‐

sectional profile of consumption by age is quite similar across countries with very different

aggregate growth rates. This finding is further supported by the data presented in Deaton and

Paxson (2000).

Gruber (2018) demonstrates empirically that household saving behaviour is determined by

relative (rather than absolute) income levels, and argues that utility from relative income and

wealth (also known as ‘keeping up with the Joneses’) can explain both the higher saving rates

by the relatively rich and the positive relation between growth and saving. In essence, a general

growth in income changes the social concept of what is considered normative consumption.

This line of argument is also supported by the conspicuous consumption literature.

5

Theoretical in nature, the current paper extends elements of the empirically supported model

presented in Gruber (2018) to further analyze its possible contribution to explaining the

relations between growth and household saving behaviour.

This paper quantifies and measures the ability of a standard life‐cycle model to generate the

following three stylized facts, gleaned from the above literature: one, a positive relation from

aggregate growth to the aggregate household saving rate (with growth fully affecting the

income path of individual cohorts); two, a correlation between the aggregate growth rate and

the household expenditure growth rate over the life‐cycle; and three, a consumption‐age cross‐

sectional distribution that is largely invariant to aggregate growth.

Finding that the standard model is completely unable to generate the three stylized facts

above, utility from relative consumption is added to the model, which then allows it to fully

replicate all three stylized facts: the correlation between growth and saving, the rapid increase

of consumption expenditure over the household life‐cycle, and the stability of the consumption‐

age cross‐section, as observed in growing economies. Furthermore, this paper looks at the effect

of augmenting the standard life‐cycle model with two alternative elements—uncertainty about

future growth and credit constraints—on its ability to generate the above‐stylized facts, and

finds that these are insufficient in accounting for the growth–saving relation. Section 2presents

the life‐cycle model used. Section 3describes the modelling of utility from relative

consumption. Section 4adds growth uncertainty and credit constraints to the model.

Sections 5presents simulations of the different model specifications (model calibration is

explained in Appendix A). Section 6concludes.

2|THE LIFE‐CYCLE MODEL

The demand side of the economy is represented by a household life‐cycle model. Each period

t

one household is created and one is destroyed. Each household exists for

J

periods, so that one

household exists for each household age

j

from one to

J

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