Is the Age Structure of the Population One of the Determinantsof the Household Saving Rate in China?
A Spatial Panel Analysis of Provincial Data
Jingwen Yin
Graduate School of Economics, Kobe University
Charles Yuji Horioka
Research Institute for Economics and Business Administration, Kobe University; Asian
Growth Research Institute; Institute of Social and Economic Research, Osaka University;
Institute of Economic Research, Kyoto University; and National Bureau of Economic
Research

Working Paper Series Vol. 2022-05
March 2022

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Asian Growth Research InstituteIs the Age Structure of the Population One of theDeterminants of the Household Saving Rate in China?
A Spatial Panel Analysis of Provincial Data
Jingwen Yin
Graduate School of Economics, Kobe University

Charles Yuji Horioka*
Research Institute for Economics and Business Administration, Kobe University;
Asian Growth Research Institute; Institute of Social and Economic Research, Osaka
University; Institute of Economic Research, Kyoto University; and National Bureau
of Economic Research
March 2022

Abstract
In this paper, we use provincial panel data on China for the 2002-19 period to conduct
a spatial autocorrelation analysis of household saving rates as well as a dynamic panel
analysis of the determinants of household saving rates using a spatial Durbin model. To
summarize our main findings, we find that, in China, the household saving rate shows
significant positive spatial autocorrelation with an overall “high-high” and “low-low”
clustering pattern, that, as predicted by the life-cycle hypothesis, the youth dependency
ratio and the old-age dependency ratio have a negative and significant impact on thehousehold saving rate, and that the logarithm of per capita household disposable income,the regional economic growth rate, the share of the urban population, theindustrialization rate, and the income disparity between urban and rural areas also havea significant impact on the household saving rate.
Key words: age structure of the population; China; dependency ratio; household saving
rate; life-cycle hypothesis or model; old-age dependency ratio; spatial autocorrelation;
spatial Durbin model; youth dependency ratio
Journal of Economic Literature classification codes: D14, D15, E21, G51, J11, O16,
and R20*Corresponding author: Research Institute for Economics and Business Administration,
Kobe University, 2-1, Rokkodai-cho, Nada-ku, Kobe, Hyogo 657-8501, JAPAN.
Email: horioka@rieb.kobe-u.ac.jp

1

Introduction

China’s economy has continued to grow at a rapid rate and has received increasing
attention since the implementation of reform and open policies over 30 years ago.
However, in comparison to other nations in the world, China’s final consumption rate
remains low. In 2014, China’s final consumption rate (the share of final consumption
in GDP) was 46%, whereas nations such as the United States, the United Kingdom,
India, and Brazil all had rates above 80%.
The lack of consumption in China is reflected in the high household saving rate. The
household saving rate in China has been increasing since the implementation of reformand open policies in 1978. China’s national saving rate surpassed 50% in 2014, making
it the highest in the world, with the household saving rate hovering around 20%. On the
one hand, China remains a lower middle-income country in terms of per capita GDP,but on the other hand, household saving rate in China is high. The term “Chinese Saving
Puzzle” has been coined to describe this paradox. The phenomenon of high saving in
China has attracted the attention of many scholars around the world. Numerous scholars
have offered different explanations for this phenomenon. Qi (2000), Shi and Zhu (2004)
and Zhou (2010) suggest that China’s high saving rate is mainly due to the fact that
China is undergoing a transition from a planned economy to a market economy and thatthe uncertainty of residents’ future income and expenditure has led to a sharp increasein precautionary saving. According to Long et al. (2002) and Ai and Wang (2008), thehigh saving phenomena is due to Chinese people’s traditional lifestyles andconsumption behavior. Luo and Kinugasa (2020) use generalized moments estimation
to investigate the determinants of the household saving rate in China, finding thatfactors that are typically thought to promote China’s economic development, such as
state-owned enterprise reform, are the primary cause of the excess saving problem andthat negative factors in the traditional sense, such as the real estate bubble, actually
mitigate the excess saving problem.
China’s household saving rate has been continuously high for more than three
decades, during which China experienced the world’s longest development cycle andhighest growth rate. As a result, there must have been some persistent factors that were
responsible for China’s high saving rate. One possibility is that the age structure of the
population is an important determinant of China’s household saving rate. The life-cycle
hypothesis or model assumes that individual save during their working years to prepare
for life after retirement and that they dissave during their retirement years to financetheir living expenses, implying that the old-age dependency ratio (the ratio of the oldage population to the working-age population) will have a negative impact on theaggregate household saving rate. Thus, if this hypothesis applies in the case of China,
the low level of the old-age dependency ratio can help explain China’s high householdsaving rate.
To restrict population increase, China began implementing the “one-child policy” inthe late 1970s. The one-child policy is an interesting natural experiment for examining
the relationship between the age structure of the population and the household savingrate because it makes fertility largely exogenous and enables us to assess the impact of1

the age structure of the population on the household saving rate without worrying about
endogeneity issues. Furthermore, because the one-child policy was applied moreleniently to ethnic minorities, differences in ethnic composition resulted in significant
differences in population age structures across provinces, allowing us to precisely
estimate the impact of the age structure of the population on the household saving rate.
The “one-child policy” has aided the rapid transformation of the age structure of
China’s population, with low birth rates and rapid aging becoming unavoidable
tendencies. According to the Seventh National Population Census in 2020, China’s
population between the ages of 0 and 14 is 253.38 million or 17.95%; the population
between the ages of 15 and 59 is 894.38 million or 63.35%; and the population between
the ages of 60 and above is 264.02 million or 18.70% (of which the population aged 65
and above is 190.64 million, accounting for 13.50%). Compared with 2010, theproportion of the population aged 0-14, 15-59, and 60 and above increased by 1.35
percentage points, decreased by 6.79 percentage points, and increased by 5.44
percentage points, respectively. China has already become an aging society, with the
speed of population aging accelerating, and it will continue to confront the challenge of
how to achieve long-term balanced population growth. Thus, it is critical to investigate
the influence of the age structure of the population on the household saving rate.
Agglomeration effects may cause the economic activities of a specific industry tocluster in certain regions as the industrial division of labor, urbanization, and regional
economic integration deepen, and this clustering effect may cause developed regions to
attract more economic activities and intensify the economic development imbalance
between regions. Liu and Zhao (2018) use a spatial Durbin model with panel data on
31 Chinese provinces from 1998 to 2015 to look at the geographical spillover effects of
population aging on regional economic development in China. According to thefindings of their empirical study, economic activity in China’s provinces is spatiallyclustered, and population aging has a large negative spatial spillover effect onneighboring provinces’ economic growth.
It is quite possible that saving behavior is also spatially correlated due to the flow ofresidents between neighboring prefectures for work, study, shopping, leisure, and otheractivities. As a result, it is crucial to take account not only of the age structure of the
population in the province in question but also the impact of factors such as thehousehold saving rate and the age structure of the population in neighboring provinces
when researching the determinants of the household saving rate.
Accordingly, the purpose of this paper is to use provincial panel data on China forthe 2002-19 period to conduct a spatial autocorrelation analysis of household saving
rates as well as a dynamic panel analysis of the determinants of household saving rates
using a spatial Durbin model. In so doing, we hope to provide an answer to the question:
Is the age structure of the population one of the primary determinants of China’s
household saving rate?
The remainder of this paper is organized as follows: In section 2, we conduct a surveyof the relevant literature; in section 3, we describe each variable in detail and perform
a descriptive statistical analysis; in section 4, we conduct a spatial autocorrelation
analysis; in section 5, we discuss the estimation method; and in section 6, we present2the estimation results. Section 7 is a brief concluding section.

2

Literature Review

As discussed above, the life-cycle hypothesis of Modigliani (2005) predicts that theage structure of the population will be an important determinant of the household savingrate and, in particular, that the old-age dependency ratio will have a negative impact on
the household saving rate. Moreover, the hypothesis also predicts that the youth
dependency ratio (the ratio of children to the working-age population) will also have anegative impact on the household saving rate because children consume but do not earn
income.
Scholars from all over the globe have researched the impact of the age structure of
the population, particularly the youth dependency ratio and the old-age dependency
ratio, on the household saving rate and have obtained varied results using data fromvarious nations and regions. This research may be classified into two groups—studies
that find that the youth dependency ratio and the old-age dependency ratio have anegative and significant impact on the saving rate, as predicted by the life-cycle
hypothesis, and studies that find that they do not.
2.1

Studies that support the life-cycle hypothesis

The findings of the first set of researchers support the implication of Modigliani'slife-cycle hypothesis that the youth dependency ratio and the old-age dependency ratio
will have a negative impact on the household saving rate.
Leff (1969) constructs the “Leff model” using cross-country cross-section data anddiscovers that a rise in the old-age dependency ratio lowers the household saving rate
and that there is a substantial negative association between the two. According to Yu(1996), an increase in the elderly population will reduce the level of saving and thegrowth rate of saving in China. Wang (2010) uses provincial panel data from the 19892006 period to examine the effects of economic growth, changes in the age structure of
the population, and their interactions on China’s saving rate and finds that higheconomic growth and declining dependency ratios caused by population aging areimportant factors contributing to the increase in China’s saving rate. The regression
results of Yang and Zhang (2013), based on provincial data for China for the 1994-2010
period, show that the youth dependency ratio has a significantly positive impact on thehousehold saving rate, whereas the old-age dependency ratio has a significantly
negative impact on the household saving rate. Fan and Zhu (2012) use differential
generalized moment estimation and systematic generalized moment estimation
methods to empirically examine the influence of the change in the age structure of the
population on China’s household saving rate using provincial panel data for the 19902009 period. Their findings show that, when the time dimension is taken into account,an increase in the youth dependency ratio raises the national saving rate, whereas anincrease in the old-age dependency ratio reduces it. Liu and Liu (2015) use provincial
panel data on China for the 1989-2012 period to conduct a systematic generalized3moments estimation and threshold regression, and their results show that the youth
dependency ratio has a significantly negative impact on the household saving rate, with
the negative effect decreasing as income levels rise; however, they find that the old-age
dependency ratio has a positive and significant impact on the household saving rate,with the positive effect increasing as income levels rise.
2.2

Studies that do not support the life-cycle hypothesis

The findings of the second set of researchers refute the link between changes in theage structure of the population and the household saving rate, claiming that the youth
dependency ratio and the old-age dependency ratio do not have a negative impact on
the household saving rate, as predicted by the life-cycle hypothesis.
Contrary to Leff (1969), Gupta (1971) argues that the dependency ratio is not asignificant determinant of the household saving rate in most underdeveloped countries.
Ram (1982) also disagrees with Leff’s conclusion. Wilson (2000) finds that both
Australia and Canada experienced long-term growth in their saving rates in thetwentieth century using a cointegration regression and a comparison study of time series
data on household saving rate in the two nations. The regression findings do not show
a link between the age structure of the population and the household saving rate. The
main cause for the rise in Australia’s and Canada’s saving rates is found to be income
growth. As a result, productivity gains, rather than declining fertility rates, provide amore comprehensive and satisfactory explanation for these countries’ household savingrate shifts. Deaton and Paxson (1997) also suggest that changes in the age structure of
the population do not explain the relationship between economic growth and thehousehold saving rate. Kraay (2000) examines the determinants of rural and urban
families’ saving rates over the 1978-83 and 1984-89 periods using panel data from
China’s household survey and finds that the dependency ratio has no meaningful
influence on the household saving rate. Similarly, Horioka and Wan (2007) use a lifecycle model and panel data on China’s provinces for the 1995-2004 period from ahousehold survey to conduct a dynamic panel analysis of the determinants of thehousehold saving rate in China and find that variables relating to the age structure of
the population have little impact on the household saving rate.
However, none of the studies mentioned above takes into account the householdsaving rate’s geographical influence. The domestic saving rate in China has asubstantial positive spatial autocorrelation (i.e., an overall “high-high” and “low-low”
agglomeration pattern), with the household saving rate in the eastern area being muchhigher than in the central and western regions. As a result, spatial methods should be
employed to investigate the geographical implications of China’s household saving rate.
Wang et al. (2016) analyze the determinants of the household saving rate using a spatial
lagged model (SLM) and a spatial error model (SEM) and discover that both the youth
dependency ratio and the old-age dependency ratio have a negative and significant
influence. However, Wang et al. (2016) do not consider using the more general spatial
Durbin model in their empirical research, which includes both the spatial error andspatial lag models as particular examples. LeSage (2008) indicate that the appropriate
spatial econometric model should be chosen using the LM test or the LR and Wald tests.
4

The LM test and the LR and Wald test will be employed in this research to assess if thespatial Durbin model should be chosen.
2.3

Summary

As this survey has shown, although there is a large literature on the impact ofdemographic factors on the household saving rate, they have reached differing
conclusions. Some studies have found that demographic factors have a significant
impact on the saving rate while others have not. The results differ drastically depending
on data sources, variable selection, and estimating methodologies. A unified consensus
on the influence of the age structure of the population on China’s household saving rate
has yet to be reached, necessitating further research and analysis.
In terms of research methodologies, most studies have used traditional econometricapproaches, such as cross-sectional, time series, and panel data models, to analyze thedeterminants of the household saving rate. However, these traditional approaches
regard units of observation as self-contained and homogenous areas that do not haveany spatial associations with one another even though the household saving rate in one
area is likely to be affected by that in other areas, especially areas that are more closely
located. Thus, geographical considerations must be taken into account when analyzing
the determinants of the household saving rate.
The current study improves upon earlier studies in a number of respects: (1) It uses
the most recently available data. China’s economy and the age structure of its
population have shifted in recent years, particularly after 2010, but the majority ofprevious studies use data before 2010, making them less relevant to present-day China.
This analysis uses the most recent data for 2002-2019 from the China Statistical
Yearbook, and thus the conclusions are more persuasive. (2) It surveys previous studies
and chooses a comprehensive set of explanatory variables as possible determinants of
the household saving rate. (3) It employs a novel econometric approach to explore theinfluence of the age structure of the population on the household saving rate. In
particular, it conducts a spatial autocorrelation analysis and chooses to use a spatial
Durbin model based on the results of the LM test and the LR and Wald tests.

3

Variable Selection and Data Description

In this paper, we use provincial panel data for the 2002-19 period from the China
Statistical Yearbook, which is compiled by the National Bureau of Statistics of China(annual). The data were taken from http://www.stats.gov.cn/tjsj/ndsj/ (the Englishlanguage equivalent is http://www.stats.gov.cn/english/Statisticaldata/Annual Data/ ).
3.1

Variable selection

This subsection discusses what variables we used and how they were defined. The
choice of explanatory variables differs greatly across studies. Horioka and Wan (2007)
use the income growth rate, the one-year lag of the saving rate, the real interest rate,5etc., as explanatory variables, while Luo and Kinugasa (2020) include the sex ratio, thetransfer income ratio, the urbanization ratio, the growth and level of income, etc. Wanget al. (2016) focus on the impact of demographic factors (the dependency ratio, the sex
ratio, household size, the proportion of the urban population, etc.) on the householdsaving rate. Liu and Liu (2015) use the logarithm of per capita disposable income, theregional economic growth rate, the urban-rural income gap, the proportion of the urban
population in total population, the industrialization rate, the ratio of government
expenditures to GDP, etc., and Fan and Zhu (2012) use the death rate as a proxy for life
expectancy.
Learning from previous studies, we use the household saving rate as the dependent
variable and the youth dependency ratio and the old-age dependency ratio as the core
explanatory variables and the logarithm of per capita disposable income, the death rate,
the regional economic growth rate, the proportion of the urban population, theindustrialization rate, the ratio between the per capita incomes of urban and rural
residents, and the real interest rate as additional explanatory variables.
3.2

Variable definitions

The specific definitions of the variables we used in our analysis are as follows:
The household saving rate (SR) is defined as the ratio of household saving tohousehold disposable income, and the formula for calculating it is as follows:
𝑝𝑝𝑝𝑝𝑝𝑝 𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐 𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑 𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖−𝑝𝑝𝑝𝑝𝑝𝑝 𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐 𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒

𝑆𝑆𝑆𝑆 = �𝑝𝑝𝑝𝑝𝑝𝑝 𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐 𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑 𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖

� × 100%(1)

The dependency ratio is the proportion of persons who are not of working age tothose who are of working age in the population as a whole, given as a percentage. The
dependency ratio can be divided into the youth dependency ratio (YD) and the old-age
dependency ratio (OD), which are the core explanatory variables in this paper. The
formulas for calculating them are as follows:
𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃 𝑜𝑜𝑜𝑜 𝑐𝑐ℎ𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖 𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎 0−14

𝑌𝑌𝑌𝑌 = �𝑊𝑊𝑊𝑊𝑊𝑊𝑊𝑊𝑊𝑊𝑊𝑊𝑊𝑊−𝑎𝑎𝑎𝑎𝑎𝑎 𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝 𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎 15−64� × 100% (2)
𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃 65 𝑦𝑦𝑦𝑦𝑦𝑦𝑦𝑦𝑦𝑦 𝑜𝑜𝑜𝑜𝑜𝑜 𝑜𝑜𝑜𝑜 𝑜𝑜𝑜𝑜𝑜𝑜𝑜𝑜

𝑂𝑂𝑂𝑂 = �𝑊𝑊𝑊𝑊𝑊𝑊𝑊𝑊𝑊𝑊𝑊𝑊𝑊𝑊−𝑎𝑎𝑎𝑎𝑎𝑎 𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝 𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎 15−64� × 100% (3)lnPI is calculated by taking the logarithm of per capita household disposable income.
Data on the death rate (DR) were taken directly from the Chinese Statistical Yearbook.
The regional economic growth rate (GR) is defined as the growth rate of the grossregional product of each province. The formula for calculating it is as follows:
𝑡𝑡ℎ𝑖𝑖𝑖𝑖 𝑦𝑦𝑦𝑦𝑦𝑦𝑦𝑦′𝑠𝑠 𝑔𝑔𝑔𝑔𝑔𝑔𝑔𝑔𝑔𝑔 𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟 𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝−𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙 𝑦𝑦𝑦𝑦𝑦𝑦𝑦𝑦′𝑠𝑠 𝑔𝑔𝑔𝑔𝑔𝑔𝑔𝑔𝑔𝑔 𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟 𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝

𝐺𝐺𝐺𝐺 = �𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙 𝑦𝑦𝑦𝑦𝑦𝑦𝑦𝑦′𝑠𝑠 𝑔𝑔𝑔𝑔𝑔𝑔𝑔𝑔𝑔𝑔 𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟 𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝

6

� × 100% (4)The proportion of the urban population in the total population (UP) was taken directlyfrom the Chinese Statistical Yearbook.
The industrialization rate (INR) is defined as the proportion of industrial value added
to regional GDP is known as. The formula for calculating it is as follows:
𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎 𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖 𝑣𝑣𝑣𝑣𝑣𝑣𝑣𝑣𝑣𝑣

𝐼𝐼𝐼𝐼𝐼𝐼 = �

𝑔𝑔𝑔𝑔𝑔𝑔𝑔𝑔𝑔𝑔 𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟 𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝

� × 100% (5)Income disparity between urban and rural areas (IND) is measured as the ratio of percapita disposable income in cities to per capita disposable income in rural areas. The
formula for calculating it is as follows:𝑈𝑈𝑈𝑈𝑈𝑈𝑈𝑈𝑈𝑈 𝑝𝑝𝑝𝑝𝑝𝑝 𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐 𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑 𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖

𝐼𝐼𝐼𝐼𝐼𝐼 = � 𝑅𝑅𝑅𝑅𝑟𝑟𝑎𝑎𝑎𝑎 𝑝𝑝𝑝𝑝𝑝𝑝 𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐 𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑 𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖 � × 100% (6)The real interest rate (RI) was taken directly from the following World Bank Open
Data website: https://data.worldbank.org.cn/indicator/FR.INR.RINR?locations=CN
3.3

Descriptive statistics

Table 1 shows the descriptive statistics for each variable. It can be seen from thistable that most variables show a considerable range of variation. This implies that
China’s population age structure and economic indicators have changed dramaticallyover time and/or that there are substantial regional variations in these variables,
suggesting that empirical analyses need to take account of links across regions.
[Table 1 goes here.]
Table 2 shows the correlation coefficient matrix, and as can be seen from this table,
SR has negative correlations with YD, GR, IND, and RI and positive correlations withthe other variables.
[Table 2 goes here.]4

Spatial Autocorrelation Analysis

It is necessary to test for spatial autocorrelation before using a spatial econometricmodel to examine the impact of changes in population age structure on provincial
household saving rates. We use the global Moran’s I index to test for the global spatial
correlation of the household saving rate (Moran, 1950). As can be seen from Figure 1,
there is a positive spatial correlation of the household saving rate across provinces,indicating that a province’s household saving rate is positively influenced by thehousehold saving rate of neighboring provinces and that there is some geographic
similarity with the household saving rate in neighboring provinces as well as an overall
pattern of “high-high” and “low-low” clustering (the value of the global Moran’s I index
is 0.4315).
7

[Figure 1 goes here]
Given the substantial spatial correlation of the household saving rate acrossprovinces, it is necessary to estimate a spatial econometric model of the determinantsof the household saving rate in China, which is what we do in the next two sections of
the paper.

5Model Construction
5.1

Model selection

There are three standard models for analyzing spatial autocorrelation: the spatial lag
model (SLM), the spatial error model (SEM), and the spatial Durbin model (SDM). The
SLM focuses on the geographical connectivity between residents’ saving behavior andassumes that the household saving rate in the province is influenced not only by thevalues of the explanatory variables in the province in question but also by spillover
effects from the household saving rate in neighboring provinces. However, it ignores
the impact of the values of the explanatory variables in neighboring provinces on thehousehold saving rate.
The SEM takes account of the fact that the values of the explanatory variables inneighboring provinces may influence the value of the explanatory variables in theprovince in question by adding a spatial error term to the estimation equation.
The SDM model, on the other hand, takes into account not only the impact of thevalues of the explanatory variables in the province in question and the household savingrate in neighboring provinces on the household saving rate in the province in question
but also the impact of the values of the explanatory variables in neighboring provinces
thereon.
Both the spatial lag and spatial error models are variants of the spatial Durbin model.
LeSage (2008) argued that an appropriate model may be selected based on the LM testor the LR and Wald tests, and in this paper, the LM test and the LR and Wald tests
rejected the initial hypothesis of the spatial lag and spatial error models, suggesting thatthe spatial Durbin model is the correct model.
5.2

Estimation model

In this section, we briefly describe our estimation model.
𝑦𝑦𝑖𝑖𝑖𝑖 = 𝜌𝜌𝜌𝜌𝜌𝜌𝑗𝑗𝑗𝑗 + x𝑖𝑖𝑖𝑖 + δwx𝑗𝑗𝑗𝑗 + u𝑖𝑖𝑖𝑖 + ε𝑖𝑖𝑖𝑖 (7)where i denotes one’s own province, j denotes a neighboring province, t denotes year,
y denotes the household saving rate, x denotes the vector of all explanatory variables
used in the analysis, ρ and δ denote the spatial correlation coefficients of the dependentand explanatory variables, respectively, w denotes the spatial weight matrix, wy denotes
the spatial lagged term of the household saving rate of neighboring provinces, wx
denotes the spatial lagged term of the explanatory variables of neighboring provinces,8

u is a fixed effect, and ε is a random disturbance term.

6

Empirical Analysis
6.1

Estimation results

The estimation results are shown in Table 3. Columns (1) and (2) show the results
for the explanatory variables in the province in question, with column (1) showing theresults for the fixed effects model and column (2) showing the results for the random
effects model. Columns (3) and (4) show the results for the explanatory variables inneighboring provinces, with column (3) showing the results for the fixed effects modeland column (4) showing the results for the random effects model. A Hausman test
showed that the preferred model is the0 random effects model, so we focus on theestimation results in columns (2) and (4) in the subsequent discussion.
[Table 3 goes here.]
As shown in Table 3, the value of spatial rho is 0.187, and it is statistically significant.
This indicates that the household saving rate of neighboring provinces has a positiveand significant effect on the household saving rate in the province in question and thatthe household saving rate is spatially autocorrelated. This result is consistent with theresults of the analysis in Section 4.
The youth dependency ratio (YD) and the old-age dependency ratio (OD) of theprovince in question do not have a significant effect on SR, but the YD and OD ofneighboring provinces has a negative and significant effect thereon, with values of 0.277 and -0.257, respectively. Both the logarithm of per capital household disposable
income (lnPI) of the province in question and that of neighboring provinces have apositive and significant effect on SR. Neither the death rate (DR) of the province inquestion nor that of neighboring provinces has a significant effect on SR. Both theregional growth rate (GR) of the province in question and that of neighboring provinces
have a positive and significant effect on SR, but the coefficients are small. Both theshare of the urban population (UP) of the province in question and that of neighboring
provinces have a negative and significant effect on SR. The industrialization rate (INR)of the province in question has a positive and significant effect on SR, but that ofneighboring provinces does not have a significant effect thereon. The income disparity
between urban and rural areas (IND) of the province in question has a negative andsignificant effect on SR, but that of neighboring provinces has a positive and significant
effect thereon, with values of -4.239 and 2.502, respectively. Neither the real interest
rate (RI) of the province in question nor that of neighboring provinces has a significant
effect on SR.
6.2 Estimation results of direct, indirect, and total effects
LeSage (2008) suggests that direct effects, indirect effects, and total effects should
be used in spatial econometric models to analyze the influence of explanatory variables
9

on the dependent variable. The direct effect represents the influence of an explanatory
variable in the province in question on the dependent variable in the same province,
including feedback effects. Feedback effects refer to the fact that the explanatory
variables in one province may have an effect on the dependent variable in neighboring
provinces, which in turn may affect the dependent variable in that province. Indirect
effects, also known as spatial spillover effects, measure the effect of an explanatory
variable in a neighboring province on the dependent variable in the province in question.
The total effect is the sum of the direct and indirect effects.
Table 4 shows the estimation results for the random effects model, and as can be seenfrom this table, the youth dependency ratio and the old-age dependency ratio do nothave a significant direct effect on the household saving rate in the province in question
but that they have a negative and significant effect on the household saving rate throughan indirect effect, and ultimately that the total effect on the household saving rate is
negative and significant. This result is consistent with the life-cycle hypothesis.
[Table 4 goes here.]
Looking next at the coefficient of the logarithm of per capita disposable income(lnPI), its direct effect, indirect effect, and total effect are all positive and significant.
This suggests that the sustained increase in per capita disposable income over the last
three decades is an important reason for the phenomenon of a high household savingrate in China.
Looking next at the coefficient of the death rate (DR), which is used as a proxy forlife expectancy, none of its three effects was statistically significant. This suggests thatchanges in life expectancy do not have a significant effect on the household saving rate.
Similar to the case of lnPI, the direct effect, indirect effect, and total effect of theregional economic growth rate (GR) and of the proportion of the urban population to
the total population (UP) are all positive and significant.
The industrialization rate (INR) has a positive direct effect on the household saving
rate, but its significance is not high, the indirect effect is not significant, and the total
effect is positive and significant.
Looking next at the coefficient of the income disparity between urban and rural areas(IND), its direct effect, indirect effect, and total effect are all positive and significant. It
may be that the differing consumption habits of urban and rural residents havecontributed to this result.
Looking next at the coefficient of the real interest rate (RI), it has a positive andsignificant direct effect on the household saving rate, but its indirect and total effects
are not statistically significant.
Our findings imply that the one-child policy was successful in controlling China’s
population growth although the problem of declining fertility that it caused has
contributed to China’s high saving rate phenomenon.

7

Conclusion
10

In this paper, we used provincial panel data for China for the 2002-19 period to
conduct a spatial autocorrelation analysis of household saving rates as well as adynamic panel analysis of the determinants of household saving rates using a spatial
Durbin model.
To summarize our main findings, we find that, in China, the household saving rate
shows significant positive spatial autocorrelation with an overall “high-high” and “lowlow” clustering pattern, that, as predicted by the life-cycle hypothesis, the youth
dependency ratio and the old-age dependency ratio have a negative and significant
impact on the household saving rate, and that the logarithm of per capita household
disposable income, the regional economic growth rate, the share of the urban population,
the industrialization rate, and the income disparity between urban and rural areas also
have a significant impact on the household saving rate.
Our findings answer the question posed at the beginning of this paper—namely,
whether or not the age structure of the population is one of the determinants of thehousehold saving rate in China—in the affirmative. Thus, our findings imply that, as
China’s population ages (and as the rate of economic growth slows), the saving rate ofChinese households will decline in the future.
Finally, turning to directions for further research, there are a number of factors that
we were not able to consider in this analysis due to data limitations, such as borrowing
constraints, precautionary saving, bequest motives, and old-age pensions. We hope tobe able to incorporate these factors in our future research.

Acknowledgements
We are grateful to Jingjing Gui, Xiangci Lin, Xiangyun Yin, Guanwei Zeng, andespecially Tomoko Kinugasa for their valuable comments. This research was supported
by JSPS (Japan Society for the Promotion of Science) KAKENHI Grant Numbers
18H00870, 20H01513, and 20H05633 to Horioka.

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14

Table 1: Descriptive statistics
Variable

Mean

Std. Dev.

Min

Max

SR

26.72

5.345

10.59

49.25

YD

24.49

7.183

9.640

44.65

OD

12.96

3.075

6.710

23.82

lnPI

1.514

1.081

0.257

6.944

DR

6.085

0.952

4.210

13.87

GR

13.55

7.653

-25.02

60.77

UP

51.31

15.08

22.61

89.60

INR

37.93

9.917

6.808

56.49

IND

2.891

0.590

1.845

5.525

RI

1.855

2.349

-2.3105.530

Note: The number of observations is 558, the number of provinces is 31, and the number of years is
31.

15

16

YD

OD

UP

SR
1
YD
-0.2061
OD
0.137-0.3181
lnPI
0.365-0.5380.455
1
DR0.02030.07880.415-0.1141GR-0.0667
0.169-0.253-0.415-0.07171UP
0.219-0.7800.388
0.773-0.187-0.2311INR
0.0381-0.2210.0907-0.1530.130
0.174
0.0863IND-0.4450.625-0.378-0.5540.08060.313-0.667RI-0.05200.00630
0.05530.119
0.151-0.4840.0488
Note: The number of observations is 558, the number of provinces is 31, and the number of years is 18.

SR

Table 2: Correlation coefficient matrix
lnPI
DR
GR

1
-0.183-0.132INR

1-0.104

IND

1

RI

Figure 1: Global Moran’s I

17

-0.137**(-2.38)

Table 3: Estimation results
(2)
(3)
SR
SR
Wx
-0.0753
YD-0.268***(-1.42)(-2.90)-0.277***(-3.13)OD-0.0270(-0.29)-0.0885(-1.00)OD-0.230(-1.53)-0.257*(-1.75)lnPI

3.217***(6.24)

2.797***(7.27)

lnPI

0.387(0.53)

1.165*(1.82)

DR-0.110(-0.60)-0.0438(-0.23)DR

0.158(0.47)

0.178(0.52)

GR

0.0405*(1.72)

0.0502**(2.12)

GR

0.104***(2.59)

0.0959**(2.38)

UP-0.112***(-3.13)-0.140***(-4.42)UP-0.160**(-2.56)-0.126**(-2.07)INR

0.0733**(2.33)

0.0520*(1.78)

INR

0.0294(0.59)

0.0462(0.97)

IND-4.691***(-6.54)-4.239***(-7.15)IND

2.489**(2.38)

2.502***(2.72)

RI-0.00102(.)

0.0104(.)

RI

0.0407(0.50)

0.0211(0.25)

(1)
SR
Main
YD

Constant
Spatial
Rho

(4)
SR

40.91***(6.52)
0.193***(3.75)

0.187***(3.58)

Notes: Columns (1) and (2) show the results for the explanatory variables in the province in question,
while columns (3) and (4) show the results for the explanatory variables in neighboring provinces.
Columns (1) and (3) show the results for the fixed effects model, while columns (2) and (4) show theresults for the random effects model. Standard errors are in parentheses; *, **, and *** denote significant
at the 10%, 5%, and 1% levels, respectively.

18

Table 4: Estimation results of direct, indirect, and total effects
YD

OD

lnPI

DR

GR

UP

INR

IND

RI

Direct EffectIndirect EffectTotal Effect-0.0865-0.348***-0.434***(-1.59)(-3.48)(-3.67)-0.105-0.317*-0.422**(-1.22)(-1.73)(-2.00)2.909***

1.939***

4.848***(7.99)(2.90)(6.81)-0.0333

0.209

0.176

(-0.18)(0.50)(0.35)

0.0551**0.123***

0.178***(2.39)(2.61)(3.33)-0.146***-0.182***-0.328***(-4.47)(-2.66)(-3.98)0.0551*

0.06980.125**(1.83)(1.21)(1.99)-4.197***

1.966*-2.231**(-7.20)(1.91)(-2.03)0.0114***0.02430.0357(2.76)(0.24)(0.34)

N

558

R-squared

0.348

Notes: Standard errors are in parentheses; *, **, and *** denote significant at the 10%, 5%, and 1%
levels, respectively.

19