Towards a better understanding of pension systems
Aref Gharakhani
aref.gharakhani@gmail.com
Graduate school of Business and Economics
Teymouri Avenue, Azadi Street, Tehran, Iran.
Abstract: Pension systems are vital components of every economic system. During the last
two decades, population aging and financial insufficiencies in many countries forced
governments, corporations and private pension schemes to conduct reform to sustain their
pension systems.
This paper investigates different Pay-as-you-go and funded pension schemes in order to
provide a better understanding the dynamics and the structure behind a pension system.
Fully funded and unfunded schemes are modeled in a generic form. Issues of stability,
population dependency redistribution are discussed according to model structure and
simulation results. System dynamics provides and efficient tool to understand the nature of
each scheme.
Keywords: System Dynamics, Pension System, unfunded scheme, funded scheme,
Pension Reform.
1. Introduction to pension systems
a. What is pension system?
Pension systems are vital components of every social security system all
over the world. Objectives and general principles of pension systems
around the world actually differ, but public pension system objectives’
are to ensure that older people have a decent standard of living at
retirement.
There can be two interpretations of this primary objective [1]:
¢ To ensure a basic living standard.(Adequacy objective)
¢ To ensure a reasonable standard of living in retirement relative to
that position before retirement.(Insurance Objective)
As stated above, there are various degrees of emphasis on “adequacy” or
« a
Insurance objective.
b. Pension systems Taxonomy
Obviously there is no unique implementation for a pension system.
Pension systems can be categorized in terms of three main dimensions.
U1]
¢ How they are financed? (pay-as-you-go, fully funded, government
budget or some combination)
e¢ How they are managed?(earning related schemes, defined
contribution schemes or some combination)
¢ How the system is managed?(private or public, centralized or
decentralized management)
In Pay-as-you-go scheme contributions are paid by the currently
employed population in the form of tax (social security tax). In the
fully funded scheme, individuals save a constant fraction of their
labor income in an individual account (usually) managed by private
firms, which invests and accumulate these funds until retirement,
when these funds are used a source of retirement income. [2]
As in case of many countries, the pension plan is financed by the
government, corporations and the body of workers. For example in
Iran the system is financed by 3% of government’s contribution, 9%
contribution’s of the worker and 18% of corporation’s contribution.
c. Variables that affect pension system
Pension systems are indeed, complex systems. Their complexities rely in
demographic, economic, financial, political and social aspects of the
countries they are implemented in. In this part we discuss the influence
of different parameters -Both the past and future values- from different
sectors on pension systems.
¢ Demographics and Labor Market factors
© Population and average population growth
© Population mortality and life expectancy
o Workforce, working age, growth rate of workforce
o Average income of the workforce
¢ Macroeconomic factors
o Economic growth and GDP
Economic growth indirectly affect income growth factor.
Which specify the input flow of the pension fund.
Macroeconomic stability (Interest rate, Inflation rate)
Pension scheme coverage
How much percent of the work force is covered by the
pension scheme? Work force coverage is both a source of
threat and opportunity. In case of PAYG schemes,
extending work force coverage policies may reduce the
financial deficit of the scheme in short run. By the way, in
the long-run this policy may worsen the situation. As the
number of workers needed to be more than retirees in each
generation, when this policy is deployed, every future
generation must have more workers than the previous
generation. This mean, the population should always be
growing.
e Financial factors
© Stock markets
Stock market returns, affect the efficiency of pension
scheme investments.
2. Model
a. PAYG system
In this part, we develop a model for PAYG System.
We start with the basic structure of the model, the workforce aging-
chain. (Figure 1) “average Time in labor market” is a time constant.
In most countries, a worker usually works around 30 years in the labor
market until he/she retires. This constant usually differs between
genders.
“Life Expectancy - Avg rtmnt age” is indeed, the average years a
person receives pension. Suppose a country in which life expectancy is 80
years and workers retire at 60. So 80-60=20 is the average years a person
receives pension.
dependency ratio
fl
Time
Labor MarketGrowth
factor Average Time in
Labor market
Oo WE Retiree
Labor market retired out of Scheme
entry
Average Time as
Retiree
Figure 1 PAYG stock and flow structure (workforce)
Figure 2 illustrates the essence of PAYG structure, Taxes directly being
paid to retirees.
Proportion of
Income to fund Replacement
a Ratio
Average Income
oO PAYG fund
contribution benefits
Genome ( . eiveraper nesta
proportion i
irate
Figure 2-PAYG financial flow
Figure 3 illustrates the PAYG abstract model. “replacement rate” is a
level of a laborer’s wage to a retiree’s pension.
dependency ratio
ina? ay, Ps
Labor MarketGrowth
factor
Average Time in
Labor market
WE w| Retiree ~S
Labor market retired out of Scheme
entry
opulation
Proportion of pep
Income to fund Replacement
if Ratio
Average Income
2 we PAYG fund
contribution benefits
lemeneesietimeet ( , <Average Income
proportion i
irate
Figure 3-PAYG system stock and flow structure
Funded system
Funded scheme model does not differ with PAYG scheme so much,
except of its financial structure.
In Funded scheme, every individual account is indeed an investment
account. Accumulation of these individual accounts constituted a
Pension Fund. This fund is managed (Invested) in the country (or
abroad). At the retirement age, whole the accumulated fund a specific
account plus its major fraction of return is used as source of pension for
the owner of the account.
Figure 4 illustrates the funded scheme which is modeled by stock and
flow diagram.
The challenge of modeling of funded scheme is relied in the level of
aggregation. Differential equation models —as in system dynamics- are
based on high levels of aggregation while funded scheme is conceptually
disaggregated [6]. The challenge is handled through noting the fact that
every individual saving’s is going to be excluded from the Pension Fund
after “average time as retiree”. This solution is valid, when we assume
that individuals equally participate in the plan.
dependency ratio
Tim
:
Labor ‘at eh
factor Average Time in
Labor market
WE w| Retiree oS
Labor market retired out of Scheme
entry
Average Time as
population Retiree
Proportion of
Income to fund
Average Income a
O ~
| PAYG fund
-"_ benefits
Government + eee
proportion
irate
Figure 4 funded scheme stock and flow structure
3. Simulations
We assume that number of years an individual participated in the
scheme in equal to the number of years she/he receives pension.
As it’s stated in the literature of pension economics, PAYG schemes are
unstable facing demographic fluctuations.
Generally ,for the PAYG scheme to be stable, the labor market growth
rate should be at the exact amount of
1/Average Time in Labor market.
The financial structure is stable, when the every individual contributes
for the same amount as she/he benefits. These insights are presented in
the following Figures.
When the system is so-called mature, replacement rate should be equal
to level of contribution. If the replacement rate exceeds this number, the
system would collapse. Indeed “open-loop” PAYG system would
certainly collapse in case of any fluctuation beyond system’s threshold.
Replacement rate should not go above contribution rate, and
1/Years as employee should not drop below growth rate factor.
Figure 5 demonstrates the state of the system when it starts with no
retirees and when it starts from equilibrium. It also captures the state of
PAYG fund, when its parameters are not balanced (Replacement Rate=
0.5 instead of 0.3, which is the contribution rate).
-20M
0 0 2 30 40 50 60 7 80 90 100
Time (Year)
PAYG fund : replacement rate
PAYG fund : equilibriunr
PAYG fund: starts with no retir
Figure 5 state of the system, with different conditions.
4. Conclusion
As it is stated in [1],[4] , there is a large pool of pension systems for
countries from which to choose. Most countries follow a multi-pillar
system which includes a PAYG and a funded pillar.
Obviously there is no best design; there is optimal design for a given
situation of a country.
Open questions are, questions of transition between PAYG and Funded
scheme and whether if there is an optimal PAYG design — “a closed loop
PAYG”?
5. References
[1]. Robalino, D. (2005), Pensions in the Middle East and North Africa: Time
for change. World Bank assessment.
[2]. Cerda, R. A. (2007), The Chilean pension reform: A model to follow?,
Journal of Policy Modeling.
(3].Holzmann, R. (1998), A World Bank perspective on pension reform,
World Bank Assessment.
[4].Diamond, P. (2000), toward an optimal social security design. CePR
working paper available at http://cerp.unito.it
[5].March, C.L & Scovill, M. using System dynamics to model the social
security system. NBER Workshop on Policy Analysis with Social Security
Research Files, Social Security Administration, Office of Research, pages 459-
469.
[6].Rahmandad, Hazhir. Sterman, John (2008), Heterogeneity and Network
structure in the Dynamics of Diffusion: Comparing agent-based and
Differential Equation Models, Management Science Vol. 54(5), pp. 998-1014.
Note to referees: Work is still in progress.
