Research on Optimal Enterprise Contribution of Hunan Province Based on OLG
Model
Ni Yang
College of Economics and Management, Hunan Normal University, Changsha, China
(yangni1126@qq.com)
Abstract - Optimizing the enterprise contribution is the
key factor for promoting the reforming of public pension
system and insuring the dynamic balance of social security
fund. This paper has made a research on optimal enterprise
contribution of Hunan province based on OLG model. The
empirical result showed that life expectancy growth would
raise the optimal enterprise contribution, while population
growth rate decline would reduce the contribution, and the
latter factor made more influence. If both two factors were
introduced in the equilibrium equation, the optimal
enterprise contribution would be reduced from 20% to
10.04%, when life expectancy growth raised from 73.8 to
77.2 and population growth rate declined. The research on
optimal enterprise contribution provides theory basis and
the policy support for macroeconomic policy making and
pension reforming promoting.
Keywords - OLG model, optimal enterprise
contribution, pension reforming, life expectancy growth,
population growth rate
I. INTRODUCTION
Optimizing the enterprise contribution is an important
component of public pension reforming, which makes
sense for economic development and social progress, and
has effect on national saving, enterprises’ operating costs,
families’ consumption structure, labor’ supply and so on.
With the development of population structure changing
and population ageing turning seriously, how to get the
optimal enterprise contribution has attract more and more
attention.
Hunan province has a large population, as the age
population (65 years old and above) has reached 6.35
million by the end of 2009 accounting for 9.22% of total
population. Furthermore, the population aging of Hunan
province has characteristics of speedly growth, large
scale, “growing old before growing rich” and so on,
which makes significant impact on dependency ratio,
consumption structure and social security. Therefore,
making proper mechanism for optimal enterprise
contribution is an important premise for promoting the
stability and development of social security in long run.
As a frequently used tool for public pension
analyzing, overlapping generations model (OLG) could
examine the influence of public pension on the whole
macro economy through analyzing micro economic
agents, based on the general equilibrium frame. The
theory was advanced by Samuelson(1958), and expanded
to classic cross time dynamic model by Diamond(1965)
[1]
. Many scholars discussed the relation between social
security mechanism and economic growth based the
model from different aspect. For example, Barro(1974)
and Romer(1986) discussed the influence of pay as you
go pension on economic growth from bequests motivation
and personal savings respectively[2-3]. Casamatta(2000)
constructed a two period OLG model to analysis the
reallocation function of social security[4]. Luciano and
Luca(2007) analyzed the effects of the regulation of
wages in a standard one sector OLG model of neoclassical
growth extended to account for endogenous fertility
decisions of households and unemployment benefit
policies financed at balanced budget[5]. Sebastian and
Thomas(2010) developed a decomposition algorithm by
which a market economy with many households may be
solved through the computation of equilibria in OLG
models[6]. Moreover, many scholars explode the influence
of population changing on economic development of
OECD countries, such as Auerbach and Kotlikoff (1989),
Kiaus(1993), Hviding and Mérette(1998), Mérette and
Fougère (2000) etc[7-10].
Public pension reforming has been launched in 1997
in China. In recent years, OLG model has been used for
studying the transition cost, invisible debt, dynamic
effectiveness during the pension reforming. For example,
Bo Jie(2000) explored the influence of different
institutional arrangement on economic growth and Pareto
efficiency[11]. Yuan Zhigang and Song Zheng(2000) made
a conclusion that the personal saving rates in China was
efficient while the macro savings rate was ineffective
through constructing OLG model and simulation[12]. Yuan
Zhigang and He Zhangyong(2003) discussed the
possibility of dynamic inefficiency in free competition
economic with the help of OLG model[13]. Yang
Zaigui(2008) analyzed endowment insurance for
enterprise employees based on OLG model, to get the
optimum pension replacement rate in a general
equilibrium frame[14]. Wang Xiaofang and Zhai
Yonghui(2010) analyzed the economic effects of the
occupational pension system from macroeconomic capital
and output, microeconomic producers and microeconomic
consumers based on OLG model[15]. Li Hongxin and Bai
Xuemei(2006) constructed an OLG model by GAMS
software, whose input variable was population age
changing, to illustrate the changing of social output,
personal consumption and government revenue arise from
population ageing in China[16]. Huang Shaoan(2005)
analyzed the difference in informal institutions and
consumption modes in OLG model, and made a
theoretical analysis on households’ consumption in the
oriental culture and belief[17]. Liu Qingbin and Hao
Shenglong(2011) constructed a discrete time bilateral
generation transfer model, and discussed the optimal
investment structure and economic growth pattern[18]. Lu
Dong(2011) constructed a three period OLG model, to
explain the influence of population structure and income
growth on personal savings in China[19].
This paper makes a research on the optimal
enterprise contribution in partially funded endowment
insurance of Hunan province based on OLG equilibrium
framework. Combining the characteristics of population
structure and economic growth in Hunan Province,
parameter selection and model improvement has been
analyzed. The rest has been arrangement as follows. Part
II introduced the basic framework of OLG model and
made a deriving of optimal enterprise contribution. Part
III made an empirical research on the selection of optimal
enterprise contribution in urban old-age insurance of
Hunan province. And the last section was the conclusion
and future research suggestions.
u’(.)>0, u’’(.)<0. Enterprise produces homogeneous goods
in competitive market, satisfying first order homogeneous
production function yt=f(kt), in which function kt presents
labor capital ratio. Enterprise contribution rate for
endowment insurance is η∈(0,1).
According to Euler theorem, interest rate equals to
the marginal capital output, while (1+η)wt equals to the
marginal labor output, satisfying:
(4)
rt  r '(kt ) w  f (kt )  kt f '(kt )
t
1 
(5)
bt Nt  1   wt Nt , gt   wt
The government takes enterprises’ contribution as
overall planning account, paying as public pension for
current retirees; while personal’s contribution as
accumulated personal account, which would be drawn
after retirement. Furthermore, the capital market would
satisfy the following equation. That’s the savings plus
personal account of the tth labor equals the capital stock at
the beginning of t+1 period.
st  gt  (1  n)kt 1
(6)
B. Dynamic Equilibrium and Its Stability Conditions
II. BASIC FRAMEWORK OF OLG MODEL AND
DERIVING OF OPTIMAL ENTERPRISE
CONTRIBUTION
This paper conducts research based on equilibrium
framework raised by Yang Zaigui(2010) [20]. Suppose that
there are many persons, many enterprises and one
government in an infinite closed economy. Personal life is
finite, and experiences working period and retirement
period. At the beginning of t, there are Nt persons become
workingmen in the tth generation. The rate of population
growth can be calculated as
n
Nt
 1.
N t 1
(1)
The partially funded endowment insurance was
introduced.
A. Basic Framework of OLG Model
Supposing everyone provide a unit nonelasticly labor
while working, obtains income equals wt, contribution
rate for endowment insurance is τ, consumes c1t and saves
st. Furthermore, the individual consumes c2t+1 after
retired, including the principal and interest of savings
while working (1+rt+1)st, the payments of funded personal
account is (1+rt+1)gt, and the public pension is bt+1. The
person selected the pattern of savings and two periods
consuming for pursuing utility maximizing.
(2)
max{st ,c1t ,c2 t 1 } U t  u (c1t )   u (c2t 1 )
s.t. c1t  (1   )wt  st , c2t 1  (1  rt 1 )st  (1  rt 1 ) gt  bt 1 (3)
Parameter θ ∈ (0,1) presents discount factor. The
utility function u(.) is a monotonous increasing function
of consumption, and a strict concave function, satisfying
Supposing the dynamic system exists a stationary
equilibrium which is single, stable and no oscillation.
A dynamic equilibrium equation could be obtained
as follow.
f (kt )  kf '(kt )
 (1  n)kt 1 )   [1  f '(kt 1 )]
1 

u '((1  n)kt 1[1  f '(kt 1 )]  (1  n)
[ f (kt 1 )  kt 1 f '(kt 1 )])  0
1 
u '(
(7)
C. Equilibrium Equation for Optimal Enterprise Contribution
In order to make the state of market economy reach
the optimal state, policy parameters should be adjusted, to
obtain optimal capital labor ratio.
From functions described above, we could obtain the
equilibrium equation for optimal enterprise contribution.
p (1   )
1 n

 (1  n   )  [ p  (1  p) 
 (1  p)  (1  n)]
 


1 (1   )
1 n

 (1  n   )  [ p  (1  p) 
 (1  p)  (1  n)]
p 

(8)
According to the equation above, we could know that
the optimal enterprise contribution would be influenced
by survival probability of retirement P, social discount
factor ρ, capital income share α and population growth
rate n.
III. AN EMPIRICAL RESEARCH ON OPTIMAL
ENTERPRISE CONTRIBUTION OF HUNAN
PROVINCE
This section discussed the optimal enterprise
contribution of Hunan province through empirical
research based on OLG equilibrium framework.
There are 3 steps for empirical. Firstly, parameters
would be set according the population structure and
economic development of Hunan province, and then
social discount factor would be estimated. Secondly, the
value of parameters would be brought in the equilibrium
function. And the optimal enterprise contribution would
be obtained with the supposing of population growth
remaining unchanged. Lastly two variables, life
expectancy growth and population growth rate decline
would be introduced in the equilibrium framework, and
the combined effect would be examined.
A. Set Parameters and Estimate Social Discount Factor
Parameter capital income share α is usually equals
0.3 for developed countries. While income of labor is
lower in China, and Hunan province has a large
population density. Therefore, parameter α is 0.36.
Urban population of Hunan province is adopted as
population statistics caliber. According to the data
announced by the Department of Economic and Social
Affairs of United Nations, the life expectancy growth
would be increased to 80.3 years old in 2055-2060.
Therefore, the length of one period is set 27 years, which
satisfying the condition “three periods time span should
be equal or greater than life expectancy growth to
guarantee survival probability P of retirement less than or
equal to 1”.
According to Hunan province statistics yearbook
2007, the urban population growth rate could be
calculated n=(2619.93/639.6)-1=3.092 during 1979- 2006.
The life expectancy of Hunan province was announced to
73.8 years old by Hunan province bureau, so survival
probability of retirement could be calculated as
p=73.33%.
Furthermore, according to relevant policies, the town
enterprise contribution η=20%.
Parameter social discount factor could reflect social
planners’ preferences. Bringing all value of parameters in
(8), we obtain that ρ=0.5458.
B. Estimation of Optimal Enterprise Contribution with
Population Growth Rate Fixed
With the promotion of living quality and
improvement of medical conditions, the life expectancy is
increasing. Because of the limitation of data available, we
assume that the life expectancy in Hunan province is the
same as the whole country.
According to the data announced by Department of
Economic and Social Affairs of United Nations, we could
obtain the life expectancy of Chinese in future 30
years(the data could be seen in Table. I).
Bringing the values of parameters set above in (8),
including α=0.38, n=3.0962, ρ=0.5458, the optimal
enterprise contribution could be obtained under different
life expectancy.
According to Tab.1, the optimal enterprise
contribution increases along with the life expectancy
ascend.
TABLE I
ESTIMATION OF OPTIMAL ENTERPRISE CONTRIBUTION (FIXED
POPULATION GROWTH RATE)
Period
Life expectancy
η
P
2015-2020
74.7
0.7667
0.2104
2020-2025
75.6
0.8
0.2189
2025-2030
76.4
0.8296
0.2251
2030-2035
77.2
0.8592
0.2297
And in the next 25 years,
China would be increased from
years old. If population growth
enterprise contribution would be
22.97%.
the life expectancy in
73.8 years old to 77.2
rate fixed, the optimal
promoted from 20% to
C. Estimation of Optimal Enterprise Contribution with
Population Growth Rate Decline
China has executed very strict one-child policy since
1980s, so human fertility declined rapidly, which is the
main reason for population ageing. Low fertility, low
mortality, low population growth rate, has been the main
characteristic of the population of China. The changing of
population growth rate would influence population age
composition, social support rate, and then the optimal
enterprise contribution.
Table II shows the result of the optimal enterprise
contribution when both of the two variables, life
expectancy growth and population growth rate decline
have been brought in the equilibrium framework.
According to Tab.2, the optimal enterprise contribution
declined while both of the two variables, life expectancy
growth and population growth rate decline have been
brought in the equilibrium framework.
TABLE Ⅱ
ESTIMATION OF OPTIMAL ENTERPRISE CONTRIBUTION (TWO
VARIBLES CHNGING)
Period
Life expectancy
2015-2020
74.7
2020-2025
75.6
2025-2030
76.4
n
η
2.3133
0.1916
1.6405
0.1714
1.1032
0.1363
2030-2035
77.2
0.7928
0.1004
In the next 25 years, the life expectancy in China
would be increased from 73.8 years old to 77.2 years old
and population growth rate would decline continuously,
and then the optimal enterprise contribution would be
declined from 20% to 10.04%. Now that life expectancy
growth would increase the optimal enterprise contribution
and the changing of two variables make the optimal
enterprise contribution decline, therefore we could obtain
the conclusion that the population growth rate plays a
more important role than life expectancy growth in the
optimal enterprise contribution determine because of the
large population bass.
IV. CONCLUSION AND FUTURE RESEARCH
PROSPECT
Accompanying with population structure changing
and series problem of ageing population, reforming public
pension, pushing forward harmonious development of
social security, has becoming the focus of researches. The
optimal enterprise contribution is one of the most
important indexes, plays an important role for dynamic
balance for social security fund. OLG model could bring
the actions of personal, enterprises and the government
into an equilibrium framework, and it is a useful tool for
analyzing the influence of public pension reforming on
macro economy.
This paper has discussed the optimal enterprise
contribution of Hunan province based on the OLG model.
Firstly, we have introduced the basic framework of OLG
model and the deriving of optimal enterprise contribution;
and then we have made an empirical research on the
optimal enterprise contribution determination of Hunan
province. Empirical results show that life expectancy
growth would increase the optimal enterprise contribution
while population growth rate decline would lower the
optimal value. And the latter variable of population
growth rate plays a more important role because of the
large population base in China.
However, this paper discussed the optimal enterprise
contribution adjustment caused by parameters changing
based static equilibrium equations. How to constructing a
general dynamic equilibrium system to describe the real
state of pension operating and the dynamic changing of
parameters based social optimization, would be one of the
future research.
REFERENCES
[1] Diamond Peter A. “National debt in a neoclassical growth
model,” American Economic Review, vol. 55, no. 1, pp.
1126-1150, 1965.
[2] Barro Robert J. The impact of social security of private
saving. Washington: American Enterprise Inst, 1978, pp.2135.
[3] Romer Paul M., “Increasing returns and long run growth,”
Journal of Political Economy, vol. 94, no. 2, pp.1002-1037,
1986.
[4] Georges Casamatta, “The political economy of social
security,” Scand. J. of Economics, vol. 102, no. 3, pp.503522, 2000.
[5] Luciano Fanti, Luca Gori, “Fertility, income and welfare in
an OLG model with regulated wages,” Int. Rev. Econ.vol.54,
no.2, pp. 405–427, 2007.
[6] Sebastian Rausch, Thomas F. Rutherford, “Computation of
equilibria in OLG models with many heterogeneous
households,” Journal of Economics, vol. 36, no.2, pp. 171189, 2010.
[7] Auerbach Alan J., Laurence J. Kotlikoff, “The economic
dynamics of an ageing population: the case of four OECD
Countries,” OECD Economic Review, vol. 12, no. 1, pp. 97130, 1989.
[8] Kiaus Neusser, “Savings, social security, and bequests in an
OLG model：A Simulation Exercise for Austria,” Journal
of Economics, vol. 7, no.1, pp. 133-155, 1993.
[9] Hviding Ketil, Marcel Mérette, “Population effects of
pension reform in the context of ageing,” in OLG
simulations for seven OECD countries, OECD Working
Paper, 1998, pp.1-23.
[10] Maxime Fougère, Marcel Mérette, “Population ageing and
current account in selected OECD countries,” Working
Papers-Department of Finance Canada, vol. 4, no. 1, pp. 124, 1998.
[11] Bo Jie, “The influence of endowment insurance system
arrangement on economic growth and Pareto efficiency” (in
Chinese), Economic science, vol.27, no.1, pp.78-88, 2000.
[12] Yuan Zhigang, Song Zheng, “The age composition of
population, the endowment insurance aystem and optimal
savings ratio in China,” (in Chinese), Economic Research
Journal, vol. 11, no. 1, pp. 24-32, 2000.
[13] Yuan Zhigang, He Zhangyong, “Dynamic inefficiency in
China’s economy since 1990s,”(in Chinese), Economic
Research Journal, vol. 24, no. 7, pp. 18-27, 2003.
[14] Yang Zaigui, “The public pension for enterprise employees,
benefit replacement rate and population growth rate,” (in
Chinese), Statistical Research, vol. 25, no. 5, pp. 38-42,
2008.
[15] Wang Xiaofang, Zhai Yonghui, Yan Haifeng, “Economic
effects of the occupational pension system: the research
based on general equilibrium model,” (in Chinese). Nankai
Economic Studies, vol. 12, no. 5, pp. 46-55, 2010.
[16] Li Hongxin, Bai Xuemei, “Life-cycle model and its
application to research in aging China,” (in Chinese),
Chinese Journal of Population Science, vol.28, no.4, pp. 2835, 2006.
[17] Huang Shaoan, Sun Tao, “Informal institutions,
consumption modes and assumption of OLG model—a
theoretical analysis on households’ consumption in the
oriental culture and belief,” (in Chinese), Economic
Research Journal, vol. 24, no. 4, pp. 57-65, 2005.
[18] Liu Qingbin, Hao Shenglong, “Theoretical analysis on
uncertainty of aging issue in gift economy based on OLG
model,” (in Chinese), Statistical Research, vol. 28, no. 10,
pp. 84-90, 2011.
[19] Lu Dong, “Population structure, economic growth and
China's household saving: empirical research based on OLG
model and panel data,” (in Chinese), Shanghai Finance, vol.
32, no. 1, pp. 10-15, 2011.
[20] Yang Zaigui. OLG model analysis on public pension:
principles and applications. (in Chinese), Beijing:
Guangming Daily Press, 2010, pp. 27-45.