1. AZERBAIJAN REPUBLIC
KHAZAR UNIVERSITY
School : Economics & Management
Major : Finance
Student : Hikmet Tagiyev Sakhavet
Supervisor: Dr. Oktay Ibrahimov Vahib
BAKU 2007
2. Actuarial analysis in social security
Acknowledgments
I would like to express my gratitude to my supervisor Dr.Oktay Ibrahimov, director of the
“Capacity Building for the State Social Protection Fund of Azerbaijan Republic” Project, for the
support, encouragement and of advices provided during my research activity.
My deepest thanks go to Ms. Vafa Mutallimova, my dear instructor, whom I consider as one of
the perspective economist of Azerbaijan. She added a lot to my knowledge in Finance and
Econometrics and encouraging to continue my studies.
I profoundly thank my best friend Ilker Sirin (Actuary expert of Turkish Social Security System)
for all the help and support he provided during my stay in Turkey. My thanks go also to Prof.
Nazmi Guleyupoglu, Umut Gocmez and Salim Kiziloz.
I would like to extent my sincere thanks to Ms. Anne Drouin at International Labour Organization
(Governance, Finance and Actuarial Service Coordinator) and Mr. Heikki Oksanen at European
Commission (Directorate General for Economic and Financial Affairs). In spite of the work load
they usually have provided invaluable assistance in improving of my actuarial analysis thesis.
I am especially grateful to Patrick Wiese of Actuarial Solutions LLC who kindly shared with me
his Pension Reform Illustration & Simulation Model, PRISM, which I used for calculating the
scenarios, reported in this paper. I should never forget his useful and valuable comments on
actuarial calculations.
I would like to give the assurances of my highest consideration to Ms. Alice Wade (Deputy Chief
Actuary of Social Security Administration of USA) that she has done a great favour for me in
Helsinki at “15th International Conference of Social Security Actuaries and Statisticians” on May
23-25, 2007. I listened to her very interesting topics “Mortality projections for social security
programs in Canada and the United States" and "Optimal Funding of Social Insurance Plans". Also
I would like to thank her for getting me their long-range projection methodology.
Last but not least. I express my deepest regards and thanks for my instructors at Khazar
University: Prof.Mohammad Nouriev, Mr.Sakhavet Talibov, Ms.Nigar Ismaylova, Ms.Arzu
Iskenderova, Ms.Samira Sharifova, Mr.Gursel Aliyev, Mr.Yashar Naghiyev, Mr.Shukur
Houseynov, Mr.Eldar Hamidov, Mr.Namik Khalilov, Mr.Sohrab Farhadov, Ms.Leyla Muradkhanli.
A special thank you accompanied with my sincere apology for all the friends whom I forget to
mention in this acknowledgement.
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3. Actuarial analysis in social security
Table of contents
Introduction........................................................................................................................................4
1. The role of actuaries in social security.........................................................................................5
1.1 The goal of actuarial analysis..................................................................................................5
1.2 Principles and techniques of actuarial analysis.....................................................................6
2 Macro- economic parameters in actuarial calculations ............................................................13
2.1 Economic growth ...................................................................................................................14
2.2 Labour force, employment and unemployment..................................................................14
2.3 Wages ......................................................................................................................................15
2.4 Inflation...................................................................................................................................16
2.5 Interest rate ............................................................................................................................16
2.6 Taxes and other considerations ............................................................................................17
3. Financial Aspects of Social Security...........................................................................................18
3.1 The basics of the pension systems.........................................................................................18
3.2 Types of pension schemes......................................................................................................22
3.2.1 Pay-as-you-go (PAYG) ...................................................................................................22
3.2.2 Fully funding (FF)...........................................................................................................23
3.2.3 The respective merits of the PAYG and FF systems ...................................................23
3.2.4 Partial funding - NDC ....................................................................................................26
3.3 Pension financing ...................................................................................................................30
3.4 Benefit Calculation.................................................................................................................31
3.5 Rate of Return (ROR) ...........................................................................................................32
3.6 Internal Rate of Return (IRR) ..............................................................................................35
3.7 Net Present Value (NPV).......................................................................................................36
4. Actuarial practice in Social Security System of Turkey...........................................................37
4.1 Characteristics of Turkish Social Security System (TSSS)................................................37
4.2 Scheme- specific inputs, assumptions and projections .......................................................39
4.2.1 The population projection model ..................................................................................40
4.2.2 Data and assumptions.....................................................................................................42
4.2.3 Actuarial projections ......................................................................................................45
4.3 Sensitivity Analysis ................................................................................................................51
4.3.1 Pure scenarios..................................................................................................................51
4.3.2 Mixed scenarios...............................................................................................................53
5. Some actuarial calculations with regards to the pension system of Azerbaijan ....................55
Conclusion ........................................................................................................................................60
Appendix...........................................................................................................................................61
References .........................................................................................................................................63
Discussion of preceding paper ........................................................................................................65
3
4. Actuarial analysis in social security
Introduction
The actuarial analysis of social security schemes requires to actuary to deal with complex
demographic, economic, financial, institutional and legal aspects that all interact with each other.
Frequently, these issues retain their complexity at the national level, becoming ever more
sophisticated as social security schemes evolve in the context of a larger regional arrangement.
National or regional disparities in terms of coverage, benefit formulae, funding capabilities,
demographic evolution and economic soundness and stability complicate the actuarial analysis still
further.
Under this thesis, social security actuaries are obliged to analyse and project into the future
delicate balances in the demographic, economic, financial and actuarial fields. This requires the
handling of reliable statistical information, the formulation of prudent and safe, though realistic,
actuarial assumption and the design of models to ensure consistency between objectives and the
means of the social security scheme, together with numerous other variables of the social,
economic, demographic and financial environments.Taking into consideration these facts I have
analyzed some actuarial calculation regarding to the pension system of Azerbaijan as well in this
thesis.
In this thesis there are five main chapters: Chapter One provides a general background to the
particular context of actuarial analysis in social security, showing how the work of social security
actuary is linked with the demographic and macroeconomic context of country.
The Chapter Two focuses on the evolution of the economic and the labour market environments of
a country that is directly influence the financial development of a social security scheme. The
evolution of GDP (its primary factor income distribution), labour productivity, employment and
unemployment, wages, inflation and interest rates all have direct and indirect impacts on the
projected revenue and expenditure of a scheme.
The Chapter Three I introduce the key concepts for typical pension systems in a very simple
setting, including an assumption of a stationary population. It presents a step-by-step account of the
usual process of the actuarial analysis and tries, at each stage to give appropriate examples to
illustrate the research work concretely.
The Chapter Four summarizes the basic characteristics of the Turkish Social Security
System.(TSSS) In this chapter the TSSS is analyzed in detail. Also a brief outline of the ILO
pension model adopted for TSSS to simulate the TSSS pension scheme, data sources, assumptions,
and parameter estimation based on Turkish data are presented. Taking 1995 as the base year, and
the prevailing conditions in that year as given, several scenario analyses are carried out.
At the Chapter Five I do some actuarial calculations regarding to the pension system of
Azerbaijan.
The conclusion of this thesis summarizes the outcomes and the implications of the entire study.
4
5. Actuarial analysis in social security
1. The role of actuaries in social security
From the beginning of the operation of a social security scheme, the actuary plays a crucial role
in analyzing its financial status and recommending appropriate action to ensure its viability. More
specifically, the work of the actuary includes assessing the financial implications of establishing a
new scheme, regularly following up its financial status and estimating the effect of various
modifications that might have a bearing on the scheme during its existence.
This chapter sets out the interrelationships between social security systems and their
environments as well as their relevance for actuarial work. Meaningful actuarial work, which in
itself is only one tool in financial, fiscal and social governance, has to be fully cognizant of the
economic, demographic and fiscal environments in which social security systems operate, which
have not always been the case.
1.1 The goal of actuarial analysis
The actuarial analysis carried out at the inception of a scheme should answer one of the
following two questions: 1
• How much protection can be provided with a given level of financial resources?
• What financial resources are necessary to provide given level of protection?
The uncertainties associated with the introduction of a social security scheme require the
intervention of, among other specialists, the actuary, which usually starts during the consultation
process that serves to set the legal bases of a scheme. This process may lengthy, as negotiations
take place among the various interest groups, i.e. the government, workers and employers. Usually
each interest group presents a set of requests relating to the extent of the benefit protection that
should be offered and to the amount of financial recourses that should be allocated to cover the
risks. This is where the work of the actuary becomes crucial, since it consists of estimating the long
–term financial implications of proposals, ultimately providing a solid quantitative framework that
will guide future policy decisions.
1.1.1 Legal versus actual coverage
“Who will be covered?” One preoccupation of the actuary concerns that definition of the covered
population and the way that the coverage is enforced. Coverage may vary according to the risk
covered. A number of countries have started by covering only government employees, gradually
extending coverage to private sector employees and eventually to the self-employed. A gradual
coverage allows the administrative structure to develop its ability to support a growing insured
population and to have real compliance with the payment of contributions. Some categories of
workers, such as government employees, present no real problem of compliance because the
employer’s administrative structure assures a regular and controlled payment of contributions. For
other groups of workers, the situation may be different. These issues will have an impact on the
basic data that the actuary will need to collect on the insured population and on the assumptions
that will have to be set on the future evolution of coverage and on the projected rate of companies.
1
See for instance, Pierre Plamandon, Anne Drouin (2002)”Actuarial practice in social security” ,International Labour Office
5
6. Actuarial analysis in social security
1.1.2 Benefit provisions
“What kind of benefit protection will be provided?” Social security schemes include complex
features and actuaries are usually required, along with policy analysts, to ensure consistency
between the various rules and figures. The following design elements will affect the cost of the
scheme and require the intervention of the actuary:
• What part of workers’ earnings will be subject to contributions and used to compute
benefits? (This refers to the floor and ceiling of earnings adopted for the scheme.)
• What should be the earnings replacement rate in computing benefits?
• Should the scheme allow for cross-subsidization between income groups through the benefit
formula?
• What will be the required period of contribution as regards eligibility for the various
benefits?
• What is the normal retirement age?
• How should benefits be indexed?
As the answers to these questions will each have a different impact on the cost of the scheme, the
actuary is asked to cost the various benefit packages. The actuary should ensure that discussions are
based on solid quantitative grounds and should try to reach the right balance between generous
benefits and pressure on the scheme’s costs.
At this stage, it is usual to collect information on the approaches followed in other countries. Such
comparisons inform the policy analysts on the extent of possible design features. Furthermore,
mistakes made in other countries can, hopefully, be avoided.
1.1.3 Financing provisions
“Who pays and how much?” The financial resources of a social insurance scheme come from
contributions and sometimes from government subsidies. Contributions are generally shared
between employers and employees, except under employment schemes, which are normally fully
financed by employers.
This issue is related to determining a funding objective for the scheme or, alternatively, the level
of reserves set aside to support the scheme’s future obligations. The funding objective may be set in
the law. If not, then the actuary will recommend one. In the case of a pension scheme, however, the
funding objective will be placed in a longer-term context and may consider, for example, the need
to smooth future contribution rate increases. Different financing mechanisms are available to match
these funding objectives. For example, the pension law may provide for a scaled contribution rate
to allow for a substantial accumulation of reserves during the first 20 years and thereafter a gradual
move towards a PAYG system with minimal long-term reserves. In the case of employment injury
schemes, transfers between different generations of employers tend to be avoided; hence, these
schemes require a higher level of funding.
1.2 Principles and techniques of actuarial analysis
The actuarial analysis starts with a comparison of the scheme’s actual demographic and financial
experience against the projections. The experience analysis serves to identify items of revenue or
expenditure that have evolved differently than predicted in the assumptions and to assess the extent
of the gap. It focuses on the number of contributors and beneficiaries, average insurable earnings
and benefits and the level of administrative expenses. Each of these items is separated and analyzed
by its main components, showing, for example, a difference in the number of new retirees,
unexpected increases in average insurable earnings, higher indexing of pensions than projected, etc.
6
7. Actuarial analysis in social security
The experience analysis and the economic and demographic prospects indicate areas of
adjustment to the actuarial assumptions. For example, a recent change in retirement behaviour may
induce a new future expected retirement pattern. A slowdown in the economy will require a
database of the number of workers contributing to the scheme. However, as actuarial projections for
pensions are performed over a long period, a change in recently observed data will not necessarily
require any modifications to be made to long-term assumptions. The actuary looks primarily a
consistency between assumptions, and should not give undue weight to recent short-term
conjectural effects.
There are 2 actuarial techniques for the analysis of a pension scheme: the projection technique
and the present value technique
1.2.1 – The projection technique
There are different methodologies for social security pension scheme projections. These include:
(a) actuarial methods,
(b) econometric methods and
(c) mixed methods.
Methods classified under (a) have long been applied in the field of insurance and have also proved
valuable for social security projections.
Methods classified under (b) are in effect extrapolations of past trends, using regression
techniques. Essentially the difference between the two is that actuarial methods depend on
endogenous (internal) factors, whereas econometric methods are based on exogenous factors.
Methods classified under (c) rely partly on endogenous and partly on exogenous factors.
The first step in the projection technique is the demographic projections, production of estimates
of numbers of individuals in each of the principal population subgroups(active insured persons,
retirees, invalids, widows/widowers, orphans )at discrete time-points (t=1,2,..),starting from given
initial values (at t=0).
The demographic projection procedure can be regarded as the iteration of a matrix multiplication
operation, typified as follows: 2
nt = nt −1 ⋅ Qt −1 (1.1)
in which nt is a row vector whose elements represent the demographic projection values at time t
and Qt −1 is a square matrix of transition probabilities for the interval (t-1, t) which take the form:
nt = [A(t) R(t) I(t) W(t) O(t)]
(1.2)
p (aa) q (ar) q (ai) q (aw) q (ao)
(rr)
0 p 0 q (rw) q (ro)
(1.3)
Qt = 0 0 p (ii) q (iw) q (io)
0 0 0 p (ww) 0
0 0
0 0 p (oo)
The elements of the matrix and the symbols have the following significance:
p (rr) denotes the probability of remaining in the same r;
q (rs) denotes the probability of transition from status r to status s;
a, r , i , w and o respectively represent active lives , retirees, invalids, widows/widowers and
orphans .
2
See for instance, Subramaniam Iyer (1999)”Actuarial mathematics of social security pensions” ,International Labour Office
7
8. Actuarial analysis in social security
The above procedure, however, is not applied, at the level of total numbers in the subpopulations.
In order to improve precision, each subpopulation is subdivided at least by sex and age. Preferably,
the active population would be further subdivided by past service. The procedure is applied at the
lowest level of subdivision and the results aggregated to give various subtotals and totals. The
matrix Q will be sex-age specific, it can also be varied over time if required. As regards survivors,
an additional procedure is required after each iteration to classify new widows/widowers and
orphans arising from the deaths of males/females aged x according to the age of the
widow/widower or of the orphan before proceeding to the next iteration.
For carrying out the demographic projections it is necessary to adopt an actuarial basis,
consisting of the elements listed below. They should be understood to be sex specific. For brevity,
time is not indicated as a variable, but some or the entire basis may be varied over time.
a - The active table l xa , b ≤ x ≤ r , where b is the youngest entry age and the r the highest
retirement age. This is a double decrement table allowing for the decrements of death and invalidity
only. The associated dependent rates of decrement are denoted by q x (mortality) and i x (invalidity).
a
Retirement is assumed to take place at exact integral ages, just before each birthday, r x denoting the
proportion retiring at age x.
i
b - The life table for invalids l x , b ≤ x < D and the associated independent mortality rate q x.
i
c - The life table for retired persons, l xp , r ≤ x < D (where r is the lowest retirement age and D is
p
the death age) and the associated independent rate of mortality q x
d - The double decrement table for widows/widowers, l y , y* ≤ y ≤ D (where y *is the lowest age
w
w
of a widow /widower) and the associated dependent rates of decrement q y (mortality) and
(remarriage) h y *
o *
e - The single decrement table for orphans, l z , 0 ≤ z ≤ z where z is the age limit for orphans’
pensions and the associated independent mortality rate q o z
f - w,x the proportion of married persons among those dying at age x.
g - y x , the average age of the spouse of a person dying at age x.
h - n x , the average number of orphans of a person dying at age x.
i - z x , the average age of the above orphans.
The following expressions for the age and sex – specific one year transition probabilities are
based on the rules of addition and multiplication of probabilities:
Active to active p (aa) = (1 - q a - i x ) ⋅ (1 - rx + 1 )
x x (1.4)
Active to retiree q (ar) = (1 - q a - i x ) ⋅ rx +1
x x
(1.5)
Active to invalid q (ai)x = (1 - 0,5 ⋅ q ix ) ⋅ i x (1.6)
(1.7)
Active to widow/widower q (aw)x = q (aw1)
x + q (aw2)
x
(1.7.a)
x x [
q (aw1) = q a w x+0,5 1 - 0,5(qwx + hyx )
y ]
1 i
q (aw2) = ix
x
2
[
q x w x +0,75 1 - 0,25(qwx + hyx )
y ] (1.7b
)
Retiree to retiree p (rr) = 1 - q p
x x (1.8)
Retiree to widow/widower x x [
q (rw) = q p w x+0,5 1 - 0,5(qwx + hyx )
y ] (1.9)
8
9. Actuarial analysis in social security
Invalid to invalid p (rr) = 1 - q ix
x (1.10)
Invalid to widow/widower
[
q (iw) = q ix w x+0,5 1 - 0,5(qwx + hyx )
x y ] (1.11)
Widow/widower to widow/widower
p (ww) = 1 - q w - h x
x x (1.12)
Each iteration is assumed to operate immediately after the retirements (occurring at the end of
each year of age).Under the assumption of uniform distribution of decrements over each year of
age, the decrements affecting active persons, retirees and existing invalids –in (1.6),( 1.7a), (1.9)
and (1.11) are assumed to occur, on average at the of six months, new invalids dying before the end
of the year are assumed to die at the end of nine months in (1.7b).
It will be noted that equation (1.7) has two components: (1.7a) relating to deaths of active insured
persons in the age range (x, x+1) and (1.7b) relating to active persons becoming invalid and then
dying at by age x+1. It is understood that the values of w x corresponding to fractional ages which
occur in the above formula would be obtained by interpolation between the values at adjacent
integral ages. Expressions for transition probabilities concerning orphans, corresponding to (1.7a),
(1.7b), (1.9), (1.11) and (1.12) can be derived on the same lines as for widows/widowers.
Starting from the population data on the date of the valuation (t=0), the transition probabilities
are applied to successive projections by sex and age (and preferably by past service , in the new
entrants of the immediately preceding year have to be incorporated before proceeding to the next
iteration. The projection formula for the active insured populations are given below, the method of
projecting the beneficiary populations is illustrated with reference retirement pensioners.
Notation
• Act(x ,s ,t ) denotes the active population aged x nearest birthday , with curtate past service
duration s years at time t, b ≤ x < r, s ≥ 0
• Ac (x , t) denotes the active population aged x nearest birthday at time t. The corresponding
beneficiary populations are denoted by Re(x, t), In (x, t) and Wi (x, t).
• A(t) denotes the total active population at time t. The corresponding beneficiary populations
are denoted by R( t), I (t) and W ( t).
• The number of new entrants aged x next birthday in the projection year t, that is in the
interval (t-1,t ) is denoted by N(x,t)
The projection of the total active and beneficiary populations from time t-1 to time t is
expressed by the equation
r
A(t ) = ∑∑ Act ( x, s, t ) + Act ( x-1,s-1,t-1) ⋅ ( p (aa) − q xar ) − q xai ) − q xaw) − q x )
x-1
( ( ( a
(1.13)
x =b s >0
D
R (t ) = ∑ Ac(x − 1,t − 1) ⋅ q (ar) + Re(x − 1,t − 1) ⋅ (p (rr) − q x )
x −1 x −1
r
(1.14)
x=r
After the demographic projections is the production of estimates of the total annual insured salary
bill and of the total annual amounts of the different categories of pensions “in force” at discrete
time points (t=1, 2…) starting from given initial values at t=0. These aggregates are obtained by
applying the appropriate per capita average amounts (of salaries or of pensions, as the case may be)
to each individual element of the demographic projections and the summing. The average amounts
are computed year by year in parallel with the progress of the corresponding demographic
projection. An average per capita amount (salary or pension, as the case may be) is computed for
each distinct population element generated by the demographic projection; if different elements are
aggregated in the demographic projection –for example, existing invalids surviving from age x to
x+1 and new invalids reaching age x+1 at the same time –a weighted per capita average amount is
computed to correspond to the aggregated population element.
9
10. Actuarial analysis in social security
ILO-DIST method will be described below regard to the projection of the insured salary. This
method begins by modeling a variation over time in the age-related average salary structure and
then computes age and time –related average salaries allowing for general salary escalation.
Further, it models the salary distribution by age, which can increase the precision of the financial
projections.
The basis for the financial projections would comprise assumptions in regard to the following
elements. They are specified as functions of age or time, the age-related elements should be
understood to be sex specific and may be further varied over time, if necessary.
(a) The age –related salary scale function aged x at time t: ss(x,t)
(b) The factor average per capita pension amount of the pensioners aged x at time t: b(x,t)
(c) The rate of salary escalation (increase) in each projection year: γ t
(d) The rate of pension indexation in each projection year: β t
(e) The contribution density, that is, the fraction of the year during which contributions are
effectively payable, dc(x)
The average salary at age x in projection year t is then computed by the formula
∑ ∑ Ac(y,t)
r −1 r −1
s(y,t − 1) ⋅ Ac(y,t − 1)
s(x,t) = ss(x,t) ⋅ (1 + γ ) ⋅ b
⋅ b
(1.15)
∑ ∑ Ac(y,t − 1)
t r −1 r −1
b
ss(y,t) ⋅ Ac(y,t) b
where Ac(y,t) denotes the projected active population aged y at time t.
The total insured salary bill “in force” at time t would be estimated as:
S (t ) = ∑ Ac( x, t ) ⋅ s ( x, t ) ⋅ dc( x) (1.16)
x
The total pension amount at time t would be estimated as:
P(t ) = ∑ Re( x, t ) ⋅ b( x − 1, t − 1) ⋅ (1 + β t ) (1.17)
x
Such detailed analysis may not be justified in the case of a simple pension formula such as in
(1.17), but if the formula is more complex –involving minimum or maximum percentage rates or
varying rates of accrual , or being subject to minimum or maximum amounts –such analysis could
significantly improve the precision of the projected and would therefore be justified.
1.2.2 –The present value technique
This technique considers one cohort of insured persons at a time and computes the probable
present values of the future insured salaries, on the one hand and of the pension benefits payable to
the members of the cohort and to their survivors, on the other.
In what follows, discrete approximations to the continuous commutation functions will be
developed, in order to permit practical application of the theory. The treatment will be extended to
invalidity and survivors benefits. Reference will be made to the same demographic and financial
bases as for the projection technique. However certain simplifications in the bases will not be
considered. Thus γ t (salary growth rate), β t (pension indexation rate), δ t (interest rate) are assumed
constant and interest rates i and j and corresponding discounting factors are introduced where
1+ δ , 1 (1.18)
i= −1 v=
1+ γ 1+ i
1+ δ , 1
j= −1 u= (1.19)
1+ β 1+ j
10
11. Actuarial analysis in social security
The present value formulae will be developed for the simple case where the pension accrues at
1percent of the final salary per year of service.
Special commutation functions
A series (sex-specific) special commutation functions are needed for applying the present value
technique. These are based on one or other of the decrement tables or on combinations of them.
Functions based on the active service table will be computed at interest rate i, while those based on
the other tables will be computed at rate j.
Functions based on the active service table ( l xa , b ≤ x ≤ r )
D xa = l xa ⋅ v x (1.20)
D xas = D xa ⋅ s x (1.21)
− as as
D +D as
x x +1
Dx =
2 (1.22)
− as r −1 −
Nx = ∑D t
as
t=x (1.23)
i
Functions based on the life table for invalids ( l x , b ≤ x < D )
Dx = l x ⋅ u x
i i
(1.24)
− i D +D i i
x x +1
Dx = (1.25)
− i D −2
N x = ∑ Dti
t=x
− i
(1.26)
−i Nx
ax = i
Dx (1.27)
Functions based on the double decrement table for widows/widowers ( l y , y* ≤ y ≤ D)
w
Dy = l y ⋅ u y
w w
(1.28)
w w
− w D +D y y +1
Dy =
2 (1.29)
− w D −
N y = ∑ Dy
w
t=y (1.30)
− w
−w Ny
ay = w (1.31)
Dy i
Functions based on the active service table and the life table for invalids ( l x , b ≤ x < r )
i −
C xai = D x ⋅ i x ⋅ v 0,5 ⋅ a x + 0,5
a (1.32)
C xais = s x +0,5 ⋅ C xai
(1.33)
Functions based on the life table for retirees ( l xp , r ≤ x < D )
D xp = l xp ⋅ u x (1.34)
∑
D p p
− p
t =r
Dt + D t +1
Nx = (1.35)
− p
2
− p Nx
ax = (1.36)
D xp
11
12. Actuarial analysis in social security
The above commutation and annuity functions relate to continuously payable salaries and
pensions and may be adequate if payments are made frequently, for example weekly. They can be
adjusted to correspond more exactly to any specific payment schedule. For example, if pensions are
payable monthly and in arrears, (1.27) should be replaced by
i
i (12 ) i 11 N x +1 11 (1.37)
ax = ax + = i +
24 Dx 24
Expressions for probable present values of insured salaries and benefits
The following expressions relate to a cohort of a specific sex, aged x on the date of valuation and
refer to a unit insured salary on the date. The expressions for orphans are not indicated but can be
derived on the same lines as for widows/widowers.
Present value of insured salaries ( b ≤ x < r )
− as − as
Nx − Nr (1.38)
PVS(x) =
D xas
Present value of retirement pensions
Dras _p
PVR(x) = p (r , x) ar (1.39)
D xas
where p(r, x) denotes the retirement pension of the cohort aged x as a proportion of the final
salary.
Present value of invalidity pensions ( b ≤ x < r )
∑
r −1
r=x
p (t , x)C tais (1.40)
PVI(x) = as
D x
where p(t,x) denotes the invalidity pension as a proportion of the salary, for an entrant at age x, if
invalidity is attained in the age (t,t+1)
Present value of widows’/widowers’ pensions (death in service) ( b ≤ x < r )
∑
r −1
p (t , x)C taws
PVW1(x) = RWP r=x (1.41)
D xas
Present value of widows’/widowers’ pensions (death after invalidity) ( b ≤ x < r )
∑
r −1
p (t , x)C tiws
PVW2(x) = RWP r=x
(1.42)
D xas
12
13. Actuarial analysis in social security
2 Macro- economic parameters in actuarial calculations
The evolution of the economic and the labour market environments of a country directly
influence the financial development of a social security scheme. The evolution of GDP (its primary
factor income distribution), labour productivity, employment and unemployment, wages, inflation
and interest rates all have direct and indirect impacts on the projected revenue and expenditure of a
scheme.
The macro-economic frame for the actuarial calculation should ideally start from financial
projections. The use of just one source of both financial projections and the actuarial calculation
facilitates communications between the actuary and the financial counterparts and avoids
unnecessary discussions about assumptions. However, financial forecasts often do not extend for
more than 15 to 20 years, which is insufficient for the purposes of an actuarial calculation, which
requires projections of at least 50 years into the future. Hence, the actuary should extend financial
projections, when available, in order to satisfy the required length of time covered by an actuarial
calculation.
The financial projections of a social security scheme depend on:
• the number of people who will pay contributions to the scheme ;
• the average earnings of these contributors ;
• the number of people who will receive benefits;
• the amount of benefits that will be paid, related to past earnings and possibly indexed;
• the investment earnings on the reserve.
All these factors depend on the economic environment in which the scheme will evolve.In order
to develop robust assumptions on the future economic environment, it is necessary to analyse past
trends. The core conclusions drawn from these observations are then used as a basis for the
developmentof consistent long-term economic and labour market projections serving as a basis for
the actuarial calculation of the scheme.
The economic variables necessary to develop a suitable macroeconomic frame include :
• economic growth
• the separation of GDP between remuneration of workers and broadly, remuneration of
capital
• labour force, employment and unemployment
• wages
• inflation
• bank (interest) rate
• taxes and other consideritions.
Economic assumptions generally have to be discussed with national experts in ministries of
economic and of finance.The actuary may suggest and analyse alternative long-term
assumptions.However, it is not the objective of the actuarial calculation to run an economic model
and to take the place of economic projections performed at the national level.
Various approaches exist to project economic variables over time.Real rates of economic growth ,
labour productivity increases and inflation rates exogeneous inputs to the economic model
presented here.
13
14. Actuarial analysis in social security
2.1 Economic growth
The annual increase in GDP results from the increase in the number of workers, together with the
increase in productivity per worker. A choice must be made as to how each of these two factors will
affect the global GDP growth rate. As regards a social security scheme, a larger increase in the
number of workers affects the number of people who contribute to the scheme. In the long run, the
increase in productivity normally affects the level of wages and the payroll covered by the scheme.
Hence, the assumption on GDP growth has a direct impact on the revenue of the scheme.
For the short term, the annual GDP growth rate may be based on the estimates published by
organizations specialized in economic projections. For the long term, an ultimate growth rate is
generally established by the actuary as an exogenous assumption. The short-term and ultimate rates
are then linked together, based on an interpolation technique. Nominal GDP is calculated by
multiplying real GDP for each and every year by the GDP deflator. The GDP deflator is ex post,
calculated by dividing nominal GDP by real GDP. Its future evolution is usually based on
exogenous assumptions on future GDP inflation rates.
Figure 2.1 The general frame for macroeconomic projections
Initial general Fertility Projected
population Mortality general
Migration population
Initial labor Future evaluation of Projected labor
force the participation force
rate
Projected active Projected
population inactive
population
Future evaluation
Historical of GDP
•GDP Projected Projected
•Employment employment unemployment
•productivity Future productivity
Source: International Labor Organization (2002).
Future nominal GDP development is combined with an assumption on the evolution of the share
of wages in nominal GDP to obtain the part of GDP that represents the remuneration of workers.
Total workers’ remuneration is used later, in combination with dependent employment, to
determine the average wage.
2.2 Labour force, employment and unemployment
The projection of the labour force, that is, the number of people available for work, is obtained by
applying assumed labour force participation rates to the projected number of people in the general
population. The data on the labour force are generally readily available, by age and sex, from
14
15. Actuarial analysis in social security
national statistical offices. Recent past data should be sought and if available, the actuary should
consider national forecasts on participation rates performed by these offices. The same applies for
employment and unemployment data.
To project the evolution of participation rates is no easy task. Data and national projections are
often non-existent. One common approach is to leave the age-specific participation rates constant
during the projection period. Any projected changes in the overall participation rate then only result
from changes in the population structure. In most economies, however, the participation rates of
women are significantly lower than those observed of men. It is common in such a situation to
assume that, over time, the participation rates of women will catch up, at least in part, with those of
men.
Once the total labour force has been projected, aggregate employment can be obtained by
dividing real GDP (total output) by the average labour productivity (output per worker)
Unemployment is the measured as the difference between the projected labour force and total
employment.
2.3 Wages
Based on an allocation of total GDP between labour income and capital income, a starting
average wage is calculated by dividing total remuneration (GDP) times the share of wages (GDP)
by the total number of dependent employed persons. The share of wages in GDP is calculated from
the past factor income distribution in the economy and projected with regard to the probable future
evolution of the structure of the economy.
In the medium term, real wage development is checked against labour productivity growth. In
specific labour market situations, wages might grow faster or slower than productivity. However,
owing to the long-term nature of an actuarial study, the real wage increase is often assumed to
merge, in the long run, into the rate of growth in real labour productivity .Wage growth is also
influenced by an assumed gradual annual increase in the total labour income share of GDP over the
projection period, concomitant with the assumed GDP growth.
Figure 2.2 Determination of the average wage in the economy
Labor force supply
model
(projected active
Historical population)
•GDP
Future productivity
•Employment
•productivity Projected Projected
employment unemployment
Future evaluation
of GDP
Historical share
of wages in GDP
Projected total Projected
remuneration Average wage
Projected share
of wages in GDP
Historical total
remuneration
Source: International Labor Organization (2002).
Wage distribution assumptions are also needed to simulate the possible impact of the social
protection system on the distribution of income, for example, through minimum and maximum
15
16. Actuarial analysis in social security
pension provisions. Assumptions on the differentiation of wages by age and sex must then be
established, as well as assumptions on the dispersion of wages between income groups.
2.4 Inflation
Inflation represents the general increase in prices. This general rise is usually associated with an
average basket of goods, the price of which is followed at regular intervals. From time to time, the
contents, of the basket are changed to adapt to changes in the consumption patterns of the average
consumer. Various definitions of inflation are used in most economies, such as, for example, the
GDP deflator. However, for the purposes of the actuarial analysis, the consumer price index CPI) is
most often used as a statistical basis. In the long run, the GDP deflator and the CPI might be
assumed to converge.
Assumptions on future inflation rates are necessary for the actuarial study to project the evolution
of pensions, in the case where pensions are periodically adjusted to reflect price increases in the
economy. Past data on inflation are generally available from national statistical offices. The data
may also be available on short and even long-term forecasts by these institutions or by other
government agencies.
2.5 Interest rate
The interest rate as a random variable of great importance to the actuary is the rate of interest (or
more generally, the bank rate of investment return). Interest rates vary in many dimensions, from
time to time, from place to place, by degree of security risk, and by time to maturity. Financial
security systems are especially sensitive to the variation of interest rates over time, so actuaries
must be interested in the probability distributions, the means and variances, of a specified interest
rate as it varies over time.
Historically, actuaries have used deterministic models in their treatment of the time value of
money, but not because they were unaware of interest rate variation. Many of the discussions at
actuarial gatherings over the years have centered on the prospects for interest rate rise or fall. The
difficulty has not been a lack of concern, but rather a lack of knowledge as to the complexities of
interest rate variation. The development of computers has opened up a range of techniques whereby
interest rate variation can be modeled. It appears that this is a direction in which actuarial interest
and knowledge may be expected to grow.
The level of interest (bank) rates in the short term can be projected by looking at the level of rates
published by the central bank of the country in question. In the long term, bank rates may be
viewed as the ratio of profits over nominal investments in the economy. They are, therefore, linked
to the assumption made for GDP and its separation between workers’ remuneration and capital
income. The projected GDP multiplied by the assumption retained for the future share of wages in
GDP will provide a projection of the total projected workers’ remuneration in the country for each
future year. By subtracting the share of wages in GDP from the total GDP, we can isolate the
capital income component. From past observations, it is possible to estimate the share of “profits”
in capital income and to project that share in the future to determine a projected level of profits. To
project nominal investments in the private sector, it is necessary to project nominal GDP by its
demand components, using plausible assumptions on the future shares of private and government
assumptions, private and government investments, exports and imports. The projected ratio of
profits to nominal investments in the private sector thus gives an indication of future bank rate
levels.
For determining the specific assumption regarding the investment return on a scheme’s reserve,
appropriate adjustments to the theoretical bank rates have to take into account the composition of
the portfolio of the scheme and its projected evolution.
16
17. Actuarial analysis in social security
Another consideration is the size of the social security reserves compared with the total savings in
the country. In some small countries, social security reserves have a great influence on the level of
bank rates. In that case, at least for the short to medium term, the actuary will determine the bank
rate assumption for the scheme by referring directly to its investment policy.
2.6 Taxes and other considerations
Actuaries need to demonstrate awareness of the broader economic impact and may need to
supplement actuarial models of the social security scheme itself with simple macroeconomic models
to demonstrate the interactions of the social security, tax systems and to model the overall impact on
public expenditure.
Generally, national statistical offices provide their own projections of the economically active
population, employment and unemployment levels and GDP. In addition ministries of finance usually
make short-term forecasts, for budgetary purposes, on the levels of employment, inflation and interest
rates and taxation. These sources of information should be considered by the actuary, particularly
when performing short-term actuarial projections. It is thus imperative that at least one of the
scenarios in the actuarial report reflects the economic assumptions of the government.
17
18. Actuarial analysis in social security
3. Financial Aspects of Social Security
3.1 The basics of the pension systems
The threat to the financial sustainability of the pension systems in most countries and elsewhere
has become a major concern. Briefly, the problem stems from the fact that the pension systems
established in many countries after WWII are now about to mature and bring a full pension to most
people covered, while at the same time the ratio of pensioners to contributors (ratio of population
60 + to 20–59 years old) will increase between 2005 and 2050. 3
The objective here is to briefly summarize the very basic concepts needed to discuss pension
systems and to give a short review of the literature of the respective merits of the pay-as-you-go
(PAYG) and fully funded (FF) systems. The basics are presented with the help of figures that
resemble the orders of magnitude in many countries with relatively high replacement rates and high
and still increasing old age dependency ratios.
Samuelson’s seminal paper of 1958 first stated the simple fact that, in a PAYG pension system
in a steadily growing economy, the rate of return to pension contributions is equal to the rate of
growth. He inferred that such a system improves welfare, contrasting it with an economy having no
effective store of value, where the storing of real goods by workers for their retirement would yield
a negative rate of return (which they would have to accept if there was no better alternative).
However, that in the very same paper he also introduced a case where the existence of money
solves the problem: with a zero nominal rate of return, workers can accumulate savings and use
them during retirement. Assuming that the nominal stock of money is constant, he further inferred
that the real rate of return on money balances is equal to the rate of growth of the economy, thus
providing this real rate of return as savings for pensions. Thus, Samuelson (1958) introduced the
basic elements of both a PAYG public pension system and a fully funded system (which could be
either voluntary or mandatory by law). Under his highly theoretical (and counterfactual) cases, both
systems produce the same welfare.
Aaron (1966) extended Samuelson’s analysis to a modern economy where assets bearing a
positive rate of return are available. He correctly derived the result that if the rate of growth of the
economy (stemming from the rate of growth of population and wages) is higher than the rate of
interest, then “the introduction of some social insurance pensions on a pay-as-you-go basis will
improve the welfare position of each person”, as compared to a reserve system. Aaron may have
been partly right in considering that his result was relevant in the post-WWII growing economies,
but later research led economists to understand that in a dynamically efficient economy, the rate of
interest, in the long run, is equal to or higher than the rate of growth (this theorem of neoclassical
growth theory is attributed to Cass 1965). In this light the steady state described by Aaron is a
situation with an excessively large capital stock, which allows the economy to be adjusted to
another steady state with higher consumption.
In more recent literature the question has shifted back to asking whether there is a case for
shifting from PAYG systems to funding and privatisation of pension financing. The assertion of the
neoclassical growth theory that the rate of return in a funded system (the rate of interest in the
financial market), is normally higher than the rate of growth of the wage bill, led many authors to
conclude that the funded system is more efficient. Therefore, a shift to funding would eventually
yield additional returns which could at least partly compensate for the extra burden suffered by a
3
For population and pension expenditure projections, see Economic Policy Committee (2001), “Budgetary challenges
posed by ageing populations”.
18
19. Actuarial analysis in social security
generation which will have to save for its own pension and also honour the rights already accrued
in the PAYG system.
According to the opposing school, this reasoning is flawed, the counter-argument being that a
shift to funding does not give a net welfare gain. This was clearly formulated by Breyer (2001): a
consistent analysis requires that the returns to funds and the discount rate to compare income
streams at different points in time have to be the same, so that a shift to funding does not increase
total welfare, but rather distributes it differently across generations.
The same broad conclusion was neatly derived by Sinn (2000): The difference between the
market interest rate and the internal rate of return in the PAYG system does not indicate any
inefficiency in the latter. Rather, this difference is the implicit interest paid by current and future
generations on the implicit pension debt accumulated while some past generations received benefits
without having (fully) contributed to anybody’s pensions themselves. Under certain assumptions,
continuation of the PAYG system is a fair arrangement to distribute this past burden between the
current and all future generations.
A recent reaction and clarification from the proponents of funding is presented by Feldstein and
Liebman (2002): as our economies are still growing, it is proven that the marginal product of
capital exceeds the social discount rate of future consumption. Thus, increased national saving,
induced by a shift to funding of pensions, increases total welfare. It is therefore socially optimal to
take this gain and share it between current and future generations.
Again, the response from those sceptical towards funding is that the additional saving could be
achieved in many other ways, and that there is no convincing reason why the pension system
should be used for this more general purpose. Feldstein and Liebman (2002) admit this, but
maintain their view that it is advisable to reform the pension system to achieve this positive effect,
regardless of the possibility that some other means could, in principle, lead to similar results.
A parallel chain of arguments and counter-arguments can be followed to examine the question of
whether privatization of pension fund management increases welfare by inducing a reallocation of
capital towards investments with a higher return. The first argument is that in the long run, equity
investment has a higher return than bonds, and that the privately managed pension funds may take
advantage of this difference. The counter-arguments to this are again two-fold: (1) if it is assumed
that markets are efficient, then risk-adjusted returns are equal and there is no gain from pension
funding, or (2) if it is assumed that the markets are not efficient, there are many ways to change the
allocation of capital, including government borrowing from the market and investing in risky
assets. There is no compelling reason why the pension system should be used for this purpose (e.g.
Orszag and Stiglitz , 2001).
Thus, a transition to pension funding cannot be fully conclusively argued for on the basis of
differences in rates of return or interest rates alone. Political economy arguments referring to the
political suitability of pension funding, as compared to other means, for acquiring welfare gains
must also be explored. To assess this, the initial institutional structure must be looked at and the
prospects of finding the political will to make the required - in most cases major -changes to the
pension system must be evaluated.
Let’s assume a simplest possible earnings-related public pension system, where a pension as a
percentage of wages is accrued by working and pensions are indexed to the wage rate. Labour is
assumed to be uniform and the wage rate refers to wages after pension contribution payments.
If the age structure of the population is stable, i.e. the number of pensioners as a percentage of
workers is constant; all generations pay the same contribution rate and receive a pension which is
the same percentage of the prevailing wage rate. Note that, for this, the population need not be
stationary, but it is sufficient that its growth or decline is steady. The apparent equal treatment of all
generations under these conditions has probably led those who favour preserving a PAYG system
to regard it as a fair arrangement.
Following this same principle of fairness leads to partial funding under population ageing caused
by a decline in fertility and/or increase in longevity. In technical terms, ageing causes a transition of
the pension system from one steady state to another, not to be confused with a steady change which
19
21. Actuarial analysis in social security
Table 3.1 gives the key variables as a percentage of the wage bill in both PAYG and FF systems
under two alternative assumptions of sharing time between work and retirement, and of the interest
rate. The (real) interest rate is either two or one percentage points above the annual change of the
(real) wage rate.
Under the above assumptions pension expenditure as a percentage of the wage bill is the same in
both systems. It is also, by definition, the contribution rate in the PAYG system. Contribution rates
in the FF system are considerably lower than those in the PAYG system as the proceeds from the
fund make up the difference. Thus, the figures should illustrate clearly how the same expenditure is
financed in two different ways in the two cases. Lower interest rates naturally require higher
contributions and a larger fund.
The latter two columns show that an extension of working life, assuming that the employee earns
a two percentage point increase in pension for each additional working year, lowers the cost of
pensions by roughly seven per cent.
The fund as a percentage of the wage bill varies in these examples between roughly 560% and
670%. To obtain a rough measure of what these figures mean in terms of per cent of GDP, they
should be divided by three for the CEECs and by two for the more advanced economies (EU-15),
this difference stemming mainly from the lower ratio of wage and salary earners to labour force in
the CEECs.
Note that given the same pension rights in the two systems, the amount of fund in the FF system,
which by definition matches the present value of acquired pension rights (of both current
pensioners and employees), also gives the implicit liabilities of the PAYG system, also called
implicit pension debt, which has to covered by future contributions (for a presentation of this and
related concepts see Holzmann, Palacios and Zviniene, 2000).
Table 3.2. Pension financing: steady path with a changing population
Active years 35
Retirement years 15
Replacement rate 70%
Change of population p 0,5% -0,5%
Rate of interest-w 1,5% 0,5% 2,5% 1,5%
Rate of interest-(w+p) 2% 1% 2% 1%
Contr. In PAYG 34,0% 34,0% 26,5% 26,5%
Contr. In FF 20,5% 26,5% 15.7% 20,5%
F/wage bill 671% 748% 536,0% 600,0%
Table 3.2 gives the corresponding figures for populations which either increase or decrease
steadily by half a per cent per year. Working life is assumed to be 35 years and retirement 15 years.
The assumption of the steadily rising or declining population, with the survival rates in each age
group assumed to be given, means that the fertility rate is either above or below the 2.1 births per
woman, which would keep the population constant.
The first example resembles the growth of populations in the 1950s and 1960s in Europe, while
the latter slightly underestimates the ageing problem, as the current and expected fertility rates in
the CEECs and EU-15 indicate that populations may well be starting to decline faster than 0.5% a
year. Taking the decline at 0.5%, FF funds or implicit debt in the PAYG system would be around
700% of the wage bill.
The figures for the contribution rates and especially for the size of the fund under alternative
assumptions give a rough idea of the orders of magnitude of key variables and display the internal
logic of the two alternative financing systems.
21
22. Actuarial analysis in social security
3.2 Types of pension schemes
Pension schemes are assumed to be indefinitely in operation and there is generally no risk that the
sponsor of the scheme will go bankrupt. The actuarial equilibrium is based on the open group
approach, whereby it is assumed that there will be a continuous flow of new entrants into the scheme.
The actuary thus has more flexibility in designing financial system appropriate for a given scheme.
The final choice of a financial system will often be made taking into consideration non-actuarial
constraints, such as capacity of the economy to absorb a given level of contribution rate, the capacity
of the country to invest productively social security reserves, the cost of other pension schemes.
To confine the treatment to mandatory pension systems, while voluntary individual pensions are
merely touched upon makes no difference whether the system, or some part of it, is mandatory by law
under a collective agreement. Among mandatory schemes, three basic dimensions are relevant:
(1) Does the system provide Defined Benefits (DB) or does it require Defined Contributions (DC);
(2) what is the degree of funding; and
(3) what is the degree of actuarial fairness?
Except for one extreme case, namely a Fully Funded DC system - which is by definition also fully
actuarially fair - these three dimensions are distinct from each other, and may therefore form many
combinations. To find any degree of funding and actuarial fairness in a DB system as the system may
accumulate assets and the link between contributions may or may not be close. A DC system may
operate without reserves, in which case it is said to be a pure Pay-As-You-Go (PAYG) system, based
on notional accounts operated under an administratively set notional interest rate - i.e. an NDC
PAYG system). Alternatively, a public DC system can be funded to any degree. The degree of
actuarial fairness is always rather marked in a DC system, but it always depends on various
administrative rules, e.g. on the notional rate of interest, and the treatment of genders (see Lindbeck,
2001, and Lindbeck and Persson, 2002).
3.2.1 Pay-as-you-go (PAYG)
Under the PAYG scheme, no funds are, in principle, set a side in advance and the cost of annual
benefits and administrative expenses is fully met from current contributions collected in the same
year. Given the pattern of rising annual expenditure in a social insurance pension scheme, the PAYG
cost rate is low at the inception of the scheme and increases each year until the scheme is mature.
Figure 3.1 shows the evolution of the PAYG rate for a typical pension scheme.
Figure 3.1 Typical evolution of expenditure under a pension scheme (as a percentage of total
insured earnings)
Percentage
18
16
14
12
10
PAYG rate 8
6
4
2
0
1 6 11 16 21 26 31 36 41 46 51 56 61 66
Year
Theoretically, when the scheme is mature and the demographic structure of the insured population
and pensioners is stable, the PAYG cost rate remains constant indefinitely. Despite the financial
system being retained for a given scheme, the ultimate level of the PAYG rate is an element that
should be known at the onset of a scheme. It is important for decision-makers to be aware of the
22
23. Actuarial analysis in social security
ultimate cost of the benefit obligations so that the capacity of workers and employers to finance the
scheme in the long term can be estimated.
Except from protecting against unanticipated inflation, other advantages of the PAYG system are;
the possibility to increase the real value of pensions in line with economic growth; minimization of
impediments to labour mobility; and a relatively quick build-up of pension rights. Another advantage
is the possibility of redistribution, which can insure a certain living standard for individuals who have
never been part of the work force and thus never have had the opportunity to save any income. A
feature of the system is the sensitivity to the worker-retiree ratio, because a declining ratio must either
raise the contribution rate to keep the replacement rate fixed, or reduce the replacement rate in order
to keep the contribution rate fixed.
The two PAYG methods, Defined Contribution system (DC), where the contribution rate is
fixed and Defined Benefit (DB), where the benefit rate is fixed, have different implications to
changes in the worker-retiree ratio, and if no demographic changes occur the systems are
observationally equivalent. As such, the PAYG system is very sensitive to all sources of demographic
change, e.g. birth rates, mortality rates or length of life – current or expected ones.
In a world with no uncertainty the PAYG system will have no real effects, but when uncertainty
is taken into consideration the system will generally not produce an equivalent amount of private
savings as would be the case without PAYG social security. If the pension system is purely financed
with a PAYG scheme, it is a perfect substitute for private bequests. Hence, a forced increase in social
security will reduce bequests by an equal amount.
The risks associated with the PAYG system are primarily growth in national income and
demographics, as well as uncertainty about the level of pension benefits future generations will be
willing to finance. The rate of interest in the DC-PAYG system – the replacement rate – depends
directly on the rate of productivity and the rate of population growth. If government activity is
assumed to be limited to managing social security, then the rate of return to a DC-PAYG system is
affected by the growth in productivity, since this will raise national income for taxation. Hence, the
contribution revenue for pension benefits in a balanced budget will be larger, as well as the total level
of benefits to retirees. The other factor which influences the pay off to PAYG is the population
growth rate. If it increases, more people pay the assumed fixed level of taxes, thereby generating
larger contribution revenue to be shared by retirees.
3.2.2 Fully funding (FF)
The advantages of a funded pension system tend to mirror the disadvantages of the PAYG
system, e.g. it displays great transparency since individuals literally can keep track with their pension
savings. A funded system can be private or government-run, and can take many forms –for instance
occupational and supplementary schemes, but if it is not compulsory and no redistribution occurs, the
system is the same as private pension insurance. If the system is purely funded, it is a perfect
substitute for private savings. Consequently, a forced increase in social security will reduce private
savings by an equal amount.
The rate of interest in this system is the real interest rate, and when social security is fully funded,
it can be defined as being neutral – meaning that the savings made by individuals are the same both
with and without the fully funded system.
3.2.3 The respective merits of the PAYG and FF systems
The respective merits of the PAYG and FF systems have recently been very heated indeed, as top
experts have felt the need to clarify their views and arguments. The cornerstone of analysis and most
influential for policy was the World Bank’s “Averting the Old Age Crisis, Policies to Protect the Old
and Promote Growth”, published in 1994. The key recommendation was to create a mandatory, fully
funded, privately managed, defined contribution, individual accounts based pillar, which would cover
a large proportion of occupational pensions and hence supplement the public PAYG defined benefit
23
24. Actuarial analysis in social security
pillar, which would provide basic pension benefits. A third pillar of voluntary pension insurance,
obviously fully funded, would complement the system.
The recommendation for the second pillar - the mandatory FF pensions - later became the object of
particularly critical assessments, of which we want to mention four: (1) the UN Economic
Commission for Europe Economic Survey 3/1999 containing papers from a seminar in May 1999, (2)
Hans-Werner Sinn’s paper “Why a Funded System is Useful and Why it is Not Useful” originally
presented in August 1999, (3) Peter Orszag’s and Joseph Stiglitz’ paper “Rethinking Pension Reform:
Ten Myths About Social Security Systems” from September 1999 and (4) Nicholas Barr’s paper
“Reforming Pensions: Myths, Truths, and Policy Choices”, IMF Working Paper 00/139 from August
2000.
The criticisms triggered clarifying responses from those who advocate an introduction of a FF
pillar, e.g. in a paper by Robert Holzmann entitled “The World Bank’s Approach to Pension Reform”
from September 1999.
Prior to these recent contributions, differences of opinion were often highlighted by making a
comparison of the pure forms of the two systems (and sometimes, as Diamond (1999) put it, by
comparing a well-designed system of one kind with a poorly designed system of the other). Thanks to
serious efforts by many discussants, many questions are now more clearly formulated and answered,
and the reasons behind remaining disagreements are now better understood. Thus, there is now more
consensus also on policy advise than a few years ago. The merits of each system have become
clearer, and consequently many economists now think that the best solution is a combination of the
two systems, where details depend on the institutional environment, notably on the capacity of the
public sector to administer a public pension system and to regulate a privately run system, and on the
scope and functioning the financial markets. This also means that a lot of detailed work on specific
aspects of designing these systems is still needed.
A review of the various points covered by this discussion is worthwhile because setting up a multi-
tier system requires that the interaction of its various parts be understood to allow a coherent view of
how the entire system works.
1. A mandatory pension system
Whether the system is PAYG or FF, we mainly refer to the mandatory parts of pension systems. For
the PAYG it is self-evident that a contract between successive cohorts to contribute to the pensions of
the elderly in exchange for benefits when the contributor reaches old age has to be enforced by law.
In the case of the FF system, this is not equally evident, but the argument shared by most is that it, or
some part of it, must also be mandatory to avoid free-riding of those who would not save voluntarily
but rather, would expect that in old age the (welfare) state would support them. Once the FF system is
mandatory, the state becomes involved in it in various ways, as a regulator and guarantor.
2. Defined benefits or defined contributions
The PAYG system is often associated with defined benefit provisions, which normally means that
on top of a minimum amount the pension depends on the wage history of the individual (sometimes
up to a ceiling) and, during retirement, on average wage and/or inflation developments. The FF
system is mostly associated with defined contributions, where the ultimate pension will depend on the
contributions paid by the individual (or his employer on his behalf) and the proceeds of the invested
funds.
This dichotomy is not entirely correct as the link between benefits and contributions at the level of
an individual in a PAYG system can be made rather tight, if desired, even mimicing a FF system by
creating a notional fund with a notional interest rate. Recent examples of this are the reformed
Swedish, Polish and Latvian systems, where defined contributions are put into a notional fund with a
rate of return equal to the increase in nominal wages. Also, some basically FF systems (like the
occupational pension funds in the Netherlands) are defined benefit systems, with contributions
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adjusted according to earnings acquired (as this can be done only afterwards, it does not work exactly
like a pure FF system, but roughly so). Also, if the state guarantees, as it often does, a minimum level
of benefits in an otherwise defined contribution system, the system de facto provides defined benefits
up to a certain level.
3. Intra-generational redistribution
PAYG systems normally include an important element of intra-generational redistribution e.g. a
minimum pension level that benefits the poorest. This might be partly neutralized however, by basing
the contributions on uniform survival rates for all groups while the low income retirees in reality have
a shorter life expectancy. Advocates of the FF system see it as an advantage that individual accounts
help to eliminate redistribution. This may be a valid argument, but one should also note that
redistribution can be reduced in the PAYG system by changing the parameters, and that a FF system,
if mandatory and therefore state regulated, may also include various elements of redistribution, e.g.
by setting uniform parameters for different groups, like gender.
4. Labour-market effects
As contributions to PAYG system are often paid by employers and as the link between
contributions and pension at employee level is only loose, PAYG contributions are often treated like
any other taxes on wages, thus causing a tax wedge between the cost of labour and income received
by the employee, and a consequent loss of welfare. One of the most important arguments put forward
by advocates of the FF system is that contributions to these funds can be equated with individual
savings, thus avoiding any distortion of the labour market.
This dichotomy gives an exaggerated picture. Often in the PAYG system there is also a link
between contributions and benefits, though not a perfect one, and it can perhaps be tightened.
Furthermore, a mandatory FF system probably also causes some labour market distortion as it covers
those who would not willingly save, and because uniform parameters may cause redistribution
between different groups (See Sinn, 2000, Orszag and Stiglitz, 1999 for more detailed analysis).
5. Administrative costs
The efficiency of each system depends, among other things, on administrative costs. Not
surprisingly, they are considered to be higher in the FF system, and sometimes so high that efficiency
can be questioned (Orszag and Stiglitz, 1999). Obviously, results will vary between Western
countries and transition economies.
6. Does FF have higher rate of return than PAYG?
The most important – and the most controversial - argument put forward by advocates of the FF
system is that a transition from a PAYG to a FF system increases welfare by improving allocation of
capital, in addition to the positive effect via the labour market (point 4 above) net of possibly higher
administrative costs (point 5).
For sceptics, this is not so clear. They point out that the difference between the rate of return to
accumulated funds in the FF system and the implicit rate of return in the PAYG - which is equal to
the rate of increase of the wage bill - has misleadingly been given as a proof of the superiority of the
former. Sinn (2000, pp. 391-395) neatly develops the argument that (under certain conditions) this
difference only reflects the gains that previous generation(s) received when they did not (fully)
contribute to the newly established PAYG system but enjoyed the benefits. These ‘introductory
gains’, as Sinn calls them, led at the time to an accumulation of implicit debt, and the difference
between the two rates precisely covers the interest on this debt. The burden is either carried by all
future generations or by one or more future generations through reduction of the implicit debt by
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26. Actuarial analysis in social security
cutting future pension rights or increasing contributions. Thus, Sinn (2000) shows why the difference
in rates of return does not prove the superiority of the FF system over the PAYG (see also Sinn, 1997,
Orszag and Stiglitz, 1999).
The above argument assumes a uniform rate of return on financial assets. Advocates of FF maintain
that transition to funding makes it possible to exploit the difference between returns on equity over
bonds. However, this improves general welfare only if the rates of return on capital are generally
higher with funding than without, i.e. if real capital as a whole is allocated and used more efficiently.
Advocates of the FF system tend to answer this positively, as they believe that pension funds (if
properly administered) improve the functioning of financial and capital markets more generally (e.g.
by providing liquidity).
Sceptics do not find convincing arguments for improved allocation of capital under funding,
maintaining that the distribution of financial wealth between equity and bonds is a separate matter,
and that the individual accounts as such do not lead to welfare gains, as one form of debt, the implicit
pension debt under PAYG, is merely transformed to explicit government debt.
The advocates of funding note that abstract models of capital markets do not provide an answer,
notably in transition economies, where markets are far from perfect and funding could cause shifts in
portfolios that involve pension liabilities equal to several times annual GDP (Holzmann, 1999a).
They thus maintain that establishing a multi-tier system can increase welfare if properly
implemented.
In turn, sceptics may sarcastically ask why, if semi-public funds like mandatory pension funds are a
miracle, do governments not borrow regardless of pension financing and create trust funds that
contribute to general welfare in the same fashion. They may also doubt whether pension funds
contribute positively to better allocation of capital or improved governance of enterprises (e.g.
Eatwell, 1999). Interestingly, the said sceptics can come from quite different schools of thought.
Some neo-liberals may fear “pension fund socialism”, while some Keynesians may suspect that herd
behaviour among fund managers causes harmful instability in financial markets.
7. Each system is exposed to different risks: mixture is optimal
Both systems have their relative merits in one more respect: the sustainability of the systems as a
whole and also individuals in those systems are liable for different types of risks. In short, the PAYG
system is vulnerable to demographic risks (i.e. burden increases if ageing shifts abruptly) and
political risks, whereby at some stage the young generation may abandon the commitment to pay and
leave the elderly without pensions (see Cremer and Pestieau, 2000).
The FF system is naturally vulnerable to financial market risks (i.e. variations in rates of return that
might be affected by any exogenous shocks), but also internally to bad management or outright
corruption, a risk that should not be forgotten. It is often asserted that the FF isolates the system from
demographic risks. This is true if the rate of return on the funds does not depend on demographic
factors. This might be a relatively safe assumption, but in a closer analysis one should recognize that
as ageing affects savings, it should also affect rates of interest. Brooks (2000) has produced
simulations showing that the baby boom generation loses significantly in the FF system due to a fall
in interest rates due to population ageing. The same scenario was produced in Merrill Lynch report
“Demographics and the Funded Pension System” (2000).
Thus, although the difference in exposure to different risks might not be so big, it still plays a role,
and a mixture of the two systems is therefore probably an optimal way to reduce aggregate risk. The
content and relative size of each pillar should then depend on various institutional factors and other
details.
3.2.4 Partial funding - NDC
In this section a simple quantifiable rule according to which fairness between successive generations
leads to the need for partial funding. Thus, an aspect that should be inherent in the pension system
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