Doctoral Dissertation
Applied Dynamic Analysis on Labor andSocial Welfare:for Predicting Condition and Environment ofLabor Market, Social Security System andEconomic Growth in China

He Du
Graduate School of Social Sciences
Hiroshima University
September 2017

Contents
Introduction ...................................................................................................................... 1
Chapter 1. A Survey of Chinese Labor Market .............................................................. 5
and Social Security ........................................................................................................... 5
1.1 Overview and Problems of Chinese Labor Market ........................................................ 5

1.1.1 Development of Chinese Labor Market .................................................. 5
1.1.2 Current Situation of Chinese Labor Market ............................................ 7
1.1.3 Primary Topics of Chinese Labor Market ............................................. 12
1.2 Overview and Problems in Chinese Social Security System........................................ 14

1.2.1 Development of Modern Social Security System ................................. 14
1.2.2 Development of Chinese Social Security System ................................. 15
1.2.3 Current Situation of Main Social Security Plans in China .................... 16
1.2.4 The Important Issues of Social Security System in Future China ......... 20
1.3 Conclusion and Policy Implications ............................................................................. 23
ReferenceV .......................................................................................................................... 24

Chapter 2. Dynamic Analysis of the Regional Differences in Japanese LTCI System 27
2.1 Introduction .................................................................................................................. 27
2.2 The LTCI System in Japan; A Quick Review. .............................................................. 29

2.2.1 The Objective of the LTCI Care Insurance System ............................... 29
2.2.2 Application Process for the Long-Term Care Services ......................... 30
2.2.3 The Figures of the LTCI System ........................................................... 30
2.2.4 The Causes of Regional Differences and the 2005 Reform .................. 31
2.3 Theoretical Model Analysis of the LTCI System ......................................................... 32

2.3.1 Theoretical Model Analysis ................................................................... 32
2.3.2 Numerical Example ............................................................................... 39
2.3.3 Data Properties ...................................................................................... 40
2.4 Mobility Analysis of Regional User Rates’ Standing Order ......................................... 46
2.5 Mobility Analysis of Standing Order based on Residual User Rates ........................... 53
2.6 References for China .................................................................................................... 58
2.7 Conclusion .................................................................................................................... 60
Appendix. Data Sources and Its Properties. ....................................................................... 62
References .......................................................................................................................... 64

Chapter 3. Home or Market; Relative Importance of Learning Places on the Process of
Economic Development ................................................................................................. 67
3.1 Introduction .................................................................................................................. 67
3.2 Model............................................................................................................................ 71
3.3 Steady State and Welfare .............................................................................................. 77

3.3.1 Steady State ........................................................................................... 77
3.3.2 Welfare at Steady States ........................................................................ 82
3.4 Structural Stability and Bifurcation .............................................................................. 83

3.4.1 Phase-diagram Analysis ......................................................................... 84
3.4.2. Implication of Time Allocation for the Unified Growth Theory .......... 89
3.5 The Implications to China ............................................................................................ 93
3.6 Conclusion .................................................................................................................... 98

References .......................................................................................................................... 99

Conclusion .................................................................................................................... 103
Acknowledgement ........................................................................................................ 106

Introduction
This aim of this dissertation is to study the implications of labor market and social
security system on the process of economic development, and to predict the future
economic growth of China.
China’s economy has been undergoing a rapid development during the 30-year-plus
reform and opening-up period. As well documented in the economics literature, theeconomic growth miracle started from late 1970s is largely attributed to the so called“demographic dividend” and the “rural labor migration”1. Cai and Zhao (2012) argue thatthe growth of working-age population guarantees an ample supply of labor; a continual
decline in dependence ratio helps to maintain a high saving rate which is a foundation for
capital formation; surplus labor moved from rural areas to urban areas improves
efficiency of resource reallocation, which enhances the TFP.
Nevertheless, the impacts of demographic transition to economic development in China
have exceeded far above expected although many other countries have experienced it.
Particularly, in labor market, a remarkable change is the shortage of rural migrant laborand increased wages which occurred in 2004, which described as passing the Lewis
turning point (Zhang et al., 2011). Du and Yang (2014) argue increased cost of labor force
weakens competitiveness in labor-intensive industries and calls for the transformation of
growth pattern from input-driven growth models to productivity-driven ones. The otherimpact comes from the population aging, evidenced by negative growth of working-age
population appeared for the first time in 2011, while the population dependence ratio
began to increase. The consequence is decline in labor supply and capital formation,
which will reduce the potential economic growth rate (Cai and Lu, 2013).
As well as the slowdown of economic growth, demographic transition also exacerbates
the problem of China’s social welfare, such as the unsustainable financial guarantees
institutional segregation and the low level and narrow coverage of social security system,
especially the lack of long term care support for an increasing elderly people with full or
1

For “Demographic Dividend”, see http://www.unfpa.org/demographic-dividend
1partial disabilities. The implications of social security system are not limited to ensuring
the social stabilization and fairness, but also affecting the economic growth throughinfluencing the labor supply, human capital accumulation and allocation efficiency oflabor resources2. Therefore, the social security itself is even regarded as a production
factor3.
This study starts with a survey of labor market and social security system of China in
Chapter 1. We conclude that these is an expanding labor market reflected in an increasing
total number of employment. Although the China’s unit labor productivity grows rapidly,
the absolute level is obviously lower than the average level of the world. The relative
productivity by industry presents convergent tendency. The segmentation between ruralsector and urban sector prevents the labor mobility, which reduces the efficiency of labor
resource reallocation and thereby decreased the TFP. Under the background of population
aging, there are potential negative effects on economic growth due to the shortage of labor
supply and high aging dependency ratio. Apart from relaxing the institutional regulations,improving the labor competence by investing the human capital to meet the demand ofindustrial optimization and upgrading should be considered.
On the other hand, in the last decade, the social security undertaking in China hasdeveloped rapidly, which embodied in the perfection of corresponding laws and thecoverage expansion of beneficiary, especially the establishment of social security
programs for rural area population. However, the coverage and the level of social security
is relative low compared internationally. Moreover, the regional inequality of social
security level, which is also brought by the institutional regulations, exacerbates the labormarket segmentation and leads to negative effects on economic development. Population

2

Zhang (1995) shows when bequests are positive, an unfunded social security program
may simulate growth by reducing fertility and increasing the ratio of human capital
investment per child to per family income by employing a theoretical framework. Allenet al. (1988) show the lower job’s turnover rates of persons who are covered by pensions
are strongly associated the capital loss. Zhang and Zhang (2003) suggests the enterprise
pension prevents the human capital mobility, but not restricts enterprise to invest on
human capital.
3
See European commission (1997). “Modernising and Improving Social Protection in
the European Union”.
2aging generates an increasing demand of long-term care for elderly people, and therelevant social security system is absent.
To build up a nationally long-term care insurance (henceforth LTCI) system, the factor
that the imbalance economic development among regions should be considered. In orderto provide policy guideline for China, chapter 2 focuses on the experience of LTCI system
in Japan. We give an analysis on the dynamic properties of regional differences of theJapanese LTCI system. We also investigate the effect of the government-oriented reform
for the “expanding cost” problem and the “large regional differences” problem of LTCI
system. First, we predict that each region’s user rate converges to a unique globally stablesteady state by employing a simple theoretical model. The convergence, however, could
be conditional, i.e., each region’s user rate may converge to a region-specific steady state
which is determined by the region’s parameters.
We also calculated the user rates of 47 Japanese regions (prefectures) for the fiscal years
between 2000 and 2012. The regional user rates seem to exhibit a tendency to conditional
converge. Additionally, by using average Markov transition, we calculated the index ofstanding order mobility to evaluate the effects of the 2005 reform which aimed to remedy
the differences in regional figures of LTCI system. It turned out that the 2005 reform, did
not seem to alleviate the standing order inertia.
Moreover, the small degree of variation in the standing order suggests the existence ofregion-specific factors. With the help of preceding researches, we chose 3 factors {thecertification rate, the late-stage (75 years or older) old age ratio, and the ordinary balancerate} to account for the regional differences in user rates, and recalculated the mobility
index by using the residuals. It turned out that the degree of mobility is improved and thus
the convergence is conditional. If region-specific factors were not removed, each region’suser rate would converge to region-specific steady state, and the standing order ofregional user rate would be invariant. It turned out as well that the 2005 reform hardly
affected the standing order mobility of residual user rates. In addition, the analysis also
revealed that the improvement in the standing order variation seems small even after theregional factors are removed. Therefore, there might be factors other than our choice that
could explain the regional differences.
3

By comparing the regional differences between Japan and China, we provide
suggestions for the establishment of Chinese LTCI.
In Chapter 3, for predicting the growth trend of China, we provide theoretical frameworkand show that the relative importance of learning places (home or market) matters for theprocess of economic development by employing the ideas of “unified economic growththeory” and “family and time allocation”.
A natural framework that can deal with these issues is a two-sector model of economic
growth in which a household plans time allocation between market activity and nonmarket (home) activity to maximize utility. Under the assumption that home technology
is more labor intensive than the market technology (as presumed in many preceding
researches), when market activity is more important for human capital accumulation, thenmultiple steady states emerge in dynamic general equilibrium. Some economies converge
toward a higher growth steady state, while the others toward a lower growth steady state.
Furthermore, the divergence may depend on initial condition and self-fulfilling
expectation.
We also review the role of human capital on China’s economic growth process since thereform and opening-up, and discuss the applicability of our theoretical model for
predicting the future of economic growth of China.
Chapter 4 concludes and points out the shortcomings and future directions for further
research.

4

Chapter 1. A Survey of Chinese Labor Market
and Social Security
In this chapter, by providing a review of the history and current situation of Chineselabor market and social security system, we conclude, the skill gap due to the industrial
structure change generates labor shortage and unemployment co-existence in Chineselabor market, which could be tackled by improving the public vocational training;
relaxing the family plan and regulations on labor mobility as well as improving the level
and coverage of social security could counterbalance the potential negative effect broughtby population aging and mobility barriers created by institutional factors on economic
growth.

1.1 Overview and Problems of Chinese Labor Market
1.1.1 Development of Chinese Labor Market
From the founding of People Republic of China to the pre-reform-and-open period,
Chinese labor market experienced existing, shrinking and disappearing phase. After
reform and open, the labor market started to develop.
Chinse Labor Market before the Reform and OpenIn the initial stage of founding of People Republic of China (1949-1953), in order tomaintain social stability and 1recover economic development, the government took
continuing policy with the confiscated old China bureaucrat capitalist enterprises staff,
preserving the undeveloped labor market, which formed in few medium-and-large cities.
During the first five-year plan of planned economic system, which started from 1953,
the government implement concentrate resources configuration system and the micro
operation mechanism without autonomy (Lin et. al., 1995). Moreover, the government
push centralized labor allocation system. Under this system, because the companies haveno autonomous right on the using of labor, they cannot optimize the combination of
production resources and labor; without motivation, labor degraded; without labor flow,
resources were wasted.

5

Chinese Labor Market after Reform and Open
After reform and open, Chinese economic system gradually transferred to market
economy system, and the labor market started to work. The development of economy canbe divided into four stages as following.
The first stage (1979 - 1983): the Chinese rural area tried economic system reform, “therural responsibility system of production”, while in Chinese city area, because of thedevelopment of collective economy, individual economy and other economic system, thegovernment tried another way to solve unemployment problem – the government used“three-in-one combination”, which is the labor department job placement, resources
allocation job placement, and self-employment job placement, to replace the originalmode, “centralized labor allocation system”. Meanwhile, the government still employed
the original labor distribution model on the state-owned enterprises within the planned
economic system.
The second stage (1984 – 1992): as Chinese activated the urban economic system reform,
state-owned enterprises within the planned economic system was granted moreautonomous right on labor using. The reform of planned economic system facilitated theoutflow of labor within the system. During the same period, the rural management system
was full swing, and the farmers gained more autonomy to the labor force, stimulating thetransfer of peasant labor to non-agricultural industries.
The third stage (1993 – 1997): in the “Decision of the Central Committee of theCommunist Party of China on the Establishment of a Socialist Market Economic System”
in 1993, the Chinese government clearly presented that the government would cultivateand develop the labor market for the first time. During this period, non-state economy
developed rapidly, especially the foreign enterprises in the coastal open areas, attracting
the mainland labor force. At the same time, the competitiveness of labor force in stateowned enterprises declined, and thus rising unemployment problem and inadequate
employment problem.
The fourth stage (1998 – now): in 1998, China established the labor market in full swing.
First of all, the problem of laid-off workers, former state-owned enterprises’ workers, wassolved through the establishment of the "re-employment service center", leading the6

outflow of the labor within the economic system. In addition, the government
strengthened the management of occupational intermediary, standardize the order of thelabor market, and established labor service network, which aimed of public occupation
introduction supplemented by private occupation intermediary, covering both urban andrural area. From 2011, the ministry of labor and social security (now the ministry ofhuman resources and social security) released “the Analysis of Labor Market Supply and
Demand of Some Cities” to control the supply and demand of labor under market
economy, providing the basis for employment guidance and training. However, becauseof the existence of policies based on household registration, so far, there is no unified
labor market for industries in China.
1.1.2 Current Situation of Chinese Labor Market
Basic Situation of Economy
After open and reform, Chinese economy experienced rapid growth; from 1979 to 2011,
the actual average annual growth rate is 9.8%; to be more specific, the actual annual
growth rate of the first 10 years of 21st century is 10.5%, while the growth rate slowed
down from 2012; the rate declined from 9.5% in 2012 to 7.4% in 2014, and further
decreased to 6.7% in 20164. Moreover, according to “Global Economic Prospects 2017”,
released by World Bank, Chinese economic growth rate will continue decline to 6.3% in20195.
Labor Supply
Due to the fertility policy and extension of the average life expectancy, China becoming
an aging society with few children. By the end of 2014, the working age population (aged15 ~ 64) of China was 100,469,000, account for 73.4% of total population, falling from2010. Meanwhile, the total population dependency ratio increased from 34.2% in 2010 to4

Data of 2016 comes from “National Economic and Social Development Statistical
Bulletin 2016”, released by CNBS,
http://www.stats.gov.cn/tjsj/zxfb/201702/t20170228_1467424.html㸪February 28th,
2017; Other data comes from “National Database”, released by CNBS,
http://data.stats.gov.cn/
5“Global Economic Prospects 2017”
http://pubdocs.worldbank.org/en/216941493655495719/Global-Economic-ProspectsJune-2017-Global-Outlook.pdf
7

37% in 2015, which was composed with an increasing aged-dependency ratio and a
declining child-age dependency ratio. Furthermore, according to the population outlook
report of United Nations, the proportion of working age population in China is expected
to fall to 68% in 2030, and to 58.9% in 2050, and the total population dependency ratio
will growth from 48% in 2030 and 63.6% in 20506 7.
From the perspective of educational level and the OECD report of 2015, 24% of themain working population in China have high school degree or above, far below theaverage level, 80%, of the 35 member-countries of OECD.8
During the same period, according to “Investigation Report on Migrant Workers”,
published by CNBS, the total number of migrant workers increased from 252,780,000 to277,470,000, and the growth rate declined from 4.4% to 1.3% for 4 consecutive years9.
Employment Scale and Structure
Since 2010, China’s overall employment scale has been expanding, i.e. at the end of
2016, the total number of employees reached 776,030,000, increased 1.96% compare with
the number in 2010; specifically, the number of urban employment increased from346,870,000 to 414,280,000, increased 19.5% compare with the number in 2010 (seeTable 1.1).

6

United Nations, Department of Economic and Social Affairs, Population Division(2015). World Population Prospects: The 2015 Revision, custom data acquired via
website.
7
In general, the working-age is 15-60 year-old or 15-65 year-old people. According to
the “minimum employment age convention”, approved by the international labororganization in 1973, the lower limit of working-age is 15-year-old. Whereas, whether
the upper limit of working-age is 60 or 65 years old depends on the different expectancy
of average life in different countries. In 1998, China joined the “the minimum age for
employment” of international labor organization, requiring the lower limit of workingage is 16-year-old in China. However, there is no clear provision on the upper limit ofworking. Therefore, the statistical data on the working-age population is relative
confusion in China. This paper employs “China Statistical Yearbook”, and uses 16-64
years old as the working age.
8OECD (2015), Education at a Glance 2015: OECD Indicators, OECD Publishing,Paris. DOI: http://dx.doi.org/10.1787/eag-2015-en page 39
9China Migrant Workers Monitoring Report 2015,
http://www.stats.gov.cn/tjsj/zxfb/201604/t20160428_1349713.html
8

Table 1.1 Trend of Employment by Urban and Rural in China 2010-2015
2010

2011

2012

2013

2014

2015

Total

76105

76420

76704

76977

77253

77451

Urban Sector

34687

35914

37102

38240

39310

40410

Rural Sector

41418

40506

39602

38737

37943

37041

Source: CNBS, http://www.stats.gov.cn/

On one hand, with the acceleration of Chinese industrial structure adjustment, theemployment proportion of the three industries sector experienced significant changes.
From 2010 to 2015, the primary industry employment proportion declined from 36.7% to28.3%; that of secondary industry changed little, remained at around 29%; however, thatof tertiary industrial increased from 34.6% to 42.4% (see Figure 1.1).

Figure 1.1 Trend of Empolyment by Industry in China(2010-2015)
90000
80000
70000
60000
50000
40000
30000
20000
10000
0
2010

Total

Primary Industry

Secondary Industry

Tertiary Industry

2011

2012

2013

2014

2015

Source: CNBS, http://www.stats.gov.cn/

On the other hand, from the employment distribution, the proportion of rural migrant
workers engaged in manufacturing industry decreased from 36 % in 2011 to 31.1 % in2015, while that of other industries, such as wholesale and retail industry, rose.
Quality of Labor
Overall, Chinese labor productivity grow fast; the average education level of
employment of Chinese improved year by year, however, unlike developed countries,9China remains a significant gap.
From 2005 to 2015, in China, the unit labor productivity had an average rise of 9.1%,
from $3,088 to $7,318; to be more specific, from 2005 to 2010, the unit labor productivity
had an average rise of 10.6%, whereas it declined to 7.3% from 2010 to 2015 (see Figure
1.2).

8000

14

7000

12

6000

10

5000

8

4000

%

USD (2005 constant prices)

Figure 1.2 Per Capita labor productivity of China(2005-2015)

6

3000
2000

4

1000

2

0

0
2005 2006 2007 2008 2009 2010 2011 2012 2013 2014 2015
Labor Productivity of China

Source: CNBS http://www stats gov cn/

Meanwhile, compare to other major economies all over the world, although theincreasing of China’s unit labor productivity is relative fast, the output level is obviously
lower than the average level of the whole world, especially when compare with America,
Japan and Eurozone (see Table 1.2).

Table 1. 2 International Comparison of Labor Productivity in 2015
(Constant 2005 USD)
China

U.S.

EU

Japan

India

World

Growth Rate

6.6

0.9

0.6

0.9

5.6

1.1

Productivity

7318

98990

68631

76068

3559

18487

Source: ILO Datebases http://www.ilo.org/global/statistics-and-databases/lang-en/index.htm

From the perspective of relative labor productivity among industries, labor productivity
10ratio of the primary, secondary, and tertiary industry (i.e., the proportion of the added
value/ the employment rate) was 0.26: 1.45: 1.22 in 2010, while was 0.31: 1.39: 1.18 in2015, indicating the labor productivity in all three industries in gradually convergence(See Table 1.3).

Table 1.3 Relative Labor Productivity by Industry
Employment Ratio

Primary

Added Value

Secondary TertiaryPrimary

Relative labor Productivity

Secondary TertiaryPrimary

Secondary

Tertiary

2010

36.7

28.7

34.6

9.5

46.4

44.1

0.26

1.62

1.27

2011

34.8

29.5

35.7

9.4

46.4

44.2

0.27

1.57

1.24

2012

33.6

30.3

36.1

9.4

45.3

45.3

0.28

1.49

1.25

2013

31.4

30.1

38.5

9.3

44

46.7

0.29

1.46

1.21

2014

29.5

29.9

40.6

9.1

43.1

47.8

0.31

1.44

1.18

2015

28.3

29.3

42.4

8.9

40.9

50.2

0.31

1.39

1.18

Source: Calculated by the author in accordance with the industrial added value and employment ratio found in
China Statistical Yearbook 2016, published by CNBS.

From the perspective of overall education level of labor, according to relevant data of“Chinese Labor Statistics Yearbook”, from 2001 to 2014, the average education level ofChinese labor increased by years, from 8.18 years to 9.93 years. At the same time, thecomposition of the educational level of the employees also changed significantly. In 2001,
there were 40,770,000 people hold junior college or higher degree, which was 5.6% ofnational employment; there were 98,280,000 people hold high school degree, which was
13.5% of national employment; there were 578,970,000 people hold junior high schoolor lower degree, which was 81.0% of national employment. However, in 2014, thosenumbers changed to 124,470,000 and 16.1%, 133,090,000 and 17.2%, and 514,960,000
and 66.7% respectively. In addition, by the end of 2014, the number of people withbachelor of master degree was 52,480,000, only 6.8% of the total national employment.
The above data shows that the level of human capital is still low.
From the perspective of education level of labor in different industries, “Skills Shortagein Chinese Labor Market”, which was completed by Tsinghua University and Fudan

University and supported by JP Morgan, shows that by the end of 2010, there was a11significant gap among the education level of labor in different industries. Never educated,primary school educated and junior high school educated labor mainly worked in the
primary industry sector, and the proportion was 88%, 75% an 50% respectively. People
with high school degree, junior college degree, bachelor or higher degree can be found in
tertiary industry sector, and the proportion was 47%, 70% and 79% respectively.
Furthermore, from 1990 to 2010, as the adjustment of industrial structure, the proportionsof labor with different education level in three industry sectors are different: labor withdifferent education level can be found in the primary industry sector and tertiary sector in
declining and rising trend; and in the secondary industry sector labor with lower andhigher education level shows increasing and decreasing trend10.
1.1.3 Primary Topics of Chinese Labor Market
The mismatch of employment structure
Thanks for “demographic dividend”, Chinese economy experienced rapid growth after
open and reform. “Demographic dividend” refers to the positive effect on a country’s
economic development, affected by high labor force participation rate, high savings rateand high investment rate, which were brought by the advantage of age structure during
the process of population transition (Cai and Wang, 2004, Cai and Lu, 2013). However,in recent years, the aging of labor market and the sharp decreasing of surplus labor ofrural area led to the rapid increasing of labor cost and rapid declining of savings rate,
indicating the gradual disappearance of demographic dividend, and therefore making it
impossible for the export-and-investment-oriented economy to continuous grow.
On the one hand, because of the reduction of labor supply, the labor cost rapidly
increased. Once the increase rate of labor cost higher than the increase rate of laborproduction, the comparative advantage of labor-intensive industries of China drops,pressuring the transformation and promotion of Chinese economy, in turn raising therequirement on labor quality. On the other hand, the increase of labor wage, caused by10

https://www.jpmorganchase.com/corporate/Corporate-Responsibility/document/skillsgap-inchineselabor-market-exec-summary.pdf. In “Skills Shortage in Chinese Labor Market”, there isno definition on higher or lower education level in this paper, but in my opinion, “higher
education level” in this paper means high school or higher educated level, while “lower
education level” means lower than high school educated level.
12the decrease of labor supply, causes the increase of human capital investment cost,
deepening the contradictions of employment problems, which caused by the imbalance
between labor demand and labor supply.
Problems of Human Capital Accumulation
In addition to the contribution of the demographic dividend, the Chinese education
effectively helped the development of economy by accumulating human capital over the
past 30 years since open and reform. However, although China achieved nine-year
compulsory education and the popularized higher education in the 21st century 11, thedifference of the proportion of higher educated main labor between China and developed
countries is remarkable; especially in China’s poor rural areas, the high school entrance
rate was less than 40% in 2013 due to the relatively high tuition fees, increased
opportunity costs and weak teachers (Shi et al., 2015). Since the labor force in rural areas
will become the main source of labor supply in China, Chinese government has to think
about whether to extend the compulsory education.
Furthermore, under the background of transformation and upgrading of China’s
industries, and the increasing of job skills requirements, the in-service staff face thedemand pressure of skills upgrading. According to the analysis of “the Gap of ChineseLabor Skills Report”, the private enterprises skill training and public vocational skillingtraining are weak, while enterprises and individuals have a great demand for publictraining with low ability of paying. This situation reflects another contradiction of theemployment structure of China: supply surplus of low-end labor makes the workers
actively seek training to improve their skills; and employers can choose employees fromrich labor resources, lowering their training willingness. At the same time, since China
has not formed life-long leaning, the education level of most people was determined by
30-year-school education before career; while vocational training is another way for
China to accumulate human capital, and how to improve vocational training supply is an
important way to solve the contradiction of employment in China.

11

About China’s nine-year compulsory education, more details can be found at:
http://www.china.org.cn/english/education/184879.html.
13

The Existence of Labor Market Segmentation
In the Chinese labor market, the urban-and-rural-segmentation is still the primary form.
The segmentation of Chinses labor market started from planned economy era. The
government focus on the development of industry and related employment system,
allocation and management system and household registration system, leading to theurban-and-rural-segmentation, which can be found only in China. Even though theregulation of household registration became loose, “left-behind children”, “left-behindelderly” problems etc. rose 12 . The reason is that in order to solve the employment
problems of local labor some local governments, especially in big cities, set up barriers
to block live, work, education, health and social insurance of migrant workers. Besides,
under the background of the aging population, the urbanization of urban and rural areas
increases the migration cost of the rural labor to urban, leading to the further contractionof the labor supply in China.

1.2 Overview and Problems in Chinese Social Security System
1.2.1 Development of Modern Social Security System
Modern social security system started from the English Poor Law in 1601, but it wasdeveloped and established with the development of industrial revolution. In general,
Workers’ Sickness Insurance Law, Workmen Compensation, and Old Age and Disability
Insurance, issued by German Bismarck government, marked the birth of modern social
security system (Pampel, 1998). After German’s issuance, British, Japan, America, andAustralia established their own social security system; especially in 1935, Roosevelt
government passed the first social security act, promoting the social security systemworldwide13.
After 1945, with the introduction of “general welfare” and “welfare state”, thedevelopment of social security system entered the mature stage; especially in British, sir
12Left-behind children refers to the children who are left at home or lodged in relatives'
homes for a long time because their parents one or both work outside their hometown.
Information about the current situation of Chinese left-behind children, please check:
http://www.scmp.com/news/china/society/article/1951469/chinas-left-behind-childrenhigher-risk-life-crime-study-finds
13
For detail of the history of American social security act: Martin and Weaver (2005)
14

Beveridge began to the postwar British social security plan during the Second World War,and proposed “Social Insurance and Allied Services” (known as the Beveridge report) in
194214. According to this report, in order to achieve full employment and social welfare
program the British government passed the National Insurance Act (1946), Pensions Act(1947) and a series of related acts. During this period, with the improvement of social
productivity, social security strengthened the economy and social life, and its content isconstantly being expanded.
However, since 1980s, because of the aging population social security expenditure was
too large; meanwhile, because of the influence of liberalism many developed countries
began to tighten social security policies, such as the Reagan administration and theThatcher government. Specifically, the Reagan administration signed a series of social
security programs to reduce the social security plans in 1983; and the Thatcher
government promoted the privatization of pension funds. During this period, many
countries gradually introduced market mechanism into social security system,emphasizing the responsibility of individuals and families.
Recently, due to the global financial crisis and the European sovereign debt crisis, some
European welfare countries, such as Germany and France, adopted some policies, forinstance, improves the pension contribution rate, the payment period and tax, to reduce
the social security expenditure, and in turn to lessen the fiscal deficit. In contrast, somemiddle-income countries begin to increase the input in social security, for example, theChinese government increased the expenditures in health, education, and pension to solve
the imbalance income problems between regions in the "Twelfth Five Year Plan (20102015)".
1.2.2 Development of Chinese Social Security System
After the founding of new China, Chinese government immediately began to establish
the new China’s social security system; but a serious urban-and-rural segmentation wasformed by the heavy industrialization strategy, almost all the system set the city as thefoothold (Lin, 1998). In 1951-1955, the State Council promulgated and implemented the14

The original report:
http://news.bbc.co.uk/2/shared/bsp/hi/pdfs/19_07_05_beveridge.pdf
15

"People's Republic of China Labor Insurance Regulations", includes the retirement,
resignation, and sick of civil servicers, marking the beginning of the social security
system in China. With the establishment of the socialist system, China government
introduced a number of social security systems, such as "several issues of state organ
staff’s retirement and working years”, "the Interim Provisions of the treatment ofvoluntary retired workers issued by State Council", from 1956; these provisions madedetailed regulation on retirement, resignation and other aspects. However, in 1966, whichis the beginning of the cultural revolution, China entered the ten years’ turmoil, almost
stagnated the social security system.
After the reform and open, the construction of social security system started again. In
the late 1980s, with the expansion of the reform of state-owned enterprises, the reform of
the social security system also started, and the establishment of the system continuous
works. With the establishment of protection of laid-off workers, the unemployment
insurance system, the pension system and social assistance system were established. In
1993 the third Plenary Session of the 14th CPC Central Committee cleared the target of
establishing multi-level social security system for the first time; and from 1997 to 1999
the basic pension system, the minimum life guarantee system of city, city workers' basic
medical insurance system, the unemployment insurance system and a series of social
security system were formulated.
Subsequently, the sixteenth CPC Central Committee (2002) stated the goal of building
a socialist harmonious society, accelerating the establishment of social security system.
“The new rural cooperative medical system pilot” in 2003 and “the pilot of rural minimum
living security system” in 2007 marked the new stage of China's social security, which is
the overall development of urban and rural areas and institutional innovation15. With thepromulgation and implementation of the social insurance law in 2011, the framework of
China's social security system was basically established.
1.2.3 Current Situation of Main Social Security Plans in China
China's current social security system consists of social security system, including social
15

For more information of “The new rural cooperative medical system pilot”, pleaserefer http://china.org.cn/china/2012-09/17/content_26545922.htm
16

assistance, social welfare and social charity. Social insurance system includes endowment
insurance system, medical insurance system, unemployment insurance system, workrelated injury insurance system and maternity insurance system. Pension insurance
system can be divided into urban staff pension insurance system and urban-and-rural
residents pension insurance system, categorized by coverage.
Old-age Insurance System for Urban Workers
Before 1997, the endowment insurance and medical insurance of urban workers aremainly borne by enterprises; in other words, people without work do not have insurance.
In 1997, the state Council formally proposed the establishment of pension system thatunifies social and personal account for urban employees. The basic pension is composedof social pooling fund and individual account; the current basic pension insurance
premium is 20 % of the total employee salary, including in social pooling fund, and theindividual pay 8% of their average salary of last year, including in individual account.
People who reaches the legal retirement age (60 years male, and 55 years female) andpays the insurance monthly for more than 15 years can receive a basic pension from thepersonal account and the social pooling fund until death.
From 2010 to 2014, the number of insured people increased from 257,070,000 to341,240,000, in which the number of in-service people was 255,310,000 and the numberof retirement people was 85,930,000. On the other hand, because of the rapid increase of
the number of basic pension insurance of urban workers and the increase of contribution
base, the pension fund increased from RMB 2,397.5 billion in 2010 to RMB 4,706.5
billion in 2014, with an average annual growth rate of 18.3%; specifically, the total fundincome increased from RMB 1,342 billion in 2010 to RMB 2,531 billion in 2014, withthe growth rate of 17. 2 %; the total fund expenditure increased from RMB 1,055.5 billion
in 2010 to RMB 2,175.5 billion in 2014, with an average annual growth rate of 19.8 %;the total amount was RMB 3180 billion.
Pension Insurance for Urban and Rural Residents
The pension insurance of urban and rural residents is a combination of the new rural
cooperative medical system (NRCMs) started from 2009 and new urban residents pension
17

insurance spread from2011, formed in February, 201416. The insurance fund is consistedof individual account and basic pension; there are 12 criteria for individual payment,
ranging from RMB 100 to RMB 1,200, so that people can choose their own payment
criterion; one can get more if he or she pays more. On the other hand, the basic pension
subsidized by the government; for middle west and east region, central government
subsidizes all and 50% of the insurance respectively17. When insured individual makes
the payment for 15 years and is 60 years old, the people can withdrawal pension fromgovernment. From 2015, the government cleared that the basic pension changed to RMB
70 per month from RMB 55 per month.
The Basic Medical Insurance System for Urban Employees
Like the basic endowment insurance for urban workers, the basic medical insurance fundconsists of personal account and pooling fund. The insured individual pays 2% of one’s
wage to personal account, and the employer pays about 6% of the employee’s wage; about
30 % of the insurance are included in employee personal account, and rest of that areincluded in pooling fund. From 1999 to 2014, the number of insured employees in cities
increased from 20,650,000 to 210,410,000, and insured retirement people rose from5,560,000 to 72,550,000.
Basic Medical Insurance for City Residents
The basic medical insurance of urban residents mainly covers the urban minor and nonworking residents, and it focuses on hospitalization and outpatient expenditure. It was
first introduced to the public in 2007, and matured in 2010, covering the whole city
residents gradually. Until 2015, the number of participants reached 314,510,000. Family
pays most of this insurance, and the government subsidies according to the criteria.
From 2007 to 2015, the allowance increased from RMB 70 per person to RMB 280 perperson.
16

The insured people of the new rural cooperative medical system is rural residents,
while that of new urban residents pension insurance is city residents.
17
The middle-western of China includes more than 20 provinces, autonomous regions
and municipality directly under the central government, such as Shanxi province, theNei Monggol Autonomous Region, Chongqing and etc.; the eastern of China includes
over 10 autonomous regions and municipality directly under the central government,such as Beijing, Shanghai, Jiangsu province and so on.
18New Rural Cooperative Medical System
The new rural cooperative medical system (“NRCMs”) refers to the medical mutual
assistance system of farmers that funded by the government, voluntary participatedfarmers and personal. NRCMs raises funds by personal payment, collective support andgovernment allowance. In 2004, the government allowance for NRCMs reached RMB
320 per person, in which the central government pays RMB 120, and subsidies thewestern and middle areas 80% and 60% respectively. Personal payment per year isapproximately RMB 90. By the end of 2013, the number of participants of NRCMs was
8,020 million with the participant rate of 99% and the number of beneficiaries of 1.942
billion.
Unemployment Insurance System
China's unemployment insurance system was formed with the development of the labormarket after the reform and opening in the 1980s. In order to guarantee the basic life of
the unemployed workers, the state promulgated “the provisional regulations on
unemployment workers in state-owned enterprises”, and “the regulations on
unemployment insurance” as the legal basis of national unemployment insurance in 1999.
The current unemployment insurance system aimed at protecting the basic life andpromoting reemployment of the unemployed, covering the employees of urban
enterprises. The insurance fund is funded by the individual, the employing companies andthe local government subsidized, among which the premium rate paid by individual is no
more than 1 % of the wage, and the company did no more than 2% of the wage. The
expenditures of the fund are mainly the payment of insurance benefits and occupational
introduction subsidies. The amount of unemployment insurance is between the local
minimum wage and minimum living standard. The insured person is required to have aconsecutive premium of more than one year, and not personally wish to lose his or her
job and register unemployment to get insurance payment. The number of insured persons
in 2014 was 170,430,000.
Employment Injury and Maternity Insurance System
In addition to the pension, medical and unemployment insurance system, Chinese social
insurance also includes work-related injury insurance system and maternity insurance19system; more specifically, work-related injury insurance refers to a social insurance
system that workers or their survivors will obtain material assistance temporarily or
permanently after accidental injury or occupational disease from the state and society;and maternity insurance refers to a social policy that pregnant and childbirth women can
get help from the state through legislation, including maternity allowances, medical
services and maternity leave, and its purpose is to help those women to recover their labor
capacity and return to work.
Social Assistance Scheme
Furthermore, the social assistance system is a crucial part of Chinese social security
system. Unlike other insurance system, the social assistance system focuses on the people
who earned low income, people who suffered the natural and man-made disasters, andpeople who cannot live by themselves because of other specific reasons (Zheng, 2015).
Based on “the Interim Measures on Social Assistance” issued by the State Council in
2014, the social assistance system includes the minimum living security, support fordisaster victims, medical assistance, housing assistance, career relief, temporary
assistance and so on18. According to the report of the China development and reform
Commission, the total social assistance financial expenditure of urban and rural residents
was RMB 395.59 billion, in which the expenditure of minimum living security was RMB
153.86 billion19.
1.2.4 The Important Issues of Social Security System in Future China
Relatively Low Level of Social Security Expenditure
From 2008 to 2014, the absolute scale of social security expenditure and medical
expenditure continuous increased, from 956.1 billion RMB to 5,614.4 billion RMB, but
through the observation on the fiscal expenditure ratio and the ratio of GDP, it is easy tofind that the relative security expenditure is not significantly increased (see table 1.4). In
addition, compared with other countries in the world, the level of social security spending18

See China state Council decree 649:
http://www.gov.cn/zwgk/2014-02/27/content_2622770.htm
19
See China development and reform Commission social relief, January 2015:
http://www.sdpc.gov.cn/fzgggz/jyysr/zhdt/201501/t20150130_662741.html
20

in China is far lower than the average level in OECD countries (see table 1.5).

Table 1. 4 Trend of Expenditure of Social Security and Medical in China (2008-2014)
Expenditureof Social
Security andMedical
(RMB)






FiscalExpenditure
(RMB)

GDP
(RMB)

Expenditure ofSocial Security
andMedical/GDP(%)

Expenditure ofSocial Security andMedical/Fiscal
Expenditure (%)

2008

9561

62592

300670

15.2

3.1

2009

11600

76299

345629

15.2

3.3

2010

13934

89874

408903

15.5

3.4

2011

17538

109247484123

16.1

3.6

2012

19830

125952534123

15.7

3.7

2013

23269

140212588018

16.6

3.9

2014

26144

15178563613817.2

4.1

Source: CNBS, http://www.stats.gov.cn/

Table 1. 5 Comparison of Expenditure on Social Security (/GDP)
2008

2009

2010

2011

2012

2013

2014

Canada

16.3

18.04

17.55

17.04

17.09

16.88

16.82

France

28.2

30.54

30.66

30.47

31.03

31.49

31.94

Germany

24.22

26.67

25.92

24.66

24.56

24.76

24.85

Japan

19.59

21.89

22.07

23.12

22.94

23.06

23.87

United States

16.53

18.58

19.33

19.07

18.78

18.88

18.81

Chile

9.74

11.04

10.47

10.02

10.12

10

10.52

OECD-Total

19.02

21.18

21.07

20.75

20.97

21.12

21.07

China

3.18

3.35

3.41

3.62

3.71

3.95

4.11

Source: OECD data-social spending, https://data.oecd.org/socialexp/social-spending.htm

The Gaps Between Urban and Rural and Among Regions
Although Chinese government focused on the economic development of urban and rural
integration, driving agriculture by industry and issuing a series of documents to accelerate
the construction of rural social security, the social security gap between urban and rural21

is still significant20. Because Chinese government did not split the statistics of expenditureof social security between urban and rural (Chen, 2014), it used the transfer income ofurban residents and rural residents as the surrogate variables of urban and rural social
security expenditure and found that the proportion of rural-to-urban migrants in China
decreased from 40.5 in 1999 to 9.2 in 2012; especially after the enforcement of NRCMs
in 2009, the proportion of transfer income of urban and rural residents decreased
significantly. However, the proportion of rural residents remains low in the social security
expenditure.
In the same time, the social security gaps among provinces and regions are obvious.
Because the level of social security in China is low and more than 90% of social security
expenditure is paid by the local government, the imbalance of economic development
among the provinces is the direct reason of the obvious differences in social security
expenditure (Yin et al., 2016). Yin et al. (2016) also calculated the Theil Index ofdifferences of social security expenditures among regions and found that there are
significant differences among different provinces and the reason that the differences exist
is that there are expenditure differences among regions in provinces.
The Lack of Long-term Care for Elderly People
The demand of long-term care for the elderly is increasing because of population aging,family function weakening and so on. On the other hand, because Chinese government
took the medical insurance system, pension insurance system and the minimum living
security system as the priority targets, there is no unified security system for the health ofelderly, leading to the deficiency of long-term care for elder people in social security
system21. Jiang and his colleagues summarized three types of service mode for elders whoneeds long-term care: institutional care, community care and family care (Jiang et al.,2013). Institutional care means that the care recipients need to register in public or private

20

Central Committee No.1 in 2004: “opinions of the central Committee of the CPC
central Committee on promoting farmers' income”:
http://www.moa.gov.cn/ztzl/yhwj2014/wjhg/201301/t20130129_3209956.htm
21 “Worldwide Annual Health, Labor and Welfare Report 2015” by Ministry of Health,labor and welfare of Japan,
http://www.mhlw.go.jp/wp/hakusyo/kaigai/16/dl/t4-02.pdf
22

nursing home; however, the problems are that the demand exceeds the surplus in public
nursing home, while the infrastructures in private nursing home are too old to satisfy therequirements of elders. Community care refers to household service, rehabilitation
nursing, spiritual consolation etc. provided by community; however, the requirements ofcare recipients cannot be satisfied because of the lack of quality and quantity of caregivers.
Like the situation of community care, it is hard for family care to offer professional
service. In the above background, China faces lots of problems to establish a perfect longterm care for elder people, for example, the lack of professional caregivers, the short ofcare infrastructures, and the difficulties of raising funds etc.

1.3 Conclusion and Policy Implications
Maintain stability of Labor market is prior for China’s economy which is being adjusted
to a “New Normal” state with a slower but sustainable economic growth. The population
aging and the exhausted rural surplus labor force leads to shortage of labor supply, hencecauses contradiction between demand of supply in labor market. Furthermore, theshortage of labor supply, low capital formation rate due to the demographic transition
results in a decline in potential growth rate in long term. To deal with these challenges,
government should undertake effective action to complete the reform of householdregistration and gradually eases its family-planning policy. Moreover, improving humancapital by enhancing input in education and cultivation, especially to the low-skill labor,
is necessary.
Specifically, relaxing the household-registration and narrowing the social welfare gaps,
such as public education and social security system, could eliminate the labor market
segmentation, thus enhance efficiency of labor resource reallocation and the TFP.
Although easing the family planning will not have immediate effect, it could increase theworking-age population in future, thus generate a positive impact in potential growth rate.
Additionally, as Heckman and Yi (2012) point out that the returns of expanding public
expenditure on education is very high, since it can generate strong external effect under
the current high level of high-skill labor stock. Strengthening investment on humancapital is another choice for Chinese government to deal with the problems in labor23market.
On the other hand, with the significant population aging, an increasing number of elderly
people with partial or full disabilities boosts the demand of establishment of long-termcare insurance system, which arises great social attention. For providing suggestions, we
research the Japanese LTCI for reference to China in the following chapter.

ReferenceV
V[1]Allen, Steven G., Robert L. Clark, and Ann McDermed, (1988) "Why do pensions
reduce mobility?." No. 2509. National Bureau of Economic Research.
[2]Cai, Fang, and Dewen, Wang, (2004) “Saving and Growth Effects of Demographic
Transition: The Population Factor in the Sustainability of China’s Economic Growth”,
Population Research, Vol. 28, pp.2-11. (in Chinese)[3]Cai, Fang, and Yang Lu, (2013) "Population change and resulting slowdown inpotential GDP growth in China." China & World Economy 21.2: 1-14.
[4]Cai, Fang, and Zhao Wen, (2012) "When demographic dividend disappears: growthsustainability of China." The Chinese Economy. Palgrave Macmillan UK, pp.75-90.
[5]Chen, Cheng, (2016) “China’s Social Security Expenditure: Problems and Thinking”,
Journal of Social Sciences, No.7 pp.25-34. (in Chinese)[6]Du, Yang, and Cuifen Yang, (2014) "Demographic transition and labour market
changes: implications for economic development in China." Journal of Economic
Surveys 28.4: 617-635.
[7]Jiang, Zhenhua, et al,. (2013) “Analysis of Long Term Care of Elders in Mainland
China”, Nursing Science, No.2, pp.46-50. (in Chinese)[8]Justin, Yifu, Lin, Fang, Cai, and Zhou, Li, (1995) The China Miracle: development
strategy and economic reform, Chinese University Press(HK). (in Chinese)[9]Heckman, James J., and Junjian Yi, (2012) “Human capital, economic growth, andinequality in China.” No. w18100. National Bureau of Economic Research.
[10]Patricia, P. Martin and Weaver, David A., (2005) , “Social Security: A Program and24

Policy History”, Social Security Bulletin, Vol. 66, pp.1-15.
[11]Shi, Yaojia, et al., (2015) “Dropping Out of Rural China's Secondary Schools: A
Mixed-Methods Analysis”. The China Quarterly, Vol. 224, pp.1048-1069.
[12]Yin, Jinpeng. Fuxing, Liu and Mo, Han, (2016) “The Regional Disparity ofConvergence Analysis of Social Security in China: An Empirical Research Based on
Provincial Data 1990-2013”, Shanghai Economic Review, No.1, pp.82-91. (in Chinese)[13]Zhang, Xiaobo, et al,. (2011) "China has reached the Lewis turning point." China
Economic Review 22.4: 542-554.
[14]Zhang, Jie, (1995)"Social security and endogenous growth." Journal of Public
Economics 58.2: 185-213.
[15]Zhang, Jie, and Junsen Zhang, (2003) "Long-run effects of unfunded social security
with earnings-dependent benefits." Journal of Economic Dynamics and Control28.3:
617-641.
[16]Zheng, Gongcheng, (2013) “The Historical Logic of the Evolution of China’s Social
Security History”. Journal of Renmin University of China, No.1, pp.2-12 (in Chinese)[17]Zhong, Shiying, and Kui, Li, (2009) “Study on the relation between population
dividend and economic growth, Population and Economics”, Vol. 173, pp.55-59. (inChinese)[18]CNBS, China Statistical Yearbook, various years.
[19]CNBS, China Migrant Workers Monitoring Report 2015,
http://www.stats.gov.cn/tjsj/zxfb/201604/t20160428_1349713.html.
[20]The World Bank, http://databank.worldbank.org/data/databases.aspx.
[21]United Nations, Department of Economic and Social Affairs, Population Division(2015). World Population Prospects: The 2015 Revision, custom data acquired via
website.
[22]OECD, Education at a Glance (2015): OECD Indicators, OECD Publishing, Paris.
DOI: http://dx.doi.org/10.1787/eag-2015-en page 39.
[23] Ministry of Health, labor and welfare of Japan, “Worldwide Annual Health, Laborand Welfare Report 2015”[24] “Skills Shortages in the Chinese Labor Market” by JPMorgan, 2016.
25

[25] “Modernising and Improving Social Protection in the European Union”. European
commission, 1997.

26

Chapter 2. Dynamic Analysis of the Regional Differences inJapanese LTCI System
In this chapter, we review the Japanese LTCI system and study the problem of expanding
regional differences of user rate in order to provide policy guideline for China. We findeach Japanese region’s user rate exhibits a conditional convergence as well as its groupsof regions’ user rate. Furthermore, we show the reform implemented in 2005, which isused to remedy the regional differences, seems to have had little effect. Relevant policy
implication references for China are discussed.

2.1 Introduction
With the population aging and weakening of the family care function, rapid increasing
demand of aged care is an important issue that has yet to be resolved for China. A pilot
program of the long-term care insurance (henceforth LTCI) system was implemented by
the Chinese government in 15cities from 2016 and gradually rolled out national wide in
future22. During this explorative process, it is meaningful by learning the international
experiences which will help to build up a relatively sufficient and sustainable LTCI
system.
Under this backdrop, numerous scholars have conducted a discussion from virous pointsof views. Yang et al. (2016) show three models of financing of institutional implemented
in 3 pilot cities of Qingdao, Nanjing and Shanghai, respectively. They find the model of
Qingdao is the most desirable even a narrow definition of eligibility. Wang and Tang
(2014) survey the commercial LTCI in U.S. and the social LTCI in Germany.
As Banister et al. (2012) point out that Japan is a highly relevant example for China,
since Japan is experiencing exceeding population aging and they have similar East Asian
culture. In order to meet the increasing demand for long-term care, Japan has launched asocial LTCI system in 2000, although the Japanese LTCI has eased the problem of
population aging, there appeared the “expanding cost” problem and the “large regional
22

For guiding opinions on conducting the pilot program of long-term care insurance
released by MHRSS, see
http://www.mohrss.gov.cn/gkml/xxgk/201607/t20160705_242951.html
27differences” problem during the process of the operation. Since the regional distributionof population aging and financial condition in China is extremely uneven. For instance,
according to the China Statistical Yearbook 2014, the ratio of aging in Chongqing is13.25% and that of Tibet is 5.17% in 2013. Meanwhile, the fiscal revenue per capita in
Beijing and Shanghai is 0.256 million RMB and 0.258 million RMB, whereas in Guangxi
this index is 0.027. By introducing Japanese LCTI, studying the dynamic properties of its
regional differences and trend of the development in this chapter, we hope to findmeaningful implications for China.
There are preceding researches on the dynamic properties of LTCI system. Some of themsought elements that affect the variables of interest, such as the service cost, the numberof service users, and the insurance premium, so as to predict the future trends of thesevariables. Others employed panel data to seek elements that explain the time and crosssectional variations in these variables. [Suzuki (2002), Shimizutani and Noguchi (2004),
Kikuchi, Tajika, and Yui (2005), and Kikuchi (2008) calculated the future trends of thelong-term care insurance system. Tajika and Kikuchi (2003), Shimizutani and Inakura(2006), Ando (2008), and the annual reports by the MHLW (2005, 2007) analyzed thecauses of regional differences in the system.] There are few researches, however, that takethe long-term care insurance system as a system of dynamical equations, as we do in thisresearch, so as to seek the proof of convergence (or non-convergence thereof), and toanalyze the degree of mobility in the standing order of regional user rates. The analytical
tools employed in this research are widely used in the field of endogenous economic
growth theory. These tools are useful and powerful for analyzing the dynamic propertiesof time and cross-sectional differences in socio-economic system23.
It will be shown that each region’s user rate converges to a unique and globally stablesteady state. If regions have different parameter values, however, then each region
converges to region-specific steady state (conditional convergence). Furthermore, it will23

For the concept and analytical methods of the convergence and the conditional
convergence, see Barro and Sala-i-Martin (2004). For the application of Markov
transition matrix analysis, see Quah (1993).
28

be shown that the theoretical model can replicate the motion of regional user rates
observed in actual statistical data. Additionally, we construct average Markov transition
matrixes to analyze each region’s mobility across the standing order of regional user rates.
We also evaluate if the 2005 reform made the standing order more variable because it
tried to remedy regional differences in user rates. It will be shown that the 2005 reform
seems to have had little effect on improving the regional mobility convergence. we try to
remove region-specific elements (the rate of care need certification by municipalities, thelate-stage (75 years or older) old age population rate, and the regional ordinary balancerate) from each region’s user rate, and reevaluated the effects of 2005 reform on theregional mobility to prove the convergence is conditional.
This chapter is organized as follows. In section 2.2, we briefly review the structure of
the public long-term care insurance system; In section 2.3, we construct a simple
theoretical model of the Japanese LTCI system. Then the model is analyzed to derive
dynamic properties of the system. In section 2.4, we construct average Markov transition
matrixes to analyze each region’s mobility across the standing order of regional user rates.
In section 2.5, we prove the mobility of each region’s user rate is conditional convergence
reevaluated the effects of 2005 reform on the regional mobility. Section 2.6 is conclusion
and reference for China. We note the remaining issues in section 2.7.

2.2 The LTCI System in Japan; A Quick Review.
2.2.1 The Objective of the LTCI Care Insurance System
The LTCI system started on April 2000. Before that, in traditional Japan, the cares for
elderly people were thought to be done by family members, especially by wives. Such
tradition became unsustainable because of rapidly aging demographic structure andincreasing nuclear families. The increase in those who need long-term care relative tothose who provide put physical and psychological pressures on many families. On theother hand, medical resources were used up by those who were not ill or sick but without
enough care by family members. (The hospitalization by sociological reasons. According
to the OECD health statistics, the average length of stay of Japanese inpatients is 31.2
days (2012), while the numbers are 10.1 days in France (2012), 9.2 days in Germany29

(2012), 7.2 days in the United Kingdom (2012), and 6.1 days in the United States (2011).)It became inevitable that the long-term care services for elderly people go public.
The new system replaced public welfare system for elderly people with public insurance
system in which municipalities take role as managers. Those who contribute to theinsurance system are the primary individuals (65 years or older) and the secondary insured
individuals (40~64 years old). The national average monthly insurance premium paid bya primary insured individual is ¥4972 in 2014 fiscal year. The insurance premium of thesecondary insured individuals is collected as part of payroll tax. For example, in 2013 fy,
it is 1.55% of the salary of those covered by the health insurance association for
medium&small firms. The main beneficiaries are the primary insured individuals. The
secondary insured individuals also receive benefits, but in limited cases. In 2014 fy, thetotal cost for the long-term care services was ¥10 trillion. The service users paid 10% user
fee. (The fee varies with user’s income level.) After subtracting ¥0.7 trillion user fee, theremaining ¥9.3 trillion are financed by the insurance premium contributions and the
public (national and local) disbursement shared at 50:50.
2.2.2 Application Process for the Long-Term Care Services
For a primary insured individual, the application process for care services consists of thefollowing 3 steps.
Step 1: When a primary insured individual finds herself in need for long-term careservices, she applies for the certification of long-term care need by her municipality(insurer).
Step 2: The municipality, aided by committee members, decides if it grants thecertification to the applicant. (Depending on the necessity, from light to the most serious,
there are 7 levels of the certification.)
Step 3: If granted, the primary insured individual, aided by “care managers” about careplans, receives services where the recipient pays 10% user fee. The long-term careservices are provided by private sector business entities subject to public supervision.
There are in-home services, facility services, and community-based services.
2.2.3 The Figures of the LTCI System
As stated in the introduction, along with rapidly aging demographic structure, the figures30

related to the public long-term care insurance system have been increasing too. The
followings are some figures reported by the MHLW to grasp the magnitude.
* Total cost: ¥3.6 trillion (2000 fy) Æ ¥10.0 trillion (2014 fy) (+170%)* The number of individuals certified by municipalities for long-term care need: 2.18
million (2000 fy) Æ 5.64 million (2013 fy) (+159%)* The number of service users: 1.49 million (2000 fy) Æ 4.71 million (2013 fy) (+216%)* The national average monthly insurance premium of primary insured individual: ¥2911(2000 fy) Æ¥4972 (2014 fy) (+71%)
Because the system is managed by municipalities, there are regional differences in the
figures. For example, the monthly insurance premium at the municipal level for the 6 thplanning period (2015~2017 fy), the highest number is ¥8686 (Tenkawa village of Naraprefecture) which is 3.1 times higher than the lowest ¥2800 (Mishima village ofKagoshima prefecture). At the prefecture level, the highest is ¥5880 of Okinawa which is
1.3 times higher than the lowest ¥4409 of Tochigi.
2.2.4 The Causes of Regional Differences and the 2005 Reform
Many researches addressed the causes of the differences in the regional figures of LTCI
system. Suzuki (2002) reported that a region with higher certification rate and the faster
growth in those who need long-term care tends to have the faster growth in in-homeservice cost. The MHLW stated in 2007 annual report that faster increase in those whorequest for light support and care and faster increase in those who use in-home services
cause faster increase in municipal certifications and care service users. Tajika and Kikuchi(2006) suggested that lax discipline on municipal management, incomplete task division
between medical services and care services, and ineffectiveness of care services on
rehabilitating users may explain the speed of increase in long-term care services. Ando(2008) found that regions with more low-income individuals and more late-stage (75years or older) old individuals have higher long-term care service cost. Tajika and Kikuchi(2003), the MHLW annual report (2005), and Abrai (2006) found that a region with more
facilities tends to have higher cost because it induces more demand for facility services(which cost more relative to in-house services). These researches suggest the importanceof {shift from facility to in-home services, rigorous discipline on municipal management,
31

prevention against long-term care need}.
In accordance with the implications of these researches, Japanese government took thefollowing measures to remedy the regional differences in the 2005 reform.
*Tighter municipal discipline on the review process for certification.
* Less biased distribution of facilities across regions by limiting the total number.
* Induce private business entities to supply relatively more in-home services to thoseusers with medium serious conditions.
* Facility service users are made to pay residence and meal cost.
* Introduce community-based services that aim to prevent elderly people from being inneed for long-term care.
In the following sections, we will analyze the dynamic properties of regional
differences in long-term care insurance system and the effect of the 2005 reform.

2.3 Theoretical Model Analysis of the LTCI System
As we saw in the previous section, there are wide differences in regional figures of the
LTCI system. It is important to predict the future trend of the system because it helps
those who have concerns in the system. For example, the prediction will help
municipalities as insurers to evaluate the fiscal impact of the system, which consequently
will affect insured individuals. For this purpose, we construct a theoretical model of the
public long-term care insurance system and analyze dynamical properties of “user rate”
which is defined as the ratio of service users among insured individuals. The theoreticalmodel will be used to derive a convergence hypothesis with respect to regional user rates.
2.3.1 Theoretical Model Analysis
The Japanese LTCI system will be modeled as follows. There are I = 47 regions(prefectures). For { i = 1, 2, … , I , t = 0, 1, 2, … }, let Li , t be the number of primary
insured individuals (65 years or older) of region i in period t . In the following, theregion subscript “ i ” will be omitted unless necessary. Let n be the gross rate of change
in the number of primary insured individuals, reflecting the number of those who were
64 years old in the previous period and the number of those who moved from otherregions. Let Ɂ be the “depreciation” rate of primary insured individuals, reflecting the32

number of deceased and the number of those who moved to other regions. Then, the net
growth of the number of primary insured individuals is expressed as follows.

Li , t  1 = (1 + n - G ) Li , t , t = 0, 1, 2, …

(2.1)

Suppose the LTCI system is introduced at the beginning of period zero. Let ܺ଴ be thenumber of service users. Under the current system, ܺ଴ is determined through thefollowing 4 steps.
Step 1: Let ‫ ݌‬be the probability that an insured individual find herself in need for longterm care services (need for care rate). Then at ‫ ݐ‬ൌ Ͳ , among the primary insured
individuals‫ܮ‬଴ , ‫ ݌‬ൈ ‫ܮ‬଴ is the number of individuals who find themselves in need for longterm care services. (ͳ െ ‫ܮ×)݌‬଴ is the number of individuals who do not.
Step 2: Let q be the probability of applying for municipal certification for long-term careneed by an individual in step 1 (application rate). Then, ‫ ݍ‬ൈ ‫ ݌‬ൈ ‫ܮ‬଴ is the number ofindividuals applying for the municipal certifications. ሺͳ െ ‫ݍ‬ሻ ൈ ‫ ݌‬ൈ ‫ܮ‬଴ is the number ofindividuals not applying.
Step 3: Let ‫ ݎ‬be the probability that a municipality as insurer grants certification to an
applicant in step 3. Then, ‫ ݎ‬ൈ ‫ ݍ‬ൈ ‫ ݌‬ൈ ‫ܮ‬଴ is the number of individuals who are granted
municipal certifications (certification rate). ሺͳ െ ‫ݎ‬ሻ ൈ ‫ ݍ‬ൈ ‫ ݌‬ൈ ‫ܮ‬଴ is the number ofindividuals who are not granted.
Step 4: Let s be the probability that an individual with municipal certification use public
long-term care service (net user rate). Then ‫ ݏ‬ൈ ‫ ݎ‬ൈ ‫ ݍ‬ൈ ܲ ൈ ‫ܮ‬଴ is the number of those
who use services. ሺͳ െ ‫ݏ‬ሻ ൈ ‫ ݎ‬ൈ ‫ ݍ‬ൈ ‫ ݌‬ൈ ‫ܮ‬଴ is the number of those who do not.
As a result of step 1~step 4, in a region at ‫ ݐ‬ൌ Ͳ , the number of individuals who use
public long-term care services isܺ଴ ൌ ‫ܮݏݎݍ݌‬଴(2.2)

The rest ‫ܮ‬଴ െ ܺ଴ ൌ ሺͳ െ ‫݌‬ሻ‫ܮ‬଴ ൅ ሺͳ െ ‫ݍ‬ሻ‫ܮ݌‬଴ ൅ ሺͳ െ ‫ݎ‬ሻ‫ܮ݌ݍ‬଴ ൅ ሺͳ െ ‫ݏ‬ሻ‫ܮ݌ݍݎ‬଴ is thenumber of individuals who do not use public long-term care service. Instead, they will
choose from such alternatives as private care services, public or private medical services,no services at all and stay as they are, etc. Figure 2.1 depicts the flow process that
determinesܺ଴.
33

Figure 2.1

In the next period t = 1, the number of service users ܺଵ is calculated as follows. The
number of primary insured individuals in ‫ܮ‬ଵ is decomposed as follows.
‫ܮ‬ଵ ൌ ሺͳ ൅ ݊ െ ߜሻ‫ܮ‬଴ ൌ ݊‫ܮ‬଴ ൅ ሺͳ െ ߜሻሺ‫ܮ‬଴ െ ܺ଴ ሻ ൅ ሺͳ െ ߜሻܺ଴(2.3)

In (2.3), ݊‫ܮ‬଴ is the number of new primary insured individuals,ሺͳ െ ߜሻሺ‫ܮ‬଴ െ ܺ଴ ሻ is thesurvivors among non-users, and ሺͳ െ ߜሻܺ଴ is the survivors among service users. The
logic used to derive ܺ଴ in t = 0 is also applicable to derive ܺଵ as follows. Among the newprimary insured individuals, ‫ ݏݎݍ݌‬ൈ ݊‫ܮ‬଴ individuals use services in ‫ ݐ‬ൌ ͳ. Among thesurviving non-users, ‫ ݏݎݍ݌‬ൈ ሺͳ െ ߜሻሺ‫ܮ‬଴ െ ܺ଴ ሻ individuals use services in t = 1.
Therefore, the number of service users ܺଵ is calculated as follows.
X1= p q r s n L0 + p q r s (1 - G )( L0 - X 0 )+ (1 - G ) X 0= (1 - G )(1 - p q r s ) X 0 + p q r s L1

(2.4)

Equation (2.1) is used to derive the last line. (In the derivation of (2.4), we assumed thatonce an individual begins to use long-term care services, the individual keeps using theservices in subsequent years. This assumption reflects the observation by Tajika andKikuchi (2006) about the inability of LTCI to rehabilitate individuals under care. If
insured individuals go back and forth between “under care” state and “out of care(rehabilitated)” state, then the dynamical analyses will be much more complex, andbeyond the scope of this research.) Equation (2.4) holds in any year t = 0, 1, 2, …, Define
the user rate ‫ݔ‬௧ by34‫ݔ‬௧ = X t / Lt .

(2.5)

By dividing both sides of equation (2.4) by ‫ܮ‬௧ , we have the following linear first-orderdifference equation with respect to user rate ‫ݔ‬௧ .

xt  1 = §¨¨ (1  G ) (1  p q r s ) ·¸¸ xt + p q r s©

1 n G(2.6)¹

Equation (2.1) is used again to derive (2.6). If { p , q , r , s , n , G } are constantparameters, then in (2.6), the slope is Ͳ ൏ ሺͳ െ G ሻሺͳ െ p q r s ሻΤሺͳ ൅ ݊ െ ߜሻ ൏ ͳ .
Therefore, the dynamical system (2.6) is globally stable. That is, for any ‫ݔ‬௧ ൐ ͳ, thesequence of user rate {‫ݔ‬௧ ; t = 0, 1, 2, …,} monotonically converges to a unique steadystate ‫ כ ݔ‬where‫ = כ ݔ‬p q r s /[1 - {(1 - G )(1 - p q r s )/(1 + n - G )}].

(2.7)

In addition, it can be shown that, for any two regions i and j,
if xi , 0§ !·¨ ¸
¨ ¸ x j , 0 , then
¨ ¸
© ¹

§ ·

xi , t  1  xi , t ¨ ¸ x j , t  1  x j , t

¨ ¸
¨ !¸
© ¹

xi , txj,t, t = 0, 1, 2, … ,(2.8)
These observations imply that the regional user rates {‫ݔ‬௜ǡ௧ ; i = 1, 2, … , I, t = 0, 1, 2, … }exhibit “convergence” to the same steady state ‫ כ ݔ‬if all the regions have the same valuesof parameters ሼ‫݌‬ǡ ‫ݍ‬ǡ ‫ݎ‬ǡ ‫ݏ‬ǡ ݊ǡ ߜሽ .
The values of parameters, however, may be different across regions. For example, the
MHLW 2005 annual report documented the regional differences in municipal certification
rate r. We also expect that the parameter values are region-specific because of various
socio-economic reasons. If the parameter values in equation (2.6) are different acrossregions, then each region’s user rate‫ݔ‬௜ǡ௧ may converge to region-specific steady state ‫ݔ‬௜ ‫ כ‬.
That is, the user rate convergence is conditional on each region’s parameter values. In thenext section, we analyze the data of regional user rates to investigate the following two
hypotheses;[(Unconditional) Convergence Hypotheses] All the regional user rates {‫ݔ‬௜ǡ௧ ; i = 1, 2, … ,I, t = 0, 1, 2, … } converges to the same steady state‫ כ ݔ‬.
35

[Conditional Convergence Hypotheses] Each regional user rates {‫ݔ‬௜ǡ௧ ; i = 1, 2, … , I, t
= 0, 1, 2, … } converges to the region-specific steady state ‫ݔ‬௜ ‫ כ‬.
We add some comments on the dynamic properties of equation (2.6). The government
reviews the LTCI system and conduct major reforms at every five years. For example, the2005 reform may have affected the dynamical system (2.6) as follows.
( ) The 2005 reform made the facility service users pay residence and meal cost. Thischange might have depressed the demand for long-term care services, and hence lowered
the net user rate s.
( ) The 2005 reform enhanced the efforts of preventing insured individuals from beingin need for long-term care services. The prevention efforts might have lowered the needfor care rate p.
( ) The 2005 reform imposed more rigorous discipline on the review process forcertification by municipalities. This might have lowered the certification rate r.
( ) As the number of service users increases, the LTCI system may gain wider societal
recognition. As a result, those who previously regarded the public long-term care services
as public welfare with some stigma will be less reluctant to apply for the services. The
prevalence of the system, hence, may increase the application rate q. (The traditional view
about long-term care for elderly people may change as service users increase and as
people learn more about the system. In this case, the application rate q in equation (2.6)
may not be a constant parameter, but dependent on user rate ‫ݔ‬௧ . If it is so, then equation(2.6) is no longer a linear equation. Instead, equation (2.6) may generate a complex pathfor the use rate sequence {‫ݔ‬௧ ; t = 0, 1, 2, …}.
( ) The differences in LTCI system across municipalities may induce each insured
individual to seek a region with better services and lower cost. This may affect eachregion’s net growth rate ݊ െ ߜ of insured individuals.
By differentiating the steady state user rate ‫( כ ݔ‬equation (2.7)) with respect to theparameters ሼ‫݌‬ǡ ‫ݍ‬ǡ ‫ݎ‬ǡ ‫ݏ‬ǡ ݊ǡ ߜሽ, we verify the following comparative static properties.












x *( p , q , r , s , n , G )(2.9)

In (2.9), the “+” or “-” sign above each parameter indicates the effect of an increase in36the parameter value on the steady state user rate‫ כ ݔ‬. An increase in the need for care ratep, an increase in the application rate q, an increase in the certification rate r, or an increasein the net user rate s obviously causes the steady state user rate ‫ כ ݔ‬to increase. Although
the net growth rate of primary insured individuals is expressed as ݊ െ ߜ, an increase in
the gross growth rate n or an increase in the depreciation rate ߜ causes ‫ כ ݔ‬to decrease
because of the following reasons. An increase in the gross growth rate n causes the steadystate value of the user rate ‫ݔ‬௧ =ܺ௧ Τ‫ܮ‬௧ to decrease simply because of the faster increase indenominator ‫ܮ‬௧ . On the other hand, the increase in the depreciation rate ߜ has two effects
on the steady state user rate ‫ כ ݔ‬. While it causes the number of primary insured individuals
to decrease, it also causes the number of surviving service users to decrease. The latter
effect dominates the former because the latter works at the cumulative stock level while
the former at the flow level.
Figure 2.2 is a phase diagram of equation (2.6). The horizontal axis measures ‫ݔ‬௧ andthe vertical axis measures ‫ݔ‬௧ାଵ. If the parameters ሼ‫݌‬ǡ ‫ݍ‬ǡ ‫ݎ‬ǡ ‫ݏ‬ǡ ݊ǡ ߜሽ are constant, then thegraph of (2.6) is depicted as an upward-sloping straight line with intercept pqrs at thevertical axis. Because the slope is Ͳ ൏ ሺͳ െ G ሻሺͳ െ p q r s ሻΤሺͳ ൅ ݊ െ ߜሻ ൏ ͳ , thedynamical system (2.6) has a unique and globally stable steady state at the intersection of
the graph of (2.6) and 45-degree line in figure 2.2. That is, given any initial user rate ‫ݔ‬଴ ൐Ͳ, the sequence of user rate {‫ݔ‬௧ ; t = 0, 1, 2, … } generated by equation (2.6) monotonicallyconverges to the steady state user rate ‫ כ ݔ‬. Furthermore, if the initial user rate ‫ݔ‬௜ǡ଴ ofregion i is smaller than ‫ݔ‬௝ǡ଴ of region j, then the growth rate of region i’s user rate is larger
than that of region j for all the subsequent periods, i.e.,
if ‫ݔ‬௜ǡ଴ ൏ ‫ݔ‬௝ǡ଴ , then௫೔ǡ೟శభ ି௫೔ǡ೟௫೔ǡ೟൐௫ೕǡ೟శభ ି௫ೕǡ೟

(2.10)37௫ೕǡ೟

t = 0, 1, 2, … ,Figure 2.2

The effects of changes in the value of parameters ሼ‫݌‬ǡ ‫ݍ‬ǡ ‫ݎ‬ǡ ‫ݏ‬ǡ ݊ǡ ߜሽon the steady state userrate ‫ כ ݔ‬can be analyzed by using figure 2.2. In the figure, an increase in the need for care
rate p, an increase in the application rate q, an increase in the certification rate r, or an
increase in the net user rate s causes the vertical intercept pqrs to increase and the slopeሺͳ െ G ሻሺͳ െ p q r s ሻΤሺͳ ൅ ݊ െ ߜሻ to decrease. The combined effect is a rise in theintersection of the graph of (2.6) and 45-degree line, i.e., an increase in the steady stateuser rate ‫ כ ݔ‬. An increase in the gross growth rate n or an increase in the depreciation rateߜ does not affect the vertical intercept ‫ ݏݎݍ݌‬. However, it causes the slopeሺͳ െ G ሻሺͳ െ p q r s ሻΤሺͳ ൅ ݊ െ ߜሻ to decrease. As a result, the intersection of the graphof (2.6) and 45-degree line decreases, i.e., the steady state user rate ‫ כ ݔ‬decreases. Thesestatements

are

also

verifiedbysimplecalculus.

For

example,ଶ߲ൣሺͳ െ G ሻሺͳ െ p q r s ሻΤሺͳ ൅ ݊ െ ߜሻ൧Τ߲ߜ ൌ െ ሺͳ െ ‫ݏݎݍ݌‬ሻ݊Τ൫ሺͳ ൅ ݊ െ ߜሻ൯ ൏ Ͳprovided ݊ ൐ Ͳ.
Table 2.1 summarizes the effects of the 2005 reform on the steady state user rate ‫ כ ݔ‬.
The table suggests that the 2005 reform tried to stabilize the fiscal management of public
long-term care insurance system against rapid increase in service users and service cost.
38

Table 2.1

2.3.2 Numerical Example
Panel A of figure 2.3 depicts transitional paths of two regions, a and b, such that theinitial user rate of region a, ‫ݔ‬ሺܽǡ Ͳሻ, is smaller than that of region b, ‫ݔ‬ሺܾǡ Ͳሻ. In addition,
we assume that both of them are smaller than the steady state user rate ‫ כ ݔ‬, i.e., ‫ݔ‬ሺܽǡ Ͳሻ ൏‫ݔ‬ሺܾǡ Ͳሻ ൏ ‫ כ ݔ‬. The parameter values are same for both regions, set at {p = 0.25, q= 0.8, r=
0.15, s= 0.8, n = 0.1, Ɂ= 0.05}. Given these values, equation (2.7) implies the steadystate user rate ‫ = כ ݔ‬0.2052. The initial user rates are set at ‫ݔ‬ሺܽǡ Ͳሻ ൌ ͲǤͳand‫ݔ‬ሺܾǡ Ͳሻ ൌͲǤͳͷ . Panel B of figure 2.3 depicts the growth rates of two regions{[‫ݔ‬ሺܽǡ ‫ ݐ‬൅ ͳሻ െ ‫ݔ‬ሺܽǡ ‫ݐ‬ሻΤ‫ݔ‬ሺܽǡ ‫ݐ‬ሻ], [‫ݔ‬ሺܾǡ ‫ ݐ‬൅ ͳሻ െ ‫ݔ‬ሺܾǡ ‫ݐ‬ሻΤ‫ݔ‬ሺܾǡ ‫ݐ‬ሻ]; t = 0, 1, 2, … }. Thesefigures show that the transitional paths of user rates generated by the dynamical system(2.6) monotonically converge to the steady state, and the growth rate of user rate is higher(lower) for the region with lower (higher) initial user rate.
Panel A of figure 2.4 depicts the effects of a change in parameter value on the transitional
path of user rates. For periods t = 0, 1, 2, … , 10, we assume the same assumptions as
before, i.e., {p = 0.25, q= 0.8, r= 0.15, s= 0.8, n= 0.1, ߜ= 0.05} and {‫ݔ‬ሺܽǡ Ͳሻ = 0.1,
‫ݔ‬ሺܾǡ Ͳሻ = 0.15}, hence ‫ = כ ݔ‬0.2052. We also assume that at t = 11 the application rate q
increases from 0.8 to 0.9 and stays at the higher value thereafter which implies the newsteady state ‫ = כ ݔ‬0.2817. Panel A of figure 2.4 shows that the transitional paths, at thetime of shock t = 11, begin to converge to the new and higher steady state. As depictedby panel B of figure 2.4, the change causes a temporary increase in growth rates of both39

regions.

Figure 2.3{Vertical axis: x, Horizontal axis: t}

Figure 2.4{Vertical axis: x, Horizontal axis: t}

2.3.3 Data Properties
In this section, we look at the data of public long-term care insurance system for the40

properties of average user rate and regional differences. For the analyses, we use the data
provided by the Japan Ministry of Health, Labor, and Welfare. There are cautions on
interpreting the data. See appendix at the end of paper for details.
In figure 2.5, panel A depicts the graph of average user rate of 47 Japanese regions(prefectures), and panel B depicts the graph of growth rate of average user rate. Thesegraphs show that the average user rate increased between 2000 and 2005 at diminishinggrowth rate. After the temporal decline in 2006 and 2007, the average user rate began togrow again, but at diminishing growth rate. There seems to be a structural change before
and after the 2005 reform. Figure 2.6 is the graph of coefficient of variation of the regionaluser rates, and figure 2.7 is the graph of max/min ratio of the regional user rates. The
coefficient of variation slightly increased between 2000 and 2005. After 2006, it did notshow clear trend. The max/min ratio, on the other hand, showed declining trend
throughout the data periods. (The spikes in figure 2.6 and figure 2.7 are caused byirregular movement in Niigata’s user rate which plummeted in one and only one year
2007.) Figure 2.8 depicts the graph of Gini coefficient of the regional user rates. Like
figure 2.7 which depicts the graph of max/min ratio, the Gini coefficient showed declining
trend throughout the data periods, suggesting the diminishing regional differences in userrates.

Figure 2.5

41Figure 2.6

Figure 2.7

42Figure 2.8

Next, in order to analyze the variations in the standing order (high and low) of regionaluser rates, we sorted the 47 regions (prefectures) according to each region’s user rate, anddivided them into 5 groups {I(7 regions), II(10), III(10), IV(10), V(10)}. Group I consistof 7 regions with the highest user rates, group II consists of 10 regions with second highest
user rates, and so on. Group V consists of 10 regions with the lowest user rates. Then, for2000~2012, we calculated the mean user rate and the annual rate of change for each group.
The results are summarized in table 2.2. The table reveals the following properties;( i ) The movement of each group’s use rate resembles the movement of the average userrate. That is, they grew but at diminishing rate between 2000 and 2005, declined
temporarily in 2006 and 2007, then started to grow again after 2008 at diminishing rate.
There seems to be a structural change before and after the 2005 reform.
( ii ) In the first half (2000~2005),the years before the 2005 reform, the higher (lower)
is a group’s user rate, the slower (faster) is the subsequent growth of the group’s user rate,i.e., the regional user rates seem to converge. For example, in 2000, group I’s user rate is
2.43 and group V’s use rate is 1.62. Between 2000 and 2001, the rate of change in group
I’s user rate is 0.27 while that of group V is 0.31. Between 2000 and 2005, the average43annual growth rates are higher (lower) for the groups with lower (higher) user rate. Sucha convergence in regional user rates is not so obvious in the second half (2006~2012), theyears after the 2005 reform, although it seems to hold for the groups with higher userrates. In figure 2.9, panel A depicts the graphs of group I’s user rate and group V’s user
rate, and panel B depicts the graphs of growth rate of group I’s user rate and that of group
V’s user rate. Compare and notice the resemblance between figure 2.9 (actual data) andfigure 2.4 (calibrated data). The comparison of these figures seems to suggest that theconvergent paths of user rates were affected by the 2005 reform. The 2005 reform might
have altered the steady state, and initiated convergence to the new steady state.

Table 2.2

44

Figure 2.9

Although the regional user rates seem to exhibit a convergence property, it might not be
an unconditional convergence. As we saw in the theoretical model analysis of the user
rate, if each region has different parameter values, then each region’s user rate may
converge to region-specific steady state. If the convergence is conditional on regionspecific elements, then the standing order (high and low) of regional user rates may not
be variable. In fact, as shown in table 2.3, which is a list of 5 regions (prefectures) withthe higher user rates and 5 regions with the lowest between 2000 and 2012, there was asmall degree of variation in the standing order. For example, Wakayama, Tokushima, andHiroshima belonged to the top 5 regions for all but 3 years between 2000~2012.
Especially, Wakayama had the highest user rate in 2003 and 2005, and for all the years inthe second half (2006~2012). On the other hand, Tochigi, Ibaraki, Chiba, and Saitama, allof them are located in Kanto area, belonged to the bottom 5 regions for all the sample
years.

45

Table 2.3

Despite the small variation in the standing order of regional user rates, the 2005 reformmight have affected each region’s mobility across the ladder of standing order because its
objective is to remedy the regional differences. Therefore, if the reform had the implied
effects, if any, we could expect the increased mobility of the standing order in the second
half (2006~2012) relative to the first half (2000~2005). The objective of the next section,
hence, is to evaluate if the 2005 reform did remedy the regional differences and alleviatedthe standing order inertia.

2.4 Mobility Analysis of Regional User Rates’ Standing OrderIn this section, we develop an index for measuring the degree of regions’ mobility acrossthe ladder of user rates standing order (high and low) to see if the 2005 reform had theimplied effects. The index, which is based on Markov transition matrixes, is calculatedby the following 4 steps.
Step 1: Let {‫ݔ‬ሺ݅ǡ ‫ݐ‬ሻ; i = 1, 2, … , 47, t = 2000, 2001, … , 2012} stands for the user rate46

of region i in year t. For each year t, {‫ݔ‬ሺ݅ǡ ‫ݐ‬ሻ; i = 1, 2, … , 47} is sorted from the highest
to the lowest, and divided into 5 groups {I(7 regions), II(10), III(10), IV(10), V(10)} as
we did in 2.2.3.
Step 2: We construct a Markov transition matrix of size 5×5 from 2000 to 2001, denotedas ܲ଴ǡଵ, as follows. The (1, 1) element of the matrix, denoted asܲ଴ǡଵ (1, 1), is the numberof regions of group I in 2000 that remained in group I in the next year 2001 divided by
the group size (7 regions). For example, among seven regions of group I in 2000, if two
regions move to the other groups while five regions stay, then ܲ଴ǡଵ (1, 1) = 5/7. The otherelements {ܲ଴ǡଵ ሺͳǡ ݆ሻ; j = 2, 3, 4, 5} of the first row of ܲ଴ǡଵ imply the number of regionsof group I in 2000 that moved to group j in 2001 divided by group I’s size. Generally, we
denote {ܲ௧ǡ௧ାଵ ሺ݅ǡ ݆ሻ; i, j = 1, 2, 3, 4, 5, t =2000, 2001, … , 2011} as the number ofregions of group i in year t that moved to group j in year t+1divided by group i’s size.
Step 3. We calculate the average Markov transition matrixes for the first half by:
2004

PA = (1 / 5 )¦P(2.11)t , t 1t

2000

and for the second half by
2011

PB = (1 / 7 )¦Pt , t 1t.

(2.12)

2005

The average Markov transition matrixes {ܲ஺ , ܲ஻ } have the following properties.
( i ) By construction, the five elements of each row of ܲ௧ǡ௧ାଵ add up to one, i.e.,5¦Pt , t 1

( i , j ) = 1 for all i ‫{א‬1, 2, 3, 4, 5} and for all t ‫{א‬2000, 2001, … , 2011}.

j 1(2.13)
By the definition, the same property also holds for the average Markov transition
matrixes {ܲ஺ , ܲ஻ }. This implies that {ܲ஺ , ܲ஻ } are probability matrixes.
( ii ) For k = 1, 2, 3, … , the k-th powered average Markov transition Matrixes {ሺܲ஺ ሻ௞ ,ሺܲ஻ ሻ௞ ; k = 1, 2, 3, … } are also probability matrixes. We use the average Markov
transition matrixes to evaluate the degree of variation in the standing order of regionaluser rates as follows. Suppose, although counter factual, there was no variation in the47standing order of regional user rates in the first half, i.e., no region moved from one groupto the others in any years between 2000 and 2005. Then, each Markov transition matrix{ܲ௧ǡ௧ାଵ ; t = 2000, 2001, … , 2004} is a 5×5 unit matrix, so are the average matrix ܲ஺ andits k-th power {ሺܲ஺ ሻ௞ ,; k = 1, 2, 3, … }. On the other hand, if there are regions that moved
from one group to the others in the first half, then some of the Markov transition matrixes
have non-zero non-diagonal elements, so does the average matrix ܲ஺ . In this case, eachrow of the k-th powered average Markov transition Matrixሺܲ஺ ሻ௞ , may converge to the“uniform” distribution {7/47, 10/47, 10/47, 10/47, 10/47} as k becomes larger. For
example, the first row of ሺܲ஺ ሻ௞ ,, denoted as {ሺܲ஺ ሻ௞ ሺͳǡ ݆ሻ; j = 1, 2, 3, 4, 5}, expresses the
hypothetical probability distribution for a region in group I’s whereabouts among 5groups k years later if the degree of variation in the first half continues. Then, theconvergence of the first row to the “uniform” distribution implies that, even if the degreeof variation in the standing order of regional user rates is small in the short run, it will bevariable in the long run. In which group a region will be in the long run is a random event
described by the “uniform” distribution.
Step 4: The degree of variation in the long run, may be different in the first half and thesecond half because of the 2005 reform which aimed to remedy the regional differencesin user rates. To compare the degree of variation before and after the 2005 reform, we
calculated the distances between each row of the k-th powered average Markov transition
matrixes {ሺܲ஺ ሻ௞ , ሺܲ஻ ሻ௞ ,; k = 1, 2, 3, … } and the “uniform” distribution as follows. For{k = 1, 2, 3, … , i = 1, 2, 3, 4, 5},k2k

VA ( k , i ) = [ ( PA ) ( i , 1) - (7/47) ] + [ ( PA ) ( i , 2 ) - (10/47) ]k2+ … + [ ( PA ) ( i , 5 ) - (10/47) ] ,k(2.14)2k

VB ( k , i ) = [ ( PB ) ( i , 1) - (7/47) ] + [ ( PB ) ( i , 2 ) - (10/47) ]k

2

2+ … + [ ( PB ) ( i , 5 ) - (10/47) ] .

2(2.15)For example, VA ( k , 1) is a distance between the first row of the k -th powered averagekMarkov transition matrixes ( PA ) and the “uniform” distribution {7/47, 10/47, 10/47,
10/47, 10/47}. Then, the standing order convergence of regional user rates in the first half48

and that in the second half may be defined as follows.
lim VA ( k , i ) = 0 for all i = 1, 2, 3, 4, 5

(2.16)

lim VB ( k , i ) = 0 for all i = 1, 2, 3, 4, 5

(2.17)k of

k of

We expect the quicker convergence in the second half than the first half if the 2005
reform had the implied effects.
By using the MHLW data, the average Markov transition matrixes of the first half andthe second half are calculated as follows.

0 ·00§ 0.81 0.19
¨
¸
0 ¸
0
¨ 0.133 0.733 0.133
PA = ¨ 00 ¸0.133 0.767 0.1¨¸
0
0.1 0.833 0.067 ¸
¨ 0
¨ 0
0
0 0.067 0.933 ¸¹©

(2.18)·¸¸
0.017 ¸¸
0.17 ¸
0.833 ¸¹

(2.19)

0§ 0.976 0.024 0¨
0¨ 0.017 0.933 0.05¨
PB =00.033 0.8 0.15¨
00.15 0.733
¨ 0
¨ 0
0.017
0
0.1
©

0
0

For example, the first row of PA implies that, on average between 2000 and 2005, fora region in group I, the probability of staying in group I after one year is 0.81, theprobability of moving to group II is 0.19, and the probability of moving to any othergroups (III, IV, or V) is zero. The squared average Markov transition matrix of the firsthalf is calculated as follows.

0 ·0§ 0.681 0.294 0.025¸¨
0 ¸¨ 0.206 0.581 0.2 0.013( PA )2 = ¨ 0.0178 0.2 0.616 0.16 0.007 ¸¸¨00.013 0.16 0.709 0.118 ¸¨¨0
0 0.007 0.118 0.876 ¸¹©

(2.20)

2

The first row of ( PA ) implies that, under the degree of standing order mobility in thefirst half, for a region in group I, the probability of staying in group I after two years is
0.681, the probability of moving to group II is 0.294, the probability of moving to group
III is 0.025, and the probability of moving to group IV or group V is zero. The six panels49kof figure 2.10 show the first row of ( PA ) for k = 1, 2, 3, 5, 10, and 100. Although aregion in group I tends to stay in group I for a short period of time, it may move to theother groups in the long run, and the probability distribution of being in groups I~V seems
to converge to the “uniform” distribution {7/47, 10/47, 10/47, 10/47, 10/47}.

Figure 2.10

50

The five panels of figure 2.11 show the graphs of { VA ( k , i ) , VB ( k , i ) ; k = 1, 2, 3, … ,i = 1, 2, 3, 4, 5}. For example, panel 1 shows the graph of the distance VA ( k , 1) betweenkthe first row of average Markov transition matrix { ( PA ) (1, j ) ; k = 1, 2, 3, … , j = 1,
2, 3, 4, 5} and the “uniform” distribution {7/47, 10/47, 10/47, 10/47, 10/47} for the firsthalf {2000, 2001, … , 2005} and the graph of VB ( k , 1) for the second half {2006,
2007, … , 2012} such that the horizontal axis measures the power { k = 1, 2, 3, …} andthe vertical axis measures { VA ( k , 1) , VB ( k , 1) }. We may infer the following propertiesof figure 2.11.
(ϸ) For the groups of regions with higher user rates (such as group I and group II), thespeed of convergence to the “uniform” distribution is faster in the first half than thesecond half. There is not much difference in the speed of convergence for group III. On
the other hand, for the groups of regions with lower user rates (such as group IV andgroup V), the order seems to be reversed, i.e., the speed of convergence is quicker in thesecond half than the first half.
(Ϲ) Both in the first half and in the second half, the speed of convergence is slower forthe groups of regions with higher user rates and for the groups of regions with lower userrates, and faster for the groups of regions with intermediate user rates.
(Ϻ) In the first half, group V’s speed of convergence is the slowest. It would take 7
years to close the distance by less than half, i.e., VA (1, 5 ) = 0.6533 and VA ( 7 , 5 ) =0.2961 < VA (1, 5 ) /2. For the other groups, it would take 3~4 years to close the distanceby less than half.
(ϻ) In the second half, group I’s speed of convergence is the slowest. It would take 16
years to close the distance by less than half, i.e., VB (1, 1) = 0.8559 and VB (16 , 1) =0.4159 < VB (1, 1) /2. For the other groups, it would take 3~6 years to close the distanceby less than half.

51

Figure 2.11

If the problems of public long-term care insurance system that originate from regional
differences are more serious in regions with higher user rates, then the 2005 reform does
not seem to be effective because the standing order mobility, measured by { VA ( k , i ) ,VB ( k , i ) ; k = 1, 2, 3, … , i = 1, 2, 3, 4, 5}, did not improve after the reform. The above

analyses seem to suggest that the standing order convergence is conditional because there
seem to remain persistent regional differences even after the 2005 reform. Each region’suser rate may be converging to region-specific steady state, and the standing order of52

regional user rates may exhibit small variation for the long periods of time. On the other
hand, if we are able to remove region-specific factors from the data, then the residual userrates may converge to the same steady state, and the standing order of residual user rates
may be more variable. This is what we will try to do in the next section.

2.5 Mobility Analysis of Standing Order based on Residual User
Rates
As we saw in the previous section, the standing order (high and low) of regional userrates did not seem to become variable after the 2005 reform which had aimed to alleviate
the immobility. As table 2.3 suggests, some regions in group I (consisting of regions withthe highest user rates) or group V (consisting of regions with the lowest user rates) do notseem to move to the other groups. Preceding researches suggest that the user rate
convergence may be conditional, i.e., each region’s user rate may converge to regionspecific steady state if each region has different parameter values. Hence, if we are able
to remove region-specific elements that cause the differences in regional user rates, theremaining (residual) use rates may converge to a common steady state. Therefore, we
regress each region’s user rate on the variables that might explain the regional differences,and use the regression residuals to recalculate the speed of convergence to the “uniform”
distribution. If the explanatory variables are able to account for the regional differencesin user rates, then the speed of convergence of residual user rates will be improved. As apreliminary attempt, we looked at preceding researches and chose the following three
explanatory variables; For region (prefecture) i = 1, 2, … , 47, and for year t = 2000,
2001, … , 2012, ݄ଵ ሺ݅ǡ ‫ݐ‬ሻ is the certification rate which may represent each region’s
administrative discipline, ݄ଶ ሺ݅ǡ ‫ݐ‬ሻ is the late-stage (75 years or older) old age population
rate, and ݄ଷ ሺ݅ǡ ‫ݐ‬ሻ is the ordinary balance rate which may represent the region’s fiscal
flexibility and robustness. (These data are available from the MHLW and the Ministry ofInternal Affairs and Communications.) For each t = 2000, 2001, … , 2012, we estimate
the following model.

݈݊ ‫ݔ‬ሺ݅ǡ ‫ݐ‬ሻ ൌ ܽ଴ ൅ ܽଵ ൈ ݈݊ ݄ଵ ሺ݅ǡ ‫ݐ‬ሻ ൅ ܽଶ ൈ ݈݊ ݄ଶ ሺ݅ǡ ‫ݐ‬ሻ ൅ ܽଵ ൈ ݈݊ ݄ଵ ሺ݅ǡ ‫ݐ‬ሻ ൅ ݁ሺ݅ǡ ‫ݐ‬ሻ,53

i = 1, 2, …, 47.

(2.21)In (2.21), ‫ݔ‬ሺ݅ǡ ‫ݐ‬ሻ is the user rate. After obtaining the OLS estimates of regression
parameters {ܽ଴ ,ܽଵ, ܽଶ , ܽଷ }, we use the (exponent of) regression residuals {݁ሺ݅ǡ ‫ݐ‬ሻ; i= 1, 2, … , 47, t = 2000, 2001, … , 2012} to calculate the speed of convergence before
and after the 2005 reform as we had done in the previous section. Table 2.4 summarizes
the regression results. The fitting of the statistical model (2.21) to the data is not so good.
Although the three variables {݄ଵ , ݄ଶ , ݄ଷ } together explain 70~80% of the variation in
the user rate ‫ ݔ‬, the only significant variable is the certification rate ݄ଵ . The ordinarybalance rate ݄ଶ is marginally significant. The late-stage old age population rate ݄ଷ isinsignificant.

Table 2.4

We used the regression residuals to calculate average Markov transition matrixes,
54denoted as PAR for the first half {2000, 2001, … , 2005} and PBR for the second halfkk{2006, 2007, … , 2012}. Then we used { ( PAR ) , ( PBR ) ; k = 1, 2, … } to calculate thedistances, denoted as { VAR ( k , i ) , VBR ( k , i ) ; k = 1, 2, 3, … , i = 1, 2, 3, 4, 5}, from the“uniform” distribution {7/47, 10/47, 10/47, 10/47, 10/47} for the first half and the second
half. The five panels of figure 2.12 show the graphs of { VAR ( k , i ) , VBR ( k , i ) ; k = 1, 2,
3, … , i = 1, 2, 3, 4, 5}. Even after adjusted for the region-specific factors, like { VA ( k , i ) ,VB ( k , i ) } for the unadjusted user rates shown in figure 2.12, the speed of convergenceof group I VAR ( k , i ) is faster in the first half than the second half VBR ( k , i ) , while theorder is reversed for group V.

Figure 2.12

The five panels of figure 2.13 plot and compare the adjusted distance for the first half
55

VAR ( k , i ) and the unadjusted distance VA ( k , i ) for the first half. Similarly, the fivepanels of figure 2.14 plot and compare the adjusted distance for the second half VBR ( k , i )and the unadjusted distance VB ( k , i ) for the second half. These figures show that for the
first half and the second half, and for all the 5 groups, the speed of convergence is faster
after adjusted for the region-specific factors. This implies that the convergence might
have been conditional, i.e., each region’s user rate, if unadjusted for region-specificfactors, is converging to region-specific steady state user rate.

Figure 2.13

56

Figure 2.14

It turned out as well, however, that the standing order of regional user rates, even after
being adjusted for region-specific factors, is not quite variable yet. Table 2.5 shows the 5regions with the highest residual user rates and the 5 regions with the lowest residual userrates between 2000 and 2012. The table shows that some regions still hardly change theirpositions in the standing order. For example, Hokkaido stays the 47th for all the sample
years but 2007, while Nagano stays the first for all but two years. These observations
suggest that there are factors other than the ones we chose (the certification rate, the latestage old age population rate, and the ordinary balance rate) that cause the regional57differences in user rates.

Table 2.5

2.6 References for China
By the end of 2014, the working age population (aged 15 ~ 64) of China was100,469,000, account for 73.4% of total population, falling from 2010. During the same
period, the aging population rate (ratio of population aged 65 ~ to total) grew dramaticallyfrom 8.9% to 10.1% (CNBS, 2015), and be expected to grow to 17.1% in 2030 and 26.3
in 2050 (UN, 2017).
According to the report of “Research of Long-term Care in China 2016” presented by
Insurance Association of China, there are 7% of families with elderly people who needs
long term care in China. And in 79.9% of these families, the care service is provided by
spouses, children and relatives. Additionally, in 53% of these families, the service timespent by family members exceeds 50%.
To meet the increasing demand of long-term care, the Chinese government efforts todevelop an LTCI system over the past few years. Since 2016, a 15-cities pilot program
was started to implement. Based on the program’s guiding opinions, the pilot cities should
58

explore a LTCI system which is accustomed to each regional characteristic and a nationwide framework is aimed to accomplish in 1-2 years. As an added note, to build a nationwide LTCI, the differences of regional development should be considered. By thecalculation of the Chinese provincial data, we find, during 2010 to 2015, the Gini
coefficient of aging rate and per capita DPI grew from 0.11 to 0.13, 0.11 to 0.19,
respectively. Meanwhile, that of per capita fiscal revenue has fell from 0.33 to 0.3224(SeeTable 2.6). By contrast, those of Japan in 2015 are 0.05, 0.05 and 0.24, respectively. It is
obvious that the Chinese regional differences are more significant than Japan. Thus, basedon our preceding research, if the Chinese LCTI also take the locally conductedadministration, it is reasonable to predict that these regional factors will lead to theregional disparities of the Chinese LCTI, such as user rate, premium and benefits. In
reality, the primary responsibility for managing the current social security programs
remains with the local government in China, which is embodied in the existence of a
substantial amount of independent social security funds with various scale, various
operation modes25. These fragmented systems may be the potential factor that enlarges
the regional differences of LCTI of China, and in turn affect the regional developmentalbalance.
To prevent this, the China’s government should adopt a scheme that combined withmarket and social power. A unified social LTCI at national level ensures the supply ofbasic service to majority, especially for the most vulnerable groups-mid. On the other
hand, demand of non-basic and diversified services can be met by commercial security.
Additionally, a narrow eligibility and evaluation standards as well as the specific laws
and policies for LTCI are required.

24

Liu et al., (2014) provides a detail analysis on distribution of population aging in
China.
25
For the relationship of responsibility between central government and local
government for providing social security, see Zhu (2016).
59

Table 2.6

2.7 Conclusion
In this chapter, we analyzed the dynamic properties of the regional differences in userrates defined as the ratio of LTCI users relative to the primary insured individuals (65years or older). The main findings are summarized as follows.
60

(ϸ) A simple theoretical model predicts that each region’s user rate converges to aunique globally stable steady state. The convergence, however, could be conditional, i.e.,each region’s user rate may converge to a region-specific steady state which is determinedby the region’s parameters.
(Ϲ) We calculated the user rates of 47 Japanese regions (prefectures) for the fiscal years
between 2000 and 2012. (Data source: The Japanese Ministry of Health, Labor, andWelfare.) Then, we divided the 47 regions into 5 groups according to the standing order(high and low) of user rates. It turned out that the user rate of a group with higher (lower)user rate grows slower (faster). Hence, the regional user rates seem to exhibit a tendency
to converge. The convergence, however, may be conditional. It turned out as well that thestanding order of regional user rates is not quite variable.
(Ϻ) By using average Markov transition matrixes for the first half (2000~2005) and forthe second half (2006~2012), we calculated the index of standing order mobility so as toevaluate the effects of the 2005 reform which aimed to remedy the differences in regional
figures of LTCI system. It turned out that the degree of mobility is greater in the first halfthan the second half for the group of regions with higher user rates. The 2005 reform,
hence, did not seem to alleviate the standing order inertia.
(ϻ) The small degree of variation in the standing order suggests the existence of regionspecific factors. With the help of preceding researches, we chose 3 factors {thecertification rate, the late-stage (75 years or older) old age ratio, and the ordinary balancerate} to account for the regional differences in user rates, and recalculated the mobility
index by using the residuals. It turned out that the degree of mobility is improved for all
the 5 groups and for both before and after the 2005 reform. Thus, the convergence might
have been conditional. If region-specific factors were not removed, each region’s userrate would converge to region-specific steady state, and the standing order of regionaluser rate would be invariant. It turned out as well that the 2005 reform hardly affected thestanding order mobility of residual user rates. In addition, the analysis also revealed thatthe improvement in the standing order variation seems small even after the regional
factors are removed. Therefore, there might be factors other than our choice that could
explain the regional differences.
61

Appendix. Data Sources and Its Properties.
For the analyses in this research, we used the data provided by the Japan Ministry of
Health, Labor, and Welfare26. There are some cautions on using the data;(ϸ) The public long-term care insurance system started on April 2000. Therefore, thedata for 2000 fiscal year consists of 11 months, from April 2000 to February 2001. The
data for each fiscal year between 2001 and 2012 consists of 12 months, from March of
the year to the February of the next year.
(Ϲ) In accordance with the 2005 reform, community-based services started on April
2006. The total number of long-term care services in each fiscal year between 2000 and2005 and March 2006 is the sum of in-home services and facility services. On the other
hand, the total number of services after April 2006 includes community-based services in
addition to the formerly provided services.
(Ϻ) We analyzed the data of primary insured individuals (65 years or older). The dataof secondary insured individuals (40~64 years old) are excluded.
(ϻ) Because each primary insured individual may use in-home services, facility
services, and community-based services many times in a year, the user rate, defined as
the total number of services used by primary insured individuals divided by the numberof primary insured individuals, may exceeds one. In the theoretical model of section 3,
the user rate ‫ݔ‬௧ ൌ X t / Lt is defined as the ratio of the number of insured individuals who
use services

X t to the number of insured individuals Lt . An insured individual isincluded in X t if she uses at least one service. X t does not reflect the number of services
each insured individual uses. This implies Ͳ ൏ ‫ݔ‬௧ ൏ ͳ in the theoretical model.
Therefore, we implicitly assume that if the theoretical model is true so that the user rate‫ݔ‬௧ converges to the steady state ‫ כ ݔ‬, the same force also works on the user rate calculated
from the data in the manner stated above.
Because of the discontinuity, we looked at two series. Series [ALL] includes all the

26[The Reports on Long-term Care Insurance System: Annual Reports, 2000~2012
Fiscal Years] (URL http://www.mhlw.go.jp/topics/kaigo/joukyou.html)
62

services, while series [EXC] excludes the community-based services from the second half
data. Table 2.7 reports the basic statistics of regional user rates [ALL]; mean, annual rateof change, variance, coefficient of variation, maximum value, minimum value, andmax/min ratio. Table A1 also reports the basic statistics of regional user rates [EXC].

Table 2.7

Panel 1 of figure 2.15 depicts the graph of average user rate [ALL] and the graph of[EXC]. Because of the introduction of community-based services in the second half, theaverage user rate [ALL] is higher than [EXC] in the second half. Despite the inclusion ofcommunity-based services, these graphs show the similar movements. Between 2000 and
2005, the average user rate increased, but at diminishing growth rate. After the temporary
decline in 2006 and 2007, the average user rate began to increase again. The speed of thegrowth diminished for the last two years, 2011 and 2012. We can reconfirm theseproperties in panel 2 of figure 2.15 which depicts the growth rate of the user rate [ALL]and that of [EXC]. Since both user rates [ALL] and [EXC] show similar movements, inthis research we focus on the analyses of user rate [ALL] that includes the communitybased services in the second half.
63

Figure 2.15

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Transition. Basingstoke: Palgrave Macmillan.
[2]Barro, Robert J., and Xavier Sala-i-Martin (2004) Economic Growth, 2nd ed., MIT
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[3]Ljungqvist, Lars, and Thomas J. Sargent (2004) Recursive Macroeconomic Theory,
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[4]Quah, Danny (1993) “Galton’s Fallacy and Tests of the Convergence Hypothesis”
Scandinavian Journal of Economics, Vol. 95, No. 4, pp.427-443.
[5]Stokey, Nancy L., and Robert E. Lucas, Jr. (with Edward C. Prescott) (1989)
Recursive Methods in Economic Dynamics, Harvard University Press.
[6]Ando, Michihito (2008) “An Empirical Analysis of Regional Differences in Provision
and Premiums of Long-term Care Insurance: An Analysis of Japanese Municipality-level
Data” The Quarterly of Social Security Research, Vol. 44, No. 1, pp.94-109. (In Japanese)[7]Kikuchi, Jun (2008) “The sustainability of the long-term care insurance in Japan:
from the viewpoint of institutional care services” The Quarterly of Social Security
64Research, Vol. 43, No. 4, pp.365-379. (In Japanese)[8]Kikuchi, Jun, Eiji Tajika, and Yuji Yui (2005) “The Present State and Sustainabilityof Long-Term Care Insurance” in Eiji Tajika and Motohiro Sato (eds.), Intergenerational
Differences in Medical and Long-Term Care: Current Situation and Issues, Toyo Keizai
Inc. (In Japanese)[9]Luo, Meng (2017) “Long-Term Care System in Taiwan and Its Implications”
Scientific Research on Aging,Vol.5, No.3 pp.52-60. (In Chinese)[10]Huajun, L., Liwei, H., & Qian, Y. (2014). “Spatial Inequality and Distributional
Dynamics of Population Ageing in China, 1989-2011” Population Research, 2, 006. (In
Chinese)[11]Shimizutani, Satoshi, and Noriko Inakura (2006) “Japan’s Public Long-term Care
Insurance and the Financial Condition of Insurers: Evidence from Municipality-Level
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Elderly and Child Care in Japan: Micro-level Investigation with Policy Implication,
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Journal of Labour Studies, No. 502, pp.6-17. (In Japanese)[14]Tajika, Eiji, and Jun Kikuchi (2003) “The Long-Term Care Insurance in Japan: Why
is Its Financing so Difficult?” The Quarterly of Social Security Research, Vol. 39, No. 2,
pp.174-188. (In Japanese)[15]Tajika, Eiji, and Jun Kikuchi (2006) “What are the problems with nursing
insurance?: study on the process of system creation and its effects on improving statesof nursing requirement” ” Financial Review, Vol. 80, pp.157-186. (In Japanese)[16]Yui, Yuji (2006) “Analysis of Long-term Care Insurance using Municipal Data: The
Case of Aomori Prefecture” Financial Review, Vol. 80, pp.187-203. (In Japanese)[17]Wei, Wang and Yongchun Tang(2014) “The International Comparative Study ofLong-Term Care Insurance System” International Journal of Business and Social
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[19]Wang, W., & Tang, Y. (2014). The International Comparative Study of Long-TermCare Insurance System. International Journal of Business and Social Science, 5(2).
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[21]Japan Ministry of Health, Labor, and Welfare White Paper 2007 Fiscal Year (2007).
[22]Data and Statistics Sources[23]Japan Ministry of Health, Labor, and Welfare[24]Japan Ministry of Internal Affairs and Communications Statistics Bureau[25]OECD Health Statistics 2015

66

Chapter 3. Home or Market; Relative Importance of Learning
Places on the Process of Economic Development
In this chapter, we provide a theoretical economic growth model with home production
sector and market production sector to show the relative importance of learning places in
the process of economic development. We assume the home production technology ismore intensive and show when market activity is more important for human capital
accumulation, multiple steady states may emerge. This result may help to explain thedivergence of economic growth among economies. The implications to China are
discussed.

3.1 Introduction
At the frontier of macroeconomic analysis to date, the “unified economic growth theory”
and the “family and time allocation” are two major fields of researches. Galor (2011)
proposed an initiative to construct unified economic growth theory which can explain (i)transition from stagnant phase to growth phase, and (ii) divergence between high growthgroup and low growth group in single framework. On the other hand, the macroeconomic
implication of family and time allocation attracts renewed interest among researchers.
[See, for example, Doepke and Tertilt (2016), and Aguiar and Hurst (2016).] In thischapter, we provide a framework which combines these two fields and show that therelative importance of learning places (home or market) matters for the process of
economic development.
A natural framework that can deal with these issues is a two-sector model of economic
growth in which a household plans time allocation between market activity and nonmarket (home) activity to maximize utility. Under the assumption that home technology
is more labor intensive than the market technology (as presumed in many preceding
researches), we show it is necessary that activity at market is more important for humancapital accumulation than activity at home for steady state multiplicity. When activity atmarket is more important for human capital accumulation than activity at home, multiple
steady states may emerge in dynamic general equilibrium. Some economies converge
67

toward a higher growth steady state, while the others toward a lower growth steady state.
Furthermore, the divergence may depend on initial condition and self-fulfilling
expectation. We also derive some testable implications.
The intuitive reason behind these observations are explained as follows. Suppose themodel economy is on a steady state where the ratio of physical capital to human capitalis constant, the resource allocation between two sectors is optimal, and the aggregate
variables grow at the rate of human capital accumulation. Then, a shock that destroys
physical capital, while leaves human capital intact, causes an upward jump in the shareof physical capital employed by market sector because market sector is more physicalcapital intensive than home sector. The shock also causes an upward jump in the share ofhuman capital employed by market sector so as to keep the temporal optimal condition
with respect to sectoral resource allocation invariant. If activity at home is relatively more
important for human capital accumulation than activity at market, then the shock
decreases the speed of human capital accumulation. As a result, the ratio of physicalcapital to human capital increases, and the process continues until the economy moves
back to the same steady state. On the other hand, if activity at market is relatively more
important for human capital accumulation than activity at home, then the shock increases
the speed of human capital accumulation so that the ratio of physical capital to humancapital decreases furthermore until the economy reaches another steady state, if any,
where the ratio of physical capital to human capital is lower and the speed of humancapital accumulation is faster than the initial steady state.
This chapter is related to the following researches. In many optimal growth models,
external effects are introduced as the Marshallian externality.27 Boldrin and Rustichini(1994) showed that in optimal growth models with one state variable (physical capital),
while a negative externality generates an indeterminate steady state, a positive externality
does not under mild conditions. Benhabib and Farmer (1994), and Farmer and Guo (1994)
showed that an indeterminate steady state could emerge in optimal growth models with aleisure-in-utility function. Perli (1998) introduced home production, and showed by27

See Boldrin and Rustichini (1994), Schmitt-Grohe (1997), Nishimura and Sorger(1999), Benhabib and Farmer (1999) for the survey of this topic.
68calibration that an indeterminate steady state could emerge. These studies introduce
external effects as the Marshallian externality. In the present model, home consumption
might also be interpreted as a leisure which requires both human capital and physicalcapital inputs, although the source of external effects is different. The "history versus
expectation" phenomenon emerges in Krugman (1991), Matsuyama(1991), Futagami and
Mino (1995), Gali (1994), and Greiner and Semmler (1996).28
The qualitative and quantitative importance of household production is widely
recognized in macroeconomic modeling. In the field of real business cycle theory,
introducing the home sector to a standard model is known to improve the matching ofartificial data to actual data in terms of standard deviation and co-variation with output.
[c.f., Benhabib, Rogerson, and Wright (1991), Greenwood and Hercowitz (1991),
Greenwood, Rogerson, and Wright (1995), McGrattan, Rogerson, and Wright (1997)] In
the field of endogenous business cycle theory, the degree of increasing returns required
to generate indeterminate equilibria is greatly reduced by introducing the home sector.
[c.f., Perli (1998)] It is also interesting to see how home sector, through its interaction
with market sector, affects the long-run growth of an economy. Greenwood andHercowitz (1991) note that "in contrast to physical capital, important components ofhuman capital are produced in the household sector" (p.1211), although the human capital
accumulation in their model is an exogenous process. On the other hand, learning-bydoing in the market sector would play an important role in the human capital
accumulation as well. Because the resources a society can spend are limited, theappropriate question might be the relative importance of each sector for human capital28

The other related research is as follows. Dynamic general equilibrium models withexternal effects could have multiple steady states due to the violation of global
concavity. Skiba (1978), and Deckert and Nishimura (1983) characterized the solutionof optimal growth models with a non-convex technology set. Ethier (1982), Howitt and
McAfee (1988), Spear (1991), Boldrin and Rustichini (1994), and Benhabib and Farmer(1994) studied indeterminacy due to external effects. Benhabib and Nishimura (1979,
1998) studied the conditions for indeterminacy in multi-sector optimal growth models.
Pelloni and Waldman (1998), and Mino (1999) studied the role of preference structureon the emergence of an indeterminate steady state. Chamley (1993), Bond, Wang andYip (1996), and Ladron-De Guevara, Ortigueira and Santos (1999) studied theindeterminacy in Uzawa-Lucas type two-sector endogenous growth models. (SeeUzawa (1964), and Lucas (1988).)69

accumulation. If people learn more through activities at home, spending too muchresource in the market may reduce the speed of human capital accumulation and (percapita) economic growth, or vice versa. In this chapter, I incorporate this consideration
into a model of economic growth driven by human capital accumulation to see theimplications of home sector for the local and global dynamics of the Hamiltonian system.
Benhabib et. al. (1991), and Greenwood and Hercowitz (1991) suggest that home sector
might be more labor-intensive than market sector. In this case, if people learn more athome than at market, the model predicts an equilibrium path converging to a globallyunique saddle-point. On the other hand, if people learn more at market than at home,multiple steady states could emerge, and the outcome might depend on both history andexpectation.
This chapter is organized as follows. In section 3.2, we present a two-sector model of
economic growth that will be used for our purpose. In the model, there are two inputs,
physical capital and human capital, and two outputs, market output and non-market (home)
output. The economic growth is driven by human capital accumulation, the speed ofwhich is assumed to be dependent on the time allocation between market activity andnon-market (home) activity. We also assume that home technology is more labor intensive
than the market technology (as presumed in many preceding researches). At the end ofsection 3.2, we derive a system of dynamic general equilibrium (DGE) equations withrespect to two variables; the ratio of physical capital to human capital and the share ofphysical capital employed by market sector. In section 3.3, we analyze the steady state ofdynamic general equilibrium. We show that when market activity is more important forhuman capital accumulation, then multiple steady states may emerge. In section 3.4, weanalyze the local and global stability of the steady states. We show that when there are
multiple steady states, depending on the initial condition and self-fulfilling expectation,some economies converge toward a higher growth steady state, while the others toward alower growth steady state. On the path to the higher growth steady state, the ratio ofphysical capital to human capital decreases (because human capital accumulation is themain engine of economic growth), and both the share of physical capital and the share ofhuman capital employed by market sector increase. On the path to the lower growth70steady state, these variables behave the opposite. In section 3.5, we summarize andconclude the paper by proposing the lines of future research.

3.2 Model
In this section, we present a two-sector model of economic growth that will be used forthe analysis of time allocation and economic growth. Consider a two-sector model of
economic growth driven by human capital accumulation. The model is described as acontinuous-time optimization problem of a representative agent. There are many identicalagents in the economy. The population size is normalized to be one. At each moment t, a
representative agent has one unit of time, H (t ) units of human capital, and K ( t ) unitsof physical capital which has been accumulated through past investment activities. The
human capital and physical capital are allocated between two types of production
activities; market good production and nonmarket (home) good production. The O ( t )u100% of time is combined with human capital H (t ) , and the P ( t ) u100% of physicalcapital is allocated to produce
market good consumption

A[ O H ]D [ P K ]1 D units of market good that is used for

Cm and gross investment K + ߜ௞ ‫ ܭ‬. (Hereafter, O isreferred as the “time share of human capital”.) A  (0, f) is market production
technology level (scale parameter), ߙ [0, 1] is the share of human capital in market
production function, and ߜ௞  [0. 1] is physical capital depreciation rate. The remainingE1 E

human capital and physical capital are used to produce B [ ( 1  O ) H ] [ ( 1  P ) K ]units of nonmarket (home) consumption good ‫ܥ‬௡ . ‫(  ܤ‬0, f) is home production
technology level, and ߚ [0, 1] is the share of human capital in home production function.
In a survey paper by Aguiar and Hurst (2016) about the macroeconomics of time
allocation, time is divided between market work and nonmarket work (homework).
Nonmarket work includes such activities as home production (cooking, cleaning,
shopping, laundry, lawn mowing, older adults caring, etc.), child caring, and leisure (TV,theatre, videogames, socializing, exercising, sleeping, etc.). In addition, Aguiar and Hurst
count such activities as job search, human capital accumulation, civic organization
71

participation, etc., as yet another group for time allocation. In our research, O is shareof time for market work, and 1  O is the share of time for all the other activities.29
Preceding researches assume that home technology is relatively more human capitalintensive than market technology. For example, Greenwood and Hercowitz (1991)
assumed D =0.7 and ߚ=0.87 in their numerical calibration analysis of real businesscycle model. Therefore, in this research, we also assume the following.
Assumption 1. ߙ ൏ ߚ
As stated in the introduction, the rate of human capital accumulation ‫ܪ‬ሶ Τ‫ ܪ‬may dependon how each individual learns at home and at market. Page (1994) compared the growthexperiences of the East Asian countries and Latin American countries. Although these
two regions had comparable initial states, the subsequent per-capita economic growth
turned out to be much higher for the East Asian countries than Latin American countries.
Page observes the differences in education system as the key factor. While Latin
American countries spent resources more on secondary and higher education, whose
return could be internalized through markets, the East Asian countries spent more on
primary education. In fact, providing very basic skills such as reading and writing to every
individual at an early stage could generate an external effect that enhances economy-widelabor-productivity. On the other hand, we often observe child-labor in the market place
among low-income, stagnant economies. In this case, economies that spend too muchresources in market sector may experience lower rate of growth in labor productivity thanthose that spend more in home sector. On the other hand, learning as by-product of market
production, and network (team) externality on learning at workplace are stressed in labor
economics. [c.f., Arrow(1962), Aoki(1984)] Therefore, each of these two cases will beconsidered in the following analysis. Specifically, we assume the following functional
form for human capital accumulation.
‫ܪ‬ሶ ൌ ߶ሺߣሻ‫ ܪ‬െ ߜு ‫ܪ‬(3.1)

G H  [0, 1] is human capital depreciation rate, and I ( O ) t 0 is the (gross) growth rate
29

Aguiar and Hurst (2016) and Doepke and Tertilt, (2016) report the trend of time
allocation since 1960s in the US. Time share for market work of male workers has been
decreasing while that of female workers increasing.
72

of human capital which is dependent on the time share of human capital O employedby market sector. I ( O ) may be increasing in O if people learn relatively more atmarket. Or, I ( O ) may be decreasing in O if people learn relatively more at home. We
will consider the following three cases with respect to the relationship between O andI( O ) .

Case 1; Home production is relatively more important for human capital accumulation.
For some O  [0, 1], I ( O ) > 0 for all O  [0, O ), I ' ( O ) < 0 for all O  [0, O ),and I ( O ) = 0 for all O  [ O , 0]. (See figure 3.1.) O is a threshold value such thatthe positive effect of home production on human capital growth ceases to effect above
this value.
Figure 3.1
Case 1: Home production is relatively more important for human capital accumulation.

Case 2; There is an interior O *  [0, 1] which maximizes the human capital growthrate. I ' ( O * ) = 0, I ' ( O ) t 0 for all O  [0, O * ), and I ' ( O ) d 0 for all O  ( O * ,1]. (See figure 3.2.)

73

Figure 3.2
Case 2: There is an interior which maximizes the human capital accumulation.

Case 3; Market production is relatively more important for human capital accumulation.
For some O  [0, 1], I ( O ) = 0 for all O  [0, O ], I ( O ) > 0 for all O  ( O , 1],

and I ' ( O ) > 0 for all O  ( O , 1]. (See figure 3.3.) O is a threshold value such that

the positive external effect of home production on human capital growth starts to effectabove this value.

Figure 3.3.
Case 3: Market production is relatively more important for human capital
accumulation.

A functional example that includes these 3 cases as special cases is presented as follows.
74

(See figure 3.4)

­ \ ( O *  O ) H  I * ,O dO dO°I( O ) = ®
°0,
O d O or O t O¯, \ > 0, H > 0, I * > 0(3.2)

Figure 3.4

In addition, we assume that the effect of O on I ( O ) is taken as external by the
representative individual in the following analysis.
Assumption 2. The effect of O on I ( O ) is taken as external by the representative
individual.
In case of market activity, assumption 2 may be plausible because the activity iscollective. On the other hand, assumption 2 may not be plausible in case of nonmarket
activity because each household internalizes the effect on human capital accumulation.
Despite the implausibility, we impose assumption 2 in the following because theassumption greatly facilitates the analyses. We would like to analyze the extended model
which incorporate the market and nonmarket asymmetry as a remaining issue.
75

The representative agent’s preference over market good Cm and home good Cn

isexpressed by the following lifetime utility function.
f³ u( C , C ) e
0

m

U t

n

dt

(3.3)

In (3.3), u( Cm , Cn ) is an instantaneous utility function of logarithmic form describedas follows.

u( Cm , Cn ) = J ln Cm + ( 1  J ) ln Cn(3.4)

In (3.3) and (3.4), U  (0, f) is subjective discount factor and J  (0, 1) is therelative importance of market good Cm over home good Cn in the instantaneous utility
function.
The representative agent’s optimization problem at time t = 0 is summarized as follows.
Given { K ( 0 ) , H ( 0 ) } and { I (t ) ; t t 0}, choose { Cm (t ) , Cn (t ) , O ( t ) , P ( t ) ,K ( t ) ; t t 0} to maximizef³ u( C , C ) e
0

m

n

U t

dt

(3.3)

subject tou( Cm , Cn ) = J ln Cm + ( 1  J ) ln Cn(3.4)

Cm + K + G K K = A[ O H ]D [ P K ]1 D
Cn = B [ ( 1  O ) H ]E [ ( 1  P ) K ]1 E

(3.5)
(3.6)

O  [0, 1]

P  [0, 1] .
The solution to this optimization problem is a dynamic general equilibrium (DGE) of
the model economy. The DGE is summarized by the following system of differential
equations {(3.7), (3.8)}with respect to the share of physical capital employed by market
sector P

and the ratio of physical capital to human capital k { K / H .

76

D
§O ·
k
D
= A ¨¨ ¸¸ > 1  M P  M @kk
©P¹

 GK  I( O )  GH

(3.7)

D
P
º
1 ª § O ·=« A ¨¨ ¸¸ 1  M (1  D )(1  P ) k  D  U  D G K  D I ( O )  D G H »P:( P ) «¬ © P ¹¼(3.8)
In (3.7) and (3.8),

O = a P /[ a P  b (1  P ) ](3.9)

a { D /( 1  D ) , b { E /( 1  E ) , M { [ J (1  D ) ] /[ (1  J )(1  E ) ] , and:( P ) { P ª (1  P )(1  D )( b  a )  a º«» .
1 P ¬a P  b (1  P )¼

At each moment t , (3.9) must hold for the optimal resource allocation between market
sector and home sector. In addition, the following transversality condition must hold aswell.
lim e U t V ( t ) k ( t ) = 0(3.10)t of

In (3.10), V ( t ) is the shadow price of k (t ) .

3.3 Steady State and Welfare
3.3.1 Steady StateAt a steady state { k s , P s } of the DGE, k / k = 0 and P / P = 0. The steady statevalue of the time share of human capital employed by market sector, ߣ௦ , is shown to bea solution to the following equation.
P( O ) = F ( O )(3.11)The left-hand side of (3.11) is
P ( O ) { b O / [ a (1  O )  b O ](3.12)by (3.9), and the right-hand side of (3.11) isF( O ) {ª (1  D )( G K  I ( O )  G H )º M » (1  M ) .
« U  G  I( O )  G
KH¬¼

The other steady state variables are expressed as functions of ߣ௦ as follows.
77(3.13)

P s = b Os / [ a (1  Os )  b Os ](3.14)
1/ D§ O ·ªº(1  D ) A
k s = ¨¨ s ¸¸«»© Ps ¹¬ U  G K  I ( Os )  G H ¼(3.15)

cm , s { Cm / H = M A ( Os / Ps )D (1  Ps ) ks1D
cn , s { Cn / H = B (1  Os )E [ (1  Ps ) ks ]1 E(3.16)(3.17)In a steady state,

K = ks H , Cm = cm, s H , and Cn = cn , s H .

(3.18)

Therefore, { K , Cm , Cn } grow at the same growth rate equal to H / H = I ( O ) 
GH .

(3.12) implies
P ( 0 ) = 0, P (1 ) = 1, and P ' ( O ) > 0 for all O  [0, 1].

(3.19)
Assume G K  I ( O )  G H t 0 for all O  [0, 1]. Then, (3.13) implies
M /( 1  M ) d F ( O ) < 1 for allO  [0, 1].

(3.20)

Therefore, equation (3.11) has at least one interior solution ߣ௦  (0, 1). (See figure 3.5.)

Figure 3.5

78

The following theorem 1 is used for checking the existence of multiple steady states.

Theorem 1.
sign [ F ' ( O ) ] = sign [ I ' ( O ) ]Proof ;w
[ ln F ( O ) ]wO(3.21)§ w·¨¨ [ ln F ( O ) ] ¸¸ I ' ( O ) . It can be shown that
© wI
¹

=

w ln F ( O ) / w I > 0.

The following corollary 1 is used for comparative dynamic analysis in section 4.
Corollary 1.
(ϸ) F ( O ;

()

()

()

()

()

()

U , GK , GH , D , E , J )(3.22)(Ϲ) F ' ( O ) = 0 for O d O or O t O .
In (3.22), “+” sign or “-” sign above each parameter implies an upward shift or adownward shift in F ( O ) caused by the change in parameter value. For example, anincrease in subjective discount factor U of future utility causes F ( O ) to shift downward.
The following theorem 2 implies I ' ( O ) t 0 is a necessary condition for (3.11) to havemultiple solutions.
Theorem 2. There is a unique steady state ߣ௦ in case 1.
Proof; A steady state ߣ௦ is a solution to (3.11). In case 1, F ' ( O ) d 0 for all O  [0,1]. On the other hand, P ' ( O ) > 0 for all O  [0, 1]. Therefore, there cannot be morethan one intersection between P ( O ) and F ( O ) .
On the other hand, multiple steady states may emerge in case 3. Figure 3.6 shows one
possible case in which there are three steady statesߣ௦

79

Figure 3.6

Five panels of figure 3.7 shows the effect of a change in parameter J (importance ofmarket consumption relative to home consumption in utility function) on the number ofsteady statesߣ௦ . An increase in J causes F ( O ) to shift upward. When J is small,there is one steady state ߣ௦ (panel 3.7.A). At the steady state, there is no growth in humancapital ( I ( Os ) = 0) because ߣ௦ < O . As J gets larger, three steady states { Os < OsLM< Os } emerge (panel 3.7.C which is same as figure 3.6). The corresponding humanHcapital growth rates are 0 = I ( Os ) < I ( Os ) < I ( Os ) . As J gets ever larger, theMLHnumber of steady states is reduced back to one (panel 3.7.E). The human capital growthrate increases along withߛ

80

Figure 3.7
Panel 3.7.a

Panel 3.7.bPanel 3.7.c

Panel 3.7.dPanel 3.7.e81Figure 3.8 displays the relationship between J and the number of steady states ߣ௦ thatare solutions to equation (3.11). As stated above, there are two critical values of J , J 'and J " , such that for J  [0, J ' ), (3.11) has a unique solution ߣ௦ , at J = J ' , (3.11)
has two solutions, for J  ( J ' , J " ), (3.11) has three solutions, at J = J " , (3.1) has two
solutions, and for J  ( J " , f), (3.11) has a unique solution.

Figure 3.8.

The following theorem 3 states that the number of steady states of the dynamical system{(3.7), (3.8)} is same as the number of steady statesߣ௦ .
Theorem 3. ݇௦ is a monotone function of ߣ௦ .
Proof ; It can be shown thatd ln k
dP

­ ½
° °
® ¾ 0
°! °
¯ ¿

 D

­!½
° °
® ¾ E
°°
¯ ¿

and P ' ( O ) > 0 for all O  [0, 1].

3.3.2 Welfare at Steady States
When there are multiple steady states, it is interesting to compare the welfare level ofeach steady state. At a steady stateߣ௦ , the growth rate of human capital is‫ܪ‬ሶ Τ‫ ܪ‬ൌ ߶ሺߣሻ െ ߜு

(3.23)The solution to this differential equation is82

H ( t ) = H ( 0 ) exp[ ( I ( Os )  G H ) t ] .

(3.24)At the steady state, the lifetime utility Ws of representative agent is calculated asfollows.
f

Ws = ³ [ J ln ( cm , s H ( t ) )  ( 1  J ) ln ( cn , s H ( t ) ) ] e  U t d t0= ( 1 / U ) [ J ln cm , s  ( 1  J ) ln cn , s ] + ( 1 / U ) ln H ( 0 ) + ( 1 / U ) ( I ( Os )  G H )2(3.25)
The first term of the right-hand side of (3.25) is "level effect", the second term is initialhuman capital, and the third term is "growth effect". Suppose there are three steady states{ Os < Os < Os } as depicted by panel 3.7.C of figure 3.7. The corresponding humanLM

H

capital growth rates are 0 = I ( Os ) < I ( Os ) < I ( Os ) . Although the "level effect"
LM

H

may be larger for the steady state with smaller Os , we expect the lifetime utility is larger
for the steady state with larger Os because the time preference factor U < 1 implies
that, while the level effect is discounted by 1 / U , the growth effect is discounted by 1 / U .
2

3.4 Structural Stability and Bifurcation
In this section, we analyze the local and global stability of the steady states, and explore
the implication of the time allocation for the unified economic growth theory.
In general, when a dynamic system has multiple steady states, the local stability of eachsteady state alternates its property. In the following, attention is paid to the possibility thatthe equilibrium path is indeterminate. Given the initial value of the ratio of physicalcapital to human capital k ( 0 ) = K ( 0 ) / H ( 0 ) , the equilibrium path is said to beindeterminate if there are multiple P ( 0 ) such that { k (t ) , P ( t ) ; ‫ ݐ‬൒ Ͳ} satisfies thesystem of differential equations, (3.7) and (3.8), and the transversality condition (3.10).
The local multiplicity of P ( 0 ) at a steady state is uncountable if the dynamic system
has a locally stable manifold of dimension two at the steady state. On the other hand, themultiplicity of P ( 0 ) may be countable if the dynamic system has a stable manifold of83

dimension zero and an "overlap" at one of the multiple steady states [c.f., Krugman (1991),
Matsuyama (1991)]. For example, a steady state might have expanding spiral paths
converging toward other steady states. In this case, for a given initial value of the ratio ofphysical capital to human capital k ( 0 ) in some neighborhood of the steady state, there
are countably many P ( 0 ) such that { k (t ) , P ( t ) ; ‫ ݐ‬൒ Ͳ} satisfies (3.7), (3.8), and thetransversality condition (3.10).
3.4.1 Phase-diagram Analysis
The stability of each steady state is analyzed by phase-diagrams. The following theorem
4 will be used for the analysis.
Theorem 4. If I ( O ) is constant, then the dynamical system {(3.7), (3.8)} has a uniquesteady state { k s , P s } which is a globally stable saddle point.
Proof ; The assumption implies I ' ( O ) = 0. By theorem 2 and theorem 3, thedynamical system {(3.7), (3.8)} has a unique steady state { k s , P s }. In { k , P } planewhere k  [0, f) and P  [0, 1], the graph of k / k = 0 locus is described as follows.
By (3.7), k / k = 0 implies

O ª A (1  M ) P  M ºk =P «¬ G K  I ( O )  G H »¼

1/ D

.

(3.26)
1/ D

At k =0, P = M /[ A ( 1  M ) ] . At k = [ { A ( 1  M )  M } /{G K  I ( O )  G H } ],P = 1. In the { k , P } plane, it can be shown that k / k > 0 above the k / k = 0 locus(4.1), and k / k < 0 below the k / k = 0 locus. In addition, k / k = 0 locus (3.26) isshown to be monotone in the { k , P } plane. Similarly, by (3.8), P / P = 0 locus isgiven by

O ª A (1  M ) (1  D ) (1  P ) ºk =P «¬ U  D G K  D I ( O )  D G H »¼

1/ D

.

(3.27)

When P = 1, O / P = 1 and k = 0. When P = 0, O / P = a / b and
84

º
aª
A (1  M ) (1  D )k = «b ¬ U  D G K  D I ( O )  D G H »¼

1/ D

.

(3.28)(3.27) also implies that P and k have monotone relationship on the P / P = 0 locus.
In addition, P / P > 0 above the P / P = 0 locus, and P / P < 0 below the P / P =0 locus.
Based on these observations, phase-diagram analysis establishes the claim of thetheorem.
In case 1 ( I ' ( O ) d 0 for all O  [0, 1]), theorem 2 states that there is a unique steadystate. By phase-diagram analysis like the one employed for the proof of theorem 4, thissteady state { k s , P s } is shown to be a globally stable saddle point.
In the following, we conduct phase-diagram analysis so as to describe the properties ofdynamical system {(3.7), (3.8)} for case 3. In case 3, I ' ( O ) > 0 for O  ( O , 1], andI ( O ) = 0 for O  [0, O ]. The k / k = 0 locus in { k ,P } { [0, f) , [0, 1] } plane

is constructed as follows. By (3.7), k / k = 0 implies
D§O·
A ¨¨ ¸¸ > 1  M P  M @ = [ G K  I ( O )  G H ] k H©P¹
In (3.29), O / P.

(3.29)= a /[ a P  b ( 1  P ) ] , a { D /( 1  D ) , b { E /( 1  E ) , andM { [ J (1  D ) ] /[ (1  J )(1  E ) ] . (3.29) has the following properties; (ϸ) the left-handside is increasing in P , (Ϲ) I ( O )  [0, I * ], and (Ϻ) O / P  [ a / b , 1] becausea P  b ( 1  P )  [ a , b ]. Therefore, when

P = M /( 1  M ) , k must be zero. On

the other hand, when k is large, P must be large. Define P { P ( O ) . Then, P 

[0, P ] corresponds to O  [0, O ] and I ( O ) = 0 in this region. In (3.29), anincrease in P causes the left-hand side to increase. Then, k must increase so as toequate the right-hand side and the left-hand side. For P  ( P , 1], such a monotone85relationship between P and k may not be necessary for (3.29) to hold because anincrease in P causes not only an increase in O but also an increase in I ( O ) in the righthand side of (3.29). This non-monotonic relationship between P and k may generate
multiple steady states. Figure 3.9 depicts a possible graph ofk / k = 0 locus whichdisplays non-monotonic relationship between P and k .

Figure 3.9

It can be shown that k / k > 0 on the left-hand side of k / k = 0 locus in { k , P } plane,
while k / k < 0 on the right-hand side of k / k = 0 locus.
Similarly, the P / P = 0 locus in { k , P }  { [0, f) , [0, 1] } plane for case 3 isconstructed as follows. By (3.8), P / P = 0 implies
D§O·
A ¨¨ ¸¸ 1  M ( 1  D )( 1  P ) = [ U  D ( G K  I ( O )  G H ) @k D
©P¹

. (3.30)(3.30) has the following properties; (ϸ) the left-hand side is decreasing in P , (Ϲ)
I ( O )  [0, I * ], and (Ϻ) O / P  [ a / b , 1]. Therefore,

P = 1 when k = 0. On theother hand, when k is large, P must be small. As before, define P { P ( O ) . It can

be shown that for both regions P  [0, P ] and P  ( P , 1], an increase in P


86



must be associated with a decrease in k for (3.30) to hold. Figure 3.10 depicts a possible
graph of P / P = 0 locus. Notice in figure 3.10, for P  [0, P ], O  [0, O ] andI ( O ) = 0. It can be shown that P / P > 0 above the P / P = 0 locus in { k ,P } plane,

while P / P < 0 below the P / P = 0 locus.

Figure 3.10

Figure 3.11 depicts a situation in which there are three steady states { S H { { k s , P s },HM

S M { { ks ,H

P sM }, S L { { k sL , P sL }} in case 3 such that k sH < k sM < k sL andP sH > P sM > P sL .
Figure 3.11

87

The corresponding time share of human capital employed by market sector, Os >H

OMs > OLs , implies I ( OHs ) > I ( OMs ) > I ( OLs ) = 0 (because OLs < O ). The above
analysis implies that { k s , P s } and { k s , P s } are saddle points. Depending on
H

H

L

L

parameter values, the middle steady state { k s , P s } might be either a source or a sinkMM

with limit cycle. Figure 3.12 depicts two possible trajectories of { k ( t ) , P ( t ) }satisfying the dynamical system {(3.7), (3.8)}. There are two expanding spirals emanatingfrom the middle steady state { k s , P s } such that one is converging toward { k s , P s }
M

M

H

H

while the other is converging toward { k s , P s }.
L

L

Figure 3.12

Under the assumption that home technology is more labor intensive than the market
technology, we saw it is necessary that market activity is more important for humancapital accumulation than nonmarket activity for the steady state multiplicity. Whenmarket activity is more important for human capital accumulation than nonmarket activity,
multiple steady states may emerge in dynamic general equilibrium. Some economies
converge toward a higher growth steady state, while the others toward a lower growth88steady state. Furthermore, the divergence may depend on initial condition and selffulfilling expectation. The intuitive reason behind these observations is explained asfollows. Suppose up to some moment ‫ א ݐ‬ሾെλǡ Ͳሻ the model economy is on a steadystate where the ratio of physical capital to human capital k is constant, the resource
allocation between two sectors { P , O } is optimal, and the aggregate variables grow at
the rate of human capital accumulation‫ܪ‬ሶ Τ‫ ܪ‬ൌ ߶ሺߣሻ െ ߜு . Suppose at moment t = 0,
there is a shock that destroys physical capital while leaves human capital intact. The shockcauses an upward jump in the share P ( 0 ) of physical capital employed by market sector
because market sector is more physical capital intensive than home sector. The shock also
causes an upward jump in the time share O ( 0 ) of human capital employed by market
sector so as to keep the temporal optimality condition with respect to sectoral resource
allocation intact. If nonmarket activity is relatively more important for human capital
accumulation than market activity ( I ' ( O ) d 0, case 1), then the shock decreases the speedof human capital accumulation. As a result, the ratio of physical capital to human capitalincreases, and the process continues until the economy moves back to the same initialsteady state. On the other hand, if market activity is relatively more important for humancapital accumulation than nonmarket activity ( I ' ( O ) t 0, case 3), then the shockincreases the speed of human capital accumulation so that the ratio of physical capital tohuman capital decreases furthermore until the economy reaches another steady state, ifany, where the ratio of physical capital to human capital is lower and the speed of humancapital accumulation is faster than the initial steady state.

3.4.2. Implication of Time Allocation for the Unified Growth Theory
This model can shed light on the implication of time allocation between market activity
and nonmarket activity for the two phases of economic growth ; (ϸ) From stagnation to
growth, and (Ϲ) divergence between group of economies with high growth rate and thosewith low growth rate. In the following, we provide two scenarios which may be capablefor explaining the two phases of economic growth.
89

Scenario 1. Consider an increase in preference parameter J which measures the relative
importance of market consumption C m to home consumption C n in utility function.
Five panels {(3.7.A), (3.7.B), (3.7.C), (3.7.D), (3.7.E)} of figure 3.7 depict the appearance
and disappearance of multiple steady state as follows.
(3.7.A) 0 < J < J ' . There is a unique steady state ߣ௦ < O where human capital

growth rate is I ( Os ) = 0.
(3.7.B) J = J ' . Second steady state appears.
(3.7.C) J ' < J < J " . There are three steady states Os > O s

M

H> Os .
L(3.7.D) J = J " . There are two steady states.
(3.7.E) J > J " . There is a unique steady state where human capital growth rate is

I ( Os ) > 0.
The five panels {(3.13.A), (3.13.B), (3.13.C), (3.13.D), (3.13.E)} of figure 3.13 depicts
the phase-diagrams corresponding to the five panels of figure 3.7.
(3.13.A) 0 < J < J ' . There is a unique steady state { k s , P s } which is a globallystable saddle point where human capital growth rate is I ( Os ) = 0 because O s < O .
(3.13.B) J = J ' . There are two steady states. One is a globally stable saddle point
without human capital growth, and the other is unstable.
(3.13.C) J ' < J < J " .There are three steady states {{ k s , P s }, { k s , P s }, { k s ,
H

H

M

M

L

P sL }}. { k sH , P sH } and { k sL , P sL } are saddle points, while { k sM , P sM } is either a source
or a sink with limit cycle. The corresponding human capital growth rates are I ( Os ) >H

I ( OMs ) > I ( OLs ) = 0.
(3.13.D) J = J " . There are two steady states.
(3.13.E) J > J " . There is a unique steady state which is a saddle point with positive90

human capital growth rate I ( Os ) > 0.
Figure 3.13
Panel 3.13.a

Panel 3.13.b

Panel 3.13.c

Panel 3.13.d

Panel 3.13.e

When 0 < J d J ' , the economy is in stagnant phase. It converges to a steady state withI ( Os ) = 0. When J ' < J < J " , the economy may converge to a steady state with91

positive growth rate of human capital I ( Os ) > 0 or to a steady state with I ( Os ) = 0.
H

L

The divergence may dependent on the initial k ( 0 ) = K ( 0 ) / H ( 0 ) , or on the belief(self-fulfilling expectation). The latter happens if the DGE is indeterminate at theneighborhood of the middle steady state { k s , P s }. Given the initial k ( 0 ) , a DGE isM

Mindeterminate if there are multiple P ( 0 ) satisfying the dynamical system {(3.7), (3.8)}.
Given the initial k ( 0 ) , the economy may choose P ( 0 ) on the DGE path converging
to { k s , P s }, or P ( 0 ) on the DGE path converging to { k s , P s }. When J > J " , the
H

H

L

L

economy converges to a steady state with positive growth rate of human capital I ( Os ) >0. (The development process described above may be caused by changes in values of any
parameter ൛ߩǡ ߜ௄ ǡ ߜுǡ ߙǡ ߚǡ ߛൟ.)Scenario 2. The two phases of development process may be caused by the change in
relative importance of learning places. Theorem 2 predicts that if nonmarket activity isrelatively more important for human capital accumulation than market activity, theneconomies with similar structure will converge toward a unique steady state (case 1). On
the other hand, if market activity is relatively more important for human capital
accumulation (case 3), then multiple steady states may emerge. Some economies may
converge toward a steady state with higher growth rate, while the others may converge
toward a steady state with lower growth rate. The divergence, as stated above, may
depend on the initial k ( 0 ) = K ( 0 ) / H ( 0 ) , or on the belief.
In addition to the two scenarios presented above, we are able to provide many otherscenarios which may explain the two phases of economic growth within our model’sframework. Which one or some of the scenarios are appropriate for explaining the reality
is a question to be explored through empirical analyses, but yet there is one testable
implication of the model. When there are three steady states as depicted in figure 3.11,
world economies in the long run will be divided into two groups. One group of economies
converges to a steady state with higher rate of human capital accumulation and economic
growth driven by larger time allocation to market activity, while the other group of92

economies converges to a steady state without economic growth because of larger time
allocation to nonmarket activity. Therefore, it may be interesting to explore if economies
which allocate relatively more time to market activity than nonmarket activity indeed
grow faster.

3.5 The Implications to China
The unified growth theory divides the transition of economy from stagnation to modern
growth into three phases: the Malthusian regime, the Post-Malthusian regime and theModern Growth regime (Galor, 2011). During the Malthusian regime, the slow
technological progress ensured a stable population as well as the income per capita. Theinteraction between population and technological generated faster technological, which
triggered a growth of income per capita and population. The economy transferred into the
Post-Malthusian regime from the industrialization and the acceleration in the rate oftechnological progress increased industrial demand for human capital, inducing asignificant human capital investment, and thus a faster technological progress. The fastertechnological progress in turn raised the demand of human capital investment. During thesame period, the preference of household gradually chose the quality of child instead ofquantity, which induced a decline in population with low fertility and low mortality. The
temporary increase of labor population proportion enhanced the labor productivity, thus
triggered the growth of income per capita and sustained economic growth.
As the description of the unified growth theory, China has also experienced thestagnation with underpopulation and low living standard for several centuries. (See figure3.14) Since the foundation of PRC, the GDP per capita and the population started to growsimultaneously. Especially from late 1970s, the reform and open has brought a growth
miracle that the GDP per capita increased nearly 7-fold with huge population by 2008.
During this period, the technological progress brought by advancing industrialization andforeign direct investment (FDI) created a massive demand of human capital investment30.
30

Liu and Wang (2003) empirically studies the effect of FDI on TFP for a cross-sectional
sample of Chinese industrial sectors. They find FDI inflow is not merely a source ofcapital, it is also a conduit for technology transfer.
93

Fig 3.15 shows the trend of the industrial structure since 1978 to 2015, a continuous
decline of the contribution to GDP of the primary sector accompanied by an increasingof that of the tertiary sector. Figure 3.16 shows the employment distribution among 3
sectors, which indicates an economic transition from rural to industrial.

Figure 3.14

Figure 3.15

94Figure 3.16

As consequences, the labor’s human capital in terms of schooling increased,
figure3.17indicates the education level of workers employed by each sector from 1990 to2010. It shows that the workers employed by the tertiary sector are better educated and in
the primary sector, the opposite is true. Additionally, with the implementation andpopularity of the 9-year compulsory education, the educational attainment compositionof China’s overall population has changed dramatically. By the end of 2010, the majority
population has attended at least junior secondary school, and the proportion of higher
educated people has doubled compared to that of 2000 (See figure 3.18). On the other
hand, the population policy of China directly triggered a low fertility rate, which would
force the household to shift their preference towards the quality of their offspring, thusincreased the investment on human capital31.

31

According to the World Bank’s database, the fertility rate of China decreased from
2.61 in 1982 to 1.57 in 2015. https://data.worldbank.org/indicator/
95

Figure 3.17

Source: “Skills Shortages in the Chinese Labor Market” by JPMorgan, 2016.

Figure 3.18

By contrast, the human capital also played a crucial role during the Japan’s high-growth96era (1955-1973). Godo (2010) suggests that the Japanese success of catching-up toadvanced economies is due to the human capital capability of borrowing advanced foreigntechnology, which in turn triggered the increasing investment on formal education.
Additionally, he attributes the poor performance of Japanese economy after 1980s to thefailure of insufficient investment on high-level education which can create innovational
idea to maintain the competitiveness respect to other advanced economies.
The different phases of economic development between Japan and China, to some extent,
could also be interpreted by the unified growth theory which points out that thedifferences in the timing of take-off from stagnation to growth contributed to thedivergence in income per capita between countries. Although there is still huge gap of the
per capita GDP between Japan and China, the gap is narrowing as well as the humancapital stock (See figure 3.19).

Figure 3.19

Another different worth noting comes from the household: in recent years, the time
allocation between home and market in China has changed significantly, whereas that inJapan is not obvious. During 1996-2011, the ratio of time spent in home production and97that in market work of Japan stabilized around 33% (See table 3.1). In China, Wang (2014)shows that the weekly average ratio of hours spent in home production and market work
has fallen from 50% to 35% during 2004-2009.

Table 3.1

It seems that these features embodied during the economic development of China andJapan could be partially interpreted by our preceding model. Under the assumption thatthe home production is more labor intensive than the market work, relatively more timespent in market generated more faster growth for China. However, since there is no direct
evidence to show that home (or market) is the relative important place for human capital
accumulation, for predicting the future of economic growth for China, it should be further
studied.

3.6 Conclusion
In this chapter, we provided a framework which combines the theory of time allocationand the unified economic growth theory, and showed that the relative importance oflearning places (home or market) matters for the process of economic development.
Under the assumption that home technology is more labor intensive than the market
98technology, when market activity is more important for human capital accumulation thanhome activity, then multiple steady states may emerge in dynamic general equilibrium.
Some economies converge toward a higher growth steady state, while the others towarda lower growth steady state. Furthermore, the divergence may depend on initial conditionand self-fulfilling expectation. This result may help to explain the convergence ofeconomic growth between China and the advanced economies.

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Conclusion
This study has aimed at predicting the condition and environment of labor market, social
security system and economic growth in China. First, we reviewed the labor market andsocial security system in China and concluded some primary topics. Then, we studied the
problem of regional differences in Japanese long-term care insurance, and the reference
for China was obtained. Additionally, we provided a theoretical framework to interpretthe divergence in economic growth, and discussed the economic growth of China basedon the theoretical results. We summarize the major characteristics of each chapter asfollow:
In chapter 1, we surveyed the labor market and social security system of China. weconcluded the skill gap due to the change of industrial structure generates labor shortage
and unemployment co-existence in Chinese labor market; population aging and mobility
barriers created by institutional factors lead to potential negative effects on economic
growth; We suggested that increasing public expenditure on education and skill training
as well as relaxing the family plan and regulation on labor mobility could generate
positive effect on economic growth and social welfare.
In chapter 2, we studied the regional differences in the user rate of Japanese LTCI systemfor providing guideline for establishment of China’s LCTI system. By employing theMarkov transition matrix to measure the degree of regions’ mobility, we found theregional user rate of Japanese LTCI exhibited a conditional convergence according to theregional-specific factors, such as the degree of aging, the fiscal capacity and theevaluation standard, and the 2005 reform which has aimed to adjust those differences inuser rates seemed to have little effect. We also calculated the China’s regional differencesin the degree of aging, fiscal capacity and income level. We found the differences ofregional factors in China were more severe that those in Japan. Thus, we suggested that ascheme combined the nationally uniform plan which provides basic social security andthe commercial security which can meet various demand seems to have effect on
circumventing the issues of regional differences.
103

In Chapter 3, for predicting the future of economic growth of China, we provided
theoretical framework and showed that the relative importance of learning places (homeor market) matters for the process of economic development by employing the ideas of“unified growth theory” and “family and time allocation”. Under the assumption thathome technology is more labor intensive than the market technology, when market
activity is more important for human capital accumulation, then multiple steady states
emerge in dynamic general equilibrium. Some economies converge toward a higher
growth steady state, while the others toward a lower growth steady state. Furthermore,
the divergence may depend on initial condition and self-fulfilling expectation. We also
discussed the future of economic growth of China based on this model. We found that thedevelopment path of China is in accord with the unified growth theory, and the featurethat less time allocated to home production accompanied with the rapid economic growth
supports our theoretical results to some extent. Thus, a relative high-speed growth of
China could be obtained if the market activities is more important for human capital
accumulation.
We point out the limitations and prospect the further research as follow:
I.

In chapter 1, empirical study for investigating how the specific types of social
security plan interacts the growth and growth determinants (saving, labor mobility,
human capital investment and fertility) in China should be addressed.

II. In chapter 2, we analyzed the regional differences among prefectures of Japan. The
difference, however, may be wider and more prominent among less aggregatedlevels such as villages, towns, and cities. For example, in each prefecture, thebehavior of covered individuals and insurers (municipalities) at countryside may bevery different from that of urbane area. Therefore, it might be desirable to employ
detailed case studies to supplement the approach employed in this research.
III. The theoretical model of chapter 2 does not have detailed structure of the market
for long-term care services. For a better understanding of the market, it is desirable
to enrich the model by incorporating such elements as demand, supply, prices, taxes,
and subsidies.
IV. In Chapter 3, we do not have microeconomic foundation that explains the104determinant of relative importance of learning places. It may be related to thecharacteristics of production technologies at market and at home.
V. Which one of the parameters ൛ߩǡ ߜ௄ ǡ ߜுǡ ߙǡ ߚǡ ߛൟ is responsible for causing theappearance and disappearance of multiple steady states? Statistical data and realworld observation are needed to answer this question. The question is also related
to the following.
VI. If the steady state multiplicity in our model economy arises under plausible andreasonable parameter values? It may be interesting to numerically calibrate ourmodel economy to explore the issue. The parameter values specified in thecalibrated real business cycle model analyses by Benhabib, Rogerson, and Wright(1991), Greenwood and Hercowitz (1991), Greenwood, Rogerson, and Wright(1995), and McGrattan, Rogerson, and Wright (1997) are valuable references.

105

Acknowledgement
Chapter 2 of the thesis was presented at the Japanese Economic Association 2015 Spring
Meeting (Niigata University, May 24, 2015), and the 2nd Annual Workshop in Businessand Economics by National ChengChi University and Hiroshima University (Taipei,
December 25, 2015). [“The Dynamic Analyses of the Regional Differences in Japanese
Public Long-Term Care Insurance System”, HE DU and HIROSHI FUTAMURA] I am
grateful to the comments by Tomoya Sakagami, Yih-Chyi Chuang, and participants at theseminars. The earlier version of the research was presented at Kumamoto Gakuen
University and Meiji Gakuin University.
Chapter 3 of the thesis was presented at the 3rd Annual Workshop in Business andEconomics by National ChengChi University, Hiroshima University, and Tohoku
University (Taipei, December 27, 2016), and the Japanese Economic Association 2017
Spring Meeting (Ritsumeikan University, Biwako-Kusatsu Campus, June 25, 2017)[“Home or Market; Relative Importance of Learning Places on the Process of Economic
Development”, HE DU and HIROSHI FUTAMURA] I am grateful to the comments by
Tomoya Sakagami, Yih-Chyi Chuang, and participants at the seminars. The earlier
version of the research was presented at Kobe University and Yokohama National
University.
Finally, I would like to express my deep gratitude to Hiroshi Futamura, Atsuhiro Taki,
Takashi Senda, and Toshikazu Oosawa of Hiroshima University for the valuablecomments and suggestions.

106