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MBA Thesis by Hikmet Tagiyev


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Actuarial analysis in Social Security

Actuarial analysis in Social Security

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  • 1. AZERBAIJAN REPUBLIC KHAZAR UNIVERSITY School : Economics & Management Major : Finance Student : Hikmet Tagiyev SakhavetSupervisor: 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 thesupport, 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 ofthe perspective economist of Azerbaijan. She added a lot to my knowledge in Finance andEconometrics 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 EuropeanCommission (Directorate General for Economic and Financial Affairs). In spite of the work loadthey 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 mehis Pension Reform Illustration & Simulation Model, PRISM, which I used for calculating thescenarios, reported in this paper. I should never forget his useful and valuable comments onactuarial calculations. I would like to give the assurances of my highest consideration to Ms. Alice Wade (Deputy ChiefActuary of Social Security Administration of USA) that she has done a great favour for me inHelsinki at “15th International Conference of Social Security Actuaries and Statisticians” on May23-25, 2007. I listened to her very interesting topics “Mortality projections for social securityprograms in Canada and the United States" and "Optimal Funding of Social Insurance Plans". AlsoI 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 KhazarUniversity: Prof.Mohammad Nouriev, Mr.Sakhavet Talibov, Ms.Nigar Ismaylova, Ms.ArzuIskenderova, Ms.Samira Sharifova, Mr.Gursel Aliyev, Mr.Yashar Naghiyev, Mr.ShukurHouseynov, 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 tomention in this acknowledgement. 2
  • 3. Actuarial analysis in social security Table of contentsIntroduction........................................................................................................................................41. The role of actuaries in social security.........................................................................................5 1.1 The goal of actuarial analysis..................................................................................................5 1.2 Principles and techniques of actuarial analysis.....................................................................62 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 ............................................................................................173. 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).......................................................................................................364. 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...............................................................................................................535. Some actuarial calculations with regards to the pension system of Azerbaijan ....................55Conclusion ........................................................................................................................................60Appendix...........................................................................................................................................61References .........................................................................................................................................63Discussion of preceding paper ........................................................................................................65 3
  • 4. Actuarial analysis in social securityIntroduction The actuarial analysis of social security schemes requires to actuary to deal with complexdemographic, economic, financial, institutional and legal aspects that all interact with each other.Frequently, these issues retain their complexity at the national level, becoming ever moresophisticated 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 stillfurther. Under this thesis, social security actuaries are obliged to analyse and project into the futuredelicate balances in the demographic, economic, financial and actuarial fields. This requires thehandling 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 themeans of the social security scheme, together with numerous other variables of the social,economic, demographic and financial environments.Taking into consideration these facts I haveanalyzed some actuarial calculation regarding to the pension system of Azerbaijan as well in thisthesis. In this thesis there are five main chapters: Chapter One provides a general background to theparticular context of actuarial analysis in social security, showing how the work of social securityactuary 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 ofa country that is directly influence the financial development of a social security scheme. Theevolution of GDP (its primary factor income distribution), labour productivity, employment andunemployment, wages, inflation and interest rates all have direct and indirect impacts on theprojected revenue and expenditure of a scheme. The Chapter Three I introduce the key concepts for typical pension systems in a very simplesetting, including an assumption of a stationary population. It presents a step-by-step account of theusual process of the actuarial analysis and tries, at each stage to give appropriate examples toillustrate the research work concretely. The Chapter Four summarizes the basic characteristics of the Turkish Social SecuritySystem.(TSSS) In this chapter the TSSS is analyzed in detail. Also a brief outline of the ILOpension 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, andthe 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 ofAzerbaijan. The conclusion of this thesis summarizes the outcomes and the implications of the entire study. 4
  • 5. Actuarial analysis in social security1. The role of actuaries in social security From the beginning of the operation of a social security scheme, the actuary plays a crucial rolein analyzing its financial status and recommending appropriate action to ensure its viability. Morespecifically, the work of the actuary includes assessing the financial implications of establishing anew scheme, regularly following up its financial status and estimating the effect of variousmodifications that might have a bearing on the scheme during its existence. This chapter sets out the interrelationships between social security systems and theirenvironments as well as their relevance for actuarial work. Meaningful actuarial work, which initself is only one tool in financial, fiscal and social governance, has to be fully cognizant of theeconomic, demographic and fiscal environments in which social security systems operate, whichhave 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 thefollowing 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 theintervention of, among other specialists, the actuary, which usually starts during the consultationprocess that serves to set the legal bases of a scheme. This process may lengthy, as negotiationstake place among the various interest groups, i.e. the government, workers and employers. Usuallyeach interest group presents a set of requests relating to the extent of the benefit protection thatshould be offered and to the amount of financial recourses that should be allocated to cover therisks. 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 thatwill 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 coveredpopulation and the way that the coverage is enforced. Coverage may vary according to the riskcovered. A number of countries have started by covering only government employees, graduallyextending coverage to private sector employees and eventually to the self-employed. A gradualcoverage allows the administrative structure to develop its ability to support a growing insuredpopulation and to have real compliance with the payment of contributions. Some categories ofworkers, such as government employees, present no real problem of compliance because theemployer’s administrative structure assures a regular and controlled payment of contributions. Forother groups of workers, the situation may be different. These issues will have an impact on thebasic data that the actuary will need to collect on the insured population and on the assumptionsthat 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 complexfeatures and actuaries are usually required, along with policy analysts, to ensure consistencybetween the various rules and figures. The following design elements will affect the cost of thescheme 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, theactuary is asked to cost the various benefit packages. The actuary should ensure that discussions arebased on solid quantitative grounds and should try to reach the right balance between generousbenefits and pressure on the scheme’s costs. At this stage, it is usual to collect information on the approaches followed in other countries. Suchcomparisons 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 fromcontributions and sometimes from government subsidies. Contributions are generally sharedbetween employers and employees, except under employment schemes, which are normally fullyfinanced by employers. This issue is related to determining a funding objective for the scheme or, alternatively, the levelof reserves set aside to support the scheme’s future obligations. The funding objective may be set inthe law. If not, then the actuary will recommend one. In the case of a pension scheme, however, thefunding objective will be placed in a longer-term context and may consider, for example, the needto smooth future contribution rate increases. Different financing mechanisms are available to matchthese funding objectives. For example, the pension law may provide for a scaled contribution rateto allow for a substantial accumulation of reserves during the first 20 years and thereafter a gradualmove towards a PAYG system with minimal long-term reserves. In the case of employment injuryschemes, transfers between different generations of employers tend to be avoided; hence, theseschemes 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 financialexperience against the projections. The experience analysis serves to identify items of revenue orexpenditure that have evolved differently than predicted in the assumptions and to assess the extentof the gap. It focuses on the number of contributors and beneficiaries, average insurable earningsand benefits and the level of administrative expenses. Each of these items is separated and analyzedby 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 ofadjustment to the actuarial assumptions. For example, a recent change in retirement behaviour mayinduce a new future expected retirement pattern. A slowdown in the economy will require adatabase of the number of workers contributing to the scheme. However, as actuarial projections forpensions are performed over a long period, a change in recently observed data will not necessarilyrequire any modifications to be made to long-term assumptions. The actuary looks primarily aconsistency between assumptions, and should not give undue weight to recent short-termconjectural effects. There are 2 actuarial techniques for the analysis of a pension scheme: the projection techniqueand the present value technique1.2.1 – 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 provedvaluable for social security projections. Methods classified under (b) are in effect extrapolations of past trends, using regressiontechniques. Essentially the difference between the two is that actuarial methods depend onendogenous (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 estimatesof 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 giveninitial values (at t=0). The demographic projection procedure can be regarded as the iteration of a matrix multiplicationoperation, 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 tand 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 andorphans .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 thelowest level of subdivision and the results aggregated to give various subtotals and totals. Thematrix 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 andorphans arising from the deaths of males/females aged x according to the age of thewidow/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 highestretirement age. This is a double decrement table allowing for the decrements of death and invalidityonly. The associated dependent rates of decrement are denoted by q x (mortality) and i x (invalidity). aRetirement is assumed to take place at exact integral ages, just before each birthday, r x denoting theproportion 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 pthe 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 wof 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 arebased 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 securityInvalid 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 ofeach year of age).Under the assumption of uniform distribution of decrements over each year ofage, 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 endof 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 insuredpersons in the age range (x, x+1) and (1.7b) relating to active persons becoming invalid and thendying at by age x+1. It is understood that the values of w x corresponding to fractional ages whichoccur in the above formula would be obtained by interpolation between the values at adjacentintegral 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 probabilitiesare applied to successive projections by sex and age (and preferably by past service , in the newentrants of the immediately preceding year have to be incorporated before proceeding to the nextiteration. The projection formula for the active insured populations are given below, the method ofprojecting 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 salarybill and of the total annual amounts of the different categories of pensions “in force” at discretetime points (t=1, 2…) starting from given initial values at t=0. These aggregates are obtained byapplying 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 amountsare computed year by year in parallel with the progress of the corresponding demographicprojection. An average per capita amount (salary or pension, as the case may be) is computed foreach distinct population element generated by the demographic projection; if different elements areaggregated in the demographic projection –for example, existing invalids surviving from age x tox+1 and new invalids reaching age x+1 at the same time –a weighted per capita average amount iscomputed 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. Thismethod begins by modeling a variation over time in the age-related average salary structure andthen 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 financialprojections. The basis for the financial projections would comprise assumptions in regard to the followingelements. They are specified as functions of age or time, the age-related elements should beunderstood 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 orvarying rates of accrual , or being subject to minimum or maximum amounts –such analysis couldsignificantly 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 probablepresent values of the future insured salaries, on the one hand and of the pension benefits payable tothe members of the cohort and to their survivors, on the other. In what follows, discrete approximations to the continuous commutation functions will bedeveloped, in order to permit practical application of the theory. The treatment will be extended toinvalidity and survivors benefits. Reference will be made to the same demographic and financialbases as for the projection technique. However certain simplifications in the bases will not beconsidered. Thus γ t (salary growth rate), β t (pension indexation rate), δ t (interest rate) are assumedconstant 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 at1percent of the final salary per year of service.Special commutation functions A series (sex-specific) special commutation functions are needed for applying the present valuetechnique. 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 onthe 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 andpensions and may be adequate if payments are made frequently, for example weekly. They can beadjusted to correspond more exactly to any specific payment schedule. For example, if pensions arepayable 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 andrefer to a unit insured salary on the date. The expressions for orphans are not indicated but can bederived 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 finalsalary. 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, ifinvalidity 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 security2 Macro- economic parameters in actuarial calculations The evolution of the economic and the labour market environments of a country directlyinfluence the financial development of a social security scheme. The evolution of GDP (its primaryfactor income distribution), labour productivity, employment and unemployment, wages, inflationand interest rates all have direct and indirect impacts on the projected revenue and expenditure of ascheme. The macro-economic frame for the actuarial calculation should ideally start from financialprojections. The use of just one source of both financial projections and the actuarial calculationfacilitates communications between the actuary and the financial counterparts and avoidsunnecessary discussions about assumptions. However, financial forecasts often do not extend formore than 15 to 20 years, which is insufficient for the purposes of an actuarial calculation, whichrequires projections of at least 50 years into the future. Hence, the actuary should extend financialprojections, when available, in order to satisfy the required length of time covered by an actuarialcalculation. 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 orderto develop robust assumptions on the future economic environment, it is necessary to analyse pasttrends. The core conclusions drawn from these observations are then used as a basis for thedevelopmentof consistent long-term economic and labour market projections serving as a basis forthe 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 ofeconomic and of finance.The actuary may suggest and analyse alternative long-termassumptions.However, it is not the objective of the actuarial calculation to run an economic modeland 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 modelpresented here. 13
  • 14. Actuarial analysis in social security2.1 Economic growth The annual increase in GDP results from the increase in the number of workers, together with theincrease in productivity per worker. A choice must be made as to how each of these two factors willaffect the global GDP growth rate. As regards a social security scheme, a larger increase in thenumber of workers affects the number of people who contribute to the scheme. In the long run, theincrease 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 byorganizations specialized in economic projections. For the long term, an ultimate growth rate isgenerally established by the actuary as an exogenous assumption. The short-term and ultimate ratesare then linked together, based on an interpolation technique. Nominal GDP is calculated bymultiplying 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 onexogenous 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 shareof 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, todetermine 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 byapplying assumed labour force participation rates to the projected number of people in the generalpopulation. The data on the labour force are generally readily available, by age and sex, from 14
  • 15. Actuarial analysis in social securitynational statistical offices. Recent past data should be sought and if available, the actuary shouldconsider national forecasts on participation rates performed by these offices. The same applies foremployment and unemployment data. To project the evolution of participation rates is no easy task. Data and national projections areoften non-existent. One common approach is to leave the age-specific participation rates constantduring the projection period. Any projected changes in the overall participation rate then only resultfrom changes in the population structure. In most economies, however, the participation rates ofwomen are significantly lower than those observed of men. It is common in such a situation toassume that, over time, the participation rates of women will catch up, at least in part, with those ofmen. Once the total labour force has been projected, aggregate employment can be obtained bydividing 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 totalemployment.2.3 Wages Based on an allocation of total GDP between labour income and capital income, a startingaverage 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 fromthe past factor income distribution in the economy and projected with regard to the probable futureevolution of the structure of the economy. In the medium term, real wage development is checked against labour productivity growth. Inspecific 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 tomerge, in the long run, into the rate of growth in real labour productivity .Wage growth is alsoinfluenced by an assumed gradual annual increase in the total labour income share of GDP over theprojection 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 socialprotection system on the distribution of income, for example, through minimum and maximum 15
  • 16. Actuarial analysis in social securitypension provisions. Assumptions on the differentiation of wages by age and sex must then beestablished, 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 anaverage basket of goods, the price of which is followed at regular intervals. From time to time, thecontents, of the basket are changed to adapt to changes in the consumption patterns of the averageconsumer. Various definitions of inflation are used in most economies, such as, for example, theGDP deflator. However, for the purposes of the actuarial analysis, the consumer price index CPI) ismost often used as a statistical basis. In the long run, the GDP deflator and the CPI might beassumed to converge. Assumptions on future inflation rates are necessary for the actuarial study to project the evolutionof pensions, in the case where pensions are periodically adjusted to reflect price increases in theeconomy. Past data on inflation are generally available from national statistical offices. The datamay also be available on short and even long-term forecasts by these institutions or by othergovernment agencies.2.5 Interest rate The interest rate as a random variable of great importance to the actuary is the rate of interest (ormore generally, the bank rate of investment return). Interest rates vary in many dimensions, fromtime to time, from place to place, by degree of security risk, and by time to maturity. Financialsecurity systems are especially sensitive to the variation of interest rates over time, so actuariesmust be interested in the probability distributions, the means and variances, of a specified interestrate as it varies over time. Historically, actuaries have used deterministic models in their treatment of the time value ofmoney, but not because they were unaware of interest rate variation. Many of the discussions atactuarial gatherings over the years have centered on the prospects for interest rate rise or fall. Thedifficulty has not been a lack of concern, but rather a lack of knowledge as to the complexities ofinterest rate variation. The development of computers has opened up a range of techniques wherebyinterest rate variation can be modeled. It appears that this is a direction in which actuarial interestand 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 ratespublished by the central bank of the country in question. In the long term, bank rates may beviewed as the ratio of profits over nominal investments in the economy. They are, therefore, linkedto the assumption made for GDP and its separation between workers’ remuneration and capitalincome. The projected GDP multiplied by the assumption retained for the future share of wages inGDP will provide a projection of the total projected workers’ remuneration in the country for eachfuture year. By subtracting the share of wages in GDP from the total GDP, we can isolate thecapital 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. Toproject nominal investments in the private sector, it is necessary to project nominal GDP by itsdemand components, using plausible assumptions on the future shares of private and governmentassumptions, private and government investments, exports and imports. The projected ratio ofprofits to nominal investments in the private sector thus gives an indication of future bank ratelevels. 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 ofthe 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 tosupplement actuarial models of the social security scheme itself with simple macroeconomic modelsto demonstrate the interactions of the social security, tax systems and to model the overall impact onpublic expenditure. Generally, national statistical offices provide their own projections of the economically activepopulation, employment and unemployment levels and GDP. In addition ministries of finance usuallymake short-term forecasts, for budgetary purposes, on the levels of employment, inflation and interestrates and taxation. These sources of information should be considered by the actuary, particularlywhen performing short-term actuarial projections. It is thus imperative that at least one of thescenarios in the actuarial report reflects the economic assumptions of the government. 17
  • 18. Actuarial analysis in social security3. Financial Aspects of Social Security3.1 The basics of the pension systems The threat to the financial sustainability of the pension systems in most countries and elsewherehas become a major concern. Briefly, the problem stems from the fact that the pension systemsestablished in many countries after WWII are now about to mature and bring a full pension to mostpeople covered, while at the same time the ratio of pensioners to contributors (ratio of population60 + 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 pensionsystems 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 thatresemble the orders of magnitude in many countries with relatively high replacement rates and highand still increasing old age dependency ratios. Samuelson’s seminal paper of 1958 first stated the simple fact that, in a PAYG pension systemin a steadily growing economy, the rate of return to pension contributions is equal to the rate ofgrowth. He inferred that such a system improves welfare, contrasting it with an economy having noeffective store of value, where the storing of real goods by workers for their retirement would yielda 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 moneysolves the problem: with a zero nominal rate of return, workers can accumulate savings and usethem during retirement. Assuming that the nominal stock of money is constant, he further inferredthat the real rate of return on money balances is equal to the rate of growth of the economy, thusproviding this real rate of return as savings for pensions. Thus, Samuelson (1958) introduced thebasic elements of both a PAYG public pension system and a fully funded system (which could beeither voluntary or mandatory by law). Under his highly theoretical (and counterfactual) cases, bothsystems produce the same welfare. Aaron (1966) extended Samuelson’s analysis to a modern economy where assets bearing apositive rate of return are available. He correctly derived the result that if the rate of growth of theeconomy (stemming from the rate of growth of population and wages) is higher than the rate ofinterest, then “the introduction of some social insurance pensions on a pay-as-you-go basis willimprove the welfare position of each person”, as compared to a reserve system. Aaron may havebeen 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 ofinterest, in the long run, is equal to or higher than the rate of growth (this theorem of neoclassicalgrowth theory is attributed to Cass 1965). In this light the steady state described by Aaron is asituation with an excessively large capital stock, which allows the economy to be adjusted toanother steady state with higher consumption. In more recent literature the question has shifted back to asking whether there is a case forshifting from PAYG systems to funding and privatisation of pension financing. The assertion of theneoclassical growth theory that the rate of return in a funded system (the rate of interest in thefinancial market), is normally higher than the rate of growth of the wage bill, led many authors toconclude that the funded system is more efficient. Therefore, a shift to funding would eventuallyyield additional returns which could at least partly compensate for the extra burden suffered by a3 For population and pension expenditure projections, see Economic Policy Committee (2001), “Budgetary challengesposed by ageing populations”. 18
  • 19. Actuarial analysis in social securitygeneration which will have to save for its own pension and also honour the rights already accruedin the PAYG system. According to the opposing school, this reasoning is flawed, the counter-argument being that ashift to funding does not give a net welfare gain. This was clearly formulated by Breyer (2001): aconsistent analysis requires that the returns to funds and the discount rate to compare incomestreams at different points in time have to be the same, so that a shift to funding does not increasetotal welfare, but rather distributes it differently across generations. The same broad conclusion was neatly derived by Sinn (2000): The difference between themarket interest rate and the internal rate of return in the PAYG system does not indicate anyinefficiency in the latter. Rather, this difference is the implicit interest paid by current and futuregenerations on the implicit pension debt accumulated while some past generations received benefitswithout 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 thecurrent and all future generations. A recent reaction and clarification from the proponents of funding is presented by Feldstein andLiebman (2002): as our economies are still growing, it is proven that the marginal product ofcapital 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 totake this gain and share it between current and future generations. Again, the response from those sceptical towards funding is that the additional saving could beachieved in many other ways, and that there is no convincing reason why the pension systemshould be used for this more general purpose. Feldstein and Liebman (2002) admit this, butmaintain 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 ofwhether privatization of pension fund management increases welfare by inducing a reallocation ofcapital towards investments with a higher return. The first argument is that in the long run, equityinvestment has a higher return than bonds, and that the privately managed pension funds may takeadvantage of this difference. The counter-arguments to this are again two-fold: (1) if it is assumedthat markets are efficient, then risk-adjusted returns are equal and there is no gain from pensionfunding, or (2) if it is assumed that the markets are not efficient, there are many ways to change theallocation of capital, including government borrowing from the market and investing in riskyassets. 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 ofdifferences in rates of return or interest rates alone. Political economy arguments referring to thepolitical suitability of pension funding, as compared to other means, for acquiring welfare gainsmust also be explored. To assess this, the initial institutional structure must be looked at and theprospects of finding the political will to make the required - in most cases major -changes to thepension system must be evaluated. Let’s assume a simplest possible earnings-related public pension system, where a pension as apercentage of wages is accrued by working and pensions are indexed to the wage rate. Labour isassumed 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 ofworkers is constant; all generations pay the same contribution rate and receive a pension which isthe same percentage of the prevailing wage rate. Note that, for this, the population need not bestationary, but it is sufficient that its growth or decline is steady. The apparent equal treatment of allgenerations under these conditions has probably led those who favour preserving a PAYG systemto regard it as a fair arrangement. Following this same principle of fairness leads to partial funding under population ageing causedby a decline in fertility and/or increase in longevity. In technical terms, ageing causes a transition ofthe pension system from one steady state to another, not to be confused with a steady change which 19
  • 20. Actuarial analysis in social securitycontinues forever, even though, it takes, for example, an average life span before the full effect of achange in fertility has fully materialised. The projected increase in the old age dependency ratio until 2040 and the leveling-off which willfollow should be understood as a transition determined by the permanent decline in fertility and thefive-year increase in longevity until 2050. Illustrations with simple numbers Let’s begin by assuming a stationary population, and in the first example, all employees areassumed to work for 35 years and enjoy retirement for 15 years. The replacement rate(pension/wage –ratio) is assumed to be 70%. This is not particularly high, since in this simplifiedcalculation, in addition to the statutory old age pension for the employee, it also includes thesurvivors and disability pensions that normally add to costs of old age pensions. We are using a setof annual data for a typical EU Candidate Country of Central and Eastern Europe(CEEC), on thebasis of which to run scenarios up to 2100 using a actuarial model developed by Patrick Wiese,named Pension Reform Illustration & Simulation Model, PRISM (Copyright © 2000 ActuarialSolutions LLC). The model produces detailed actuarial calculations for pension expenditure and itsfinancing, allowing numerous alternative financing systems. The model captures the cycles ofyearly age cohorts, based on assumptions of fertility and survival rates, pension contributions aspercentage of wages, pension expenditure stemming from accrued pension rights etc., just tomention the key features. Most parameters are changeable, thus the model can be used to run anynumber of alternative scenarios to analyse the impact of a change of any policy parameter or anydemographic or other assumption. Under these assumptions in the PAYG system, the contribution rate to cover current pensionpayments is (15/35)*0.7 = 30%. In the FF system the contributors pay a certain percentage of their wages as a contribution whichis invested in a fund that earns an interest. Pensions are paid as annuities from the capital andproceeds of this fund. We calculate the contribution required to arrive at a pension of 70% of thewage (assuming that annuities are indexed to the average wage rate to get a perfect parallel to thePAYG pensions). For a stable solution the rate of interest must be higher than the growth rate of the wage bill. Thisdifference is most often assumed to be one to two percentage points. For the CEECs, where oneexpects relatively high growth rates of real wages, this order of magnitude should be sufficient as itmaintains real interest rates above the real long term rates in EU-15 (which is a well-basedassumption otherwise). As pensions and the interest rate are assumed to be indexed to the wage rate, the wage rate istaken as the unit of account. Results drawn are thus valid for any assumptions of wage ratemovements, real or nominal, or of inflation. For an individual contributor, the pension fund first accumulates and then goes to zero after 15years of retirement. At each point in time the fund corresponds to the actuarial value of the acquiredpension rights of the employee or the rights still to be utilized by the pensioner. We aggregate overall employees/pensioners and calculate the total amount of pension funds, which is of courseconstant in a stationary world.Table 3.1 Pension financing : steady path with a constant population Active years 35 36 Retirement years 15 14 Replacement rate 70% 72% Rate of interest-w 2% 1% 2% 1% Contr. In PAYG 30,0% 30,0% 28,0% 28,0% Contr. In FF 18,0% 23,3% 16,8% 21,7% F/wage bill 600% 670% 562% 627% 20
  • 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 systemsunder two alternative assumptions of sharing time between work and retirement, and of the interestrate. 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 inboth systems. It is also, by definition, the contribution rate in the PAYG system. Contribution ratesin the FF system are considerably lower than those in the PAYG system as the proceeds from thefund make up the difference. Thus, the figures should illustrate clearly how the same expenditure isfinanced in two different ways in the two cases. Lower interest rates naturally require highercontributions and a larger fund. The latter two columns show that an extension of working life, assuming that the employee earnsa two percentage point increase in pension for each additional working year, lowers the cost ofpensions by roughly seven per cent. The fund as a percentage of the wage bill varies in these examples between roughly 560% and670%. To obtain a rough measure of what these figures mean in terms of per cent of GDP, theyshould 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 inthe 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 currentpensioners and employees), also gives the implicit liabilities of the PAYG system, also calledimplicit pension debt, which has to covered by future contributions (for a presentation of this andrelated 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 decreasesteadily 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 agegroup assumed to be given, means that the fertility rate is either above or below the 2.1 births perwoman, which would keep the population constant. The first example resembles the growth of populations in the 1950s and 1960s in Europe, whilethe latter slightly underestimates the ageing problem, as the current and expected fertility rates inthe CEECs and EU-15 indicate that populations may well be starting to decline faster than 0.5% ayear. Taking the decline at 0.5%, FF funds or implicit debt in the PAYG system would be around700% of the wage bill. The figures for the contribution rates and especially for the size of the fund under alternativeassumptions give a rough idea of the orders of magnitude of key variables and display the internallogic 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 thesponsor of the scheme will go bankrupt. The actuarial equilibrium is based on the open groupapproach, 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-actuarialconstraints, such as capacity of the economy to absorb a given level of contribution rate, the capacityof 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 aremerely touched upon makes no difference whether the system, or some part of it, is mandatory by lawunder 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 fullyactuarially fair - these three dimensions are distinct from each other, and may therefore form manycombinations. To find any degree of funding and actuarial fairness in a DB system as the system mayaccumulate assets and the link between contributions may or may not be close. A DC system mayoperate without reserves, in which case it is said to be a pure Pay-As-You-Go (PAYG) system, basedon notional accounts operated under an administratively set notional interest rate - i.e. an NDCPAYG system). Alternatively, a public DC system can be funded to any degree. The degree ofactuarial fairness is always rather marked in a DC system, but it always depends on variousadministrative 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 annualbenefits and administrative expenses is fully met from current contributions collected in the sameyear. Given the pattern of rising annual expenditure in a social insurance pension scheme, the PAYGcost 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 populationand pensioners is stable, the PAYG cost rate remains constant indefinitely. Despite the financialsystem being retained for a given scheme, the ultimate level of the PAYG rate is an element thatshould 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 securityultimate cost of the benefit obligations so that the capacity of workers and employers to finance thescheme 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 ofimpediments to labour mobility; and a relatively quick build-up of pension rights. Another advantageis the possibility of redistribution, which can insure a certain living standard for individuals who havenever been part of the work force and thus never have had the opportunity to save any income. Afeature of the system is the sensitivity to the worker-retiree ratio, because a declining ratio must eitherraise the contribution rate to keep the replacement rate fixed, or reduce the replacement rate in orderto keep the contribution rate fixed. The two PAYG methods, Defined Contribution system (DC), where the contribution rate isfixed and Defined Benefit (DB), where the benefit rate is fixed, have different implications tochanges in the worker-retiree ratio, and if no demographic changes occur the systems areobservationally equivalent. As such, the PAYG system is very sensitive to all sources of demographicchange, 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 uncertaintyis taken into consideration the system will generally not produce an equivalent amount of privatesavings as would be the case without PAYG social security. If the pension system is purely financedwith a PAYG scheme, it is a perfect substitute for private bequests. Hence, a forced increase in socialsecurity will reduce bequests by an equal amount. The risks associated with the PAYG system are primarily growth in national income anddemographics, as well as uncertainty about the level of pension benefits future generations will bewilling to finance. The rate of interest in the DC-PAYG system – the replacement rate – dependsdirectly on the rate of productivity and the rate of population growth. If government activity isassumed to be limited to managing social security, then the rate of return to a DC-PAYG system isaffected by the growth in productivity, since this will raise national income for taxation. Hence, thecontribution revenue for pension benefits in a balanced budget will be larger, as well as the total levelof benefits to retirees. The other factor which influences the pay off to PAYG is the populationgrowth rate. If it increases, more people pay the assumed fixed level of taxes, thereby generatinglarger 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 PAYGsystem, e.g. it displays great transparency since individuals literally can keep track with their pensionsavings. A funded system can be private or government-run, and can take many forms –for instanceoccupational and supplementary schemes, but if it is not compulsory and no redistribution occurs, thesystem is the same as private pension insurance. If the system is purely funded, it is a perfectsubstitute for private savings. Consequently, a forced increase in social security will reduce privatesavings 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 bothwith 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 topexperts have felt the need to clarify their views and arguments. The cornerstone of analysis and mostinfluential for policy was the World Bank’s “Averting the Old Age Crisis, Policies to Protect the Oldand Promote Growth”, published in 1994. The key recommendation was to create a mandatory, fullyfunded, privately managed, defined contribution, individual accounts based pillar, which would covera large proportion of occupational pensions and hence supplement the public PAYG defined benefit 23
  • 24. Actuarial analysis in social securitypillar, 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 ofparticularly critical assessments, of which we want to mention four: (1) the UN EconomicCommission 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” originallypresented 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 August2000. The criticisms triggered clarifying responses from those who advocate an introduction of a FFpillar, 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 acomparison of the pure forms of the two systems (and sometimes, as Diamond (1999) put it, bycomparing a well-designed system of one kind with a poorly designed system of the other). Thanks toserious 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 moreconsensus also on policy advise than a few years ago. The merits of each system have becomeclearer, and consequently many economists now think that the best solution is a combination of thetwo systems, where details depend on the institutional environment, notably on the capacity of thepublic sector to administer a public pension system and to regulate a privately run system, and on thescope and functioning the financial markets. This also means that a lot of detailed work on specificaspects 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 ofhow 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. Forthe PAYG it is self-evident that a contract between successive cohorts to contribute to the pensions ofthe 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, orsome part of it, must also be mandatory to avoid free-riding of those who would not save voluntarilybut rather, would expect that in old age the (welfare) state would support them. Once the FF system ismandatory, 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 thaton top of a minimum amount the pension depends on the wage history of the individual (sometimesup to a ceiling) and, during retirement, on average wage and/or inflation developments. The FFsystem is mostly associated with defined contributions, where the ultimate pension will depend on thecontributions paid by the individual (or his employer on his behalf) and the proceeds of the investedfunds. This dichotomy is not entirely correct as the link between benefits and contributions at the level ofan individual in a PAYG system can be made rather tight, if desired, even mimicing a FF system bycreating a notional fund with a notional interest rate. Recent examples of this are the reformedSwedish, Polish and Latvian systems, where defined contributions are put into a notional fund with arate of return equal to the increase in nominal wages. Also, some basically FF systems (like theoccupational pension funds in the Netherlands) are defined benefit systems, with contributions 24
  • 25. Actuarial analysis in social securityadjusted according to earnings acquired (as this can be done only afterwards, it does not work exactlylike a pure FF system, but roughly so). Also, if the state guarantees, as it often does, a minimum levelof benefits in an otherwise defined contribution system, the system de facto provides defined benefitsup to a certain level. 3. Intra-generational redistribution PAYG systems normally include an important element of intra-generational redistribution e.g. aminimum pension level that benefits the poorest. This might be partly neutralized however, by basingthe contributions on uniform survival rates for all groups while the low income retirees in reality havea shorter life expectancy. Advocates of the FF system see it as an advantage that individual accountshelp to eliminate redistribution. This may be a valid argument, but one should also note thatredistribution 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, 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 betweencontributions and pension at employee level is only loose, PAYG contributions are often treated likeany other taxes on wages, thus causing a tax wedge between the cost of labour and income receivedby the employee, and a consequent loss of welfare. One of the most important arguments put forwardby advocates of the FF system is that contributions to these funds can be equated with individualsavings, thus avoiding any distortion of the labour market. This dichotomy gives an exaggerated picture. Often in the PAYG system there is also a linkbetween 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 coversthose who would not willingly save, and because uniform parameters may cause redistributionbetween 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. Notsurprisingly, they are considered to be higher in the FF system, and sometimes so high that efficiencycan be questioned (Orszag and Stiglitz, 1999). Obviously, results will vary between Westerncountries 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 FFsystem is that a transition from a PAYG to a FF system increases welfare by improving allocation ofcapital, in addition to the positive effect via the labour market (point 4 above) net of possibly higheradministrative costs (point 5). For sceptics, this is not so clear. They point out that the difference between the rate of return toaccumulated funds in the FF system and the implicit rate of return in the PAYG - which is equal tothe rate of increase of the wage bill - has misleadingly been given as a proof of the superiority of theformer. Sinn (2000, pp. 391-395) neatly develops the argument that (under certain conditions) thisdifference 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 ‘introductorygains’, as Sinn calls them, led at the time to an accumulation of implicit debt, and the differencebetween the two rates precisely covers the interest on this debt. The burden is either carried by allfuture generations or by one or more future generations through reduction of the implicit debt by 25
  • 26. Actuarial analysis in social securitycutting future pension rights or increasing contributions. Thus, Sinn (2000) shows why the differencein 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 maintainthat transition to funding makes it possible to exploit the difference between returns on equity overbonds. However, this improves general welfare only if the rates of return on capital are generallyhigher 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 (ifproperly administered) improve the functioning of financial and capital markets more generally ( 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 implicitpension 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 inportfolios 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 properlyimplemented. In turn, sceptics may sarcastically ask why, if semi-public funds like mandatory pension funds are amiracle, do governments not borrow regardless of pension financing and create trust funds thatcontribute to general welfare in the same fashion. They may also doubt whether pension fundscontribute 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 herdbehaviour 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 awhole and also individuals in those systems are liable for different types of risks. In short, the PAYGsystem is vulnerable to demographic risks (i.e. burden increases if ageing shifts abruptly) andpolitical risks, whereby at some stage the young generation may abandon the commitment to pay andleave 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 thatmight be affected by any exogenous shocks), but also internally to bad management or outrightcorruption, a risk that should not be forgotten. It is often asserted that the FF isolates the system fromdemographic risks. This is true if the rate of return on the funds does not depend on demographicfactors. This might be a relatively safe assumption, but in a closer analysis one should recognize thatas ageing affects savings, it should also affect rates of interest. Brooks (2000) has producedsimulations showing that the baby boom generation loses significantly in the FF system due to a fallin 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. Thecontent and relative size of each pillar should then depend on various institutional factors and otherdetails.3.2.4 Partial funding - NDC In this section a simple quantifiable rule according to which fairness between successive generationsleads to the need for partial funding. Thus, an aspect that should be inherent in the pension system 26
  • 27. Actuarial analysis in social securityitself is the driving force, without relying on contestable arguments related to development offinancial markets and improvement in allocation of resources or any other aspects outside the pensionsystem. The starting point is the analysis by Sinn (2000) who shows, as explained above, that the differencebetween the rate of return in FF and the implicit rate of return in PAYG (the growth rate of the wagebill) as such does not prove that the former is more efficient. This difference stems from the implicitdebt that accumulated when the previous generations were given ‘introductory gains’, i.e. theyreceived benefits while not having (fully) contributed to anybody’s pensions themselves. Had the firstgeneration to benefit from pensions first contributed fully, the result would have been a FF system. Based on this, continuation of the PAYG system can be regarded, says Sinn, as distributing theburden of past introductory gains evenly over all future generations. He considers that the conditionsunder which this holds are not particularly restrictive, and he criticizes various arguments put forwardfor a transition to a FF system. In short, a rapid transition would put a heavy burden on the currentlyactive working population. The fairness of this is questionable (Sinn, 2000).Sinn then moves to the demographic roots of the crisis of the PAYG pension systems: normally theworking generation pays for old age pensions and for raising children, who in turn pay for thepensions of the previous generation. If the current working generation chooses not to raise as manychildren as the previous generation did, it is only fair that it pays part of its own pensions by savingnow and reverting to those savings when retired, hence easing the burden otherwise put on thefollowing generation, which will be smaller. This is thus an argument for partial funding. A Notional Defined Contribution (NDC) system is one more set of rules for a pension system. It ismore recent than the other two main systems described above, but it has already been implemented inSweden, Latvia and Poland and in some non-European countries as a result of pension reforms in1990s. The reforms in Italy in the 1990s also contain some NDC features. (Williamson, 2001). In an NDC system contributions are fixed, registered in notional individual accounts which areremunerated by a administratively fixed rate of interest, and the capitalized value at retirement istransformed to an annuity paid out as a pension. Applications may differ in practice, but if thenotional rate of interest is set as the rate of growth of the contribution base (which is the wage bill ifcomplete coverage is assumed), and if projections of life expectancy at retirement are continuouslyupdated, the system has the valuable property that pension expenditure equals contributions in thelong-run (though not necessarily in the short run). An NDC system is not supposed to possess reserves, or, should they exist, they have no relationshipto individual accounts. This is exactly what makes the system notional. This also means that an NDCsystem is never developed so that a new system with these rules starts from scratch. Were it so, thesystem would have accumulated funds like a FF DC system; the only difference being that the rate ofreturn would be determined administratively (and hence contain a rule for handling the surplus ordeficit stemming from the difference between the factual and the notional returns on the funds). Thus,while DB PAYG and FF FC can exist and mature on the basis of their respective rules from thebeginning, NDC represents a transformation of a DB PAYG system. This has been the case also inpractice. NDC systems normally only cover old age pensions, while disability pensions are financed from thestate budget, though perhaps administratively integrated to the old age NDC system. Also, in an NDCsystem, non-contributory periods like maternity leave are often covered by a contribution from thegovernment budget so that personal accounts continue to accumulate. The elementary case of a stationary population highlights the similarities between the DB PAYGand NDC for old age pensions. Assume the DB PAYG above, and assume that it is transformed to anNDC at a certain moment so that contributions remain at 30% of wages, but go to individualaccounts, and that previously accrued pension rights are honored. New pensions are then partlydetermined by the old DB rights and partly by the NDC annuities, so that the proportion of the formerdeclines to zero after 35 years. Of course, the total replacement rate remains at 70%, and the systemmaintains constant financial balance. 27
  • 28. Actuarial analysis in social security This opening is a useful one. We shall extend it and make it operational by putting numbers on it,deriving easily understandable arguments for partial funding and for its order of magnitude in comingdecades. For the exercise we need a definition of fairness: each generation pays the same proportion of salaryto get the same level of pension rights in “similar circumstances”, which we explain below. As already seen, in a steady path (determined by demography and a constant interest rate) both FFand PAYG systems are equally fair. Let’s first remind ourselves that such steady paths may include constantly decreasing or increasingpopulations. Thus, low fertility reducing population is not a sufficient argument for partial funding.This was illustrated in Tables 3.1 and 3.2 above where in all cases; all successive generations pay thesame proportion of salary to pensions, including the case with the steadily reducing population. However, the relevant questions arise when the pension system shifts from one steady path toanother. Each such path is determined by demographic variables like fertility and life expectancy,pension system parameters like replacement rate, retirement age etc. and the interest rate. As for thelatter, in the simplified world as described in Tables 3.1 and 3.2 above, where everything is indexedto the wage rate, it is the difference between the interest rate and the increase of wage bill thatmatters. If any of these variables or parameters change, the system departs from the previous trajectorytowards another. Depending on the arrangements, some generations may gain or lose. If the system ison a steady path, and any of these factors change, it takes at least 60 years for the system to settledown to the new steady path: this is the time required for a new entrant to the labour force to leavethe system (remember that even after his death survivors pensions may have to be paid). The crux of the matter for the next 50-60 years is that the system is not on a steady path because thedemographic factors have changed and are still changing. The burden of pensions will increaseparticularly rapidly in the next 40 years because fertility has decreased in the recent past and willremain low, and because life expectancy is increasing. To tackle the question of fairness between generations in a situation characterized by a shift fromone (hypothetical) steady path to another, an extension of the concept of introductory gains by Sinn(2000) is useful: under a pure PAYG system, all cohorts that paid contributions when burden waslower than what it will be when they retire get introductory gains. Thus, not only will past andcurrent pensioners have gained from this, but also a large number of currently working cohorts willgain because they retire before the whole system reaches a path of still higher burden. It is only fair toask whether this is justified, or whether the currently active should now pay in more than what iscurrently paid to pensioners, thus accumulating funds into a partially funded system. As simple as possible a 3-period model is used to analyse what happens to pensions under anageing population and how the rules should be designed to cope with the partial funding. The population is composed of children (E), workers (L) and retirees (R). Each of these phases ofan individual’s life is, for the purpose of managing the mathematics, set to be of equal length, whichis set as the unit period: E t = Lt +1 = Rt + 2 (3.1) To keep a rough correspondence with real life, the unit period is best considered to last 30 years:this is currently the average childbearing age of women, and also, by chance, roughly the differencebetween the average age of a pensioner (70) and that of a worker (40). Parameter f expresses the number of children per worker (population then steadily decreases at arate of 1-f): E t = f t ⋅ Lt (3.2) The assumed pension system delivers pensions accrued at a specified rate of the wage by workingand paying pension contributions. Pensions in payment are indexed to the wage rate. Taking the wagerate as the unit of account simplifies notation and allows for any movements of the wage rate, so thatthe results are solely driven by demographic dynamics, the rules of the pension system and theinterest rate. 28
  • 29. Actuarial analysis in social security Pension as a percentage of the wage is p t = σ t ⋅ π t −1 (3.3) where π t −1 is the accrual rate valid in period t-1 determining the pension to be received by theworker in the next period when retired, and σ t is a scale factor which, firstly, takes into account thatin the formal analysis we artificially assume that the period at work and in retirement are of equallength. For example, if in reality the former is 35 years and the latter 15, then σ t is 0.43(= 15/35).Secondly, an increase in longevity, assuming a constant retirement age, can be introduced byassuming an increase in σ t : if people work for 35 years and longevity increases by five years, then σincreases to 0.571 (= 20/35). The interest factor is noted as ρ t is the rate of interest. The interest rate is measured as the excessover the rate of change of the wage rate. In the example it is 50% over the unit period, whichcorresponds to 1.36% per annum over 30 years. The population is assumed to have been stationary for at least two unit periods before any change indemographics. Thus in period 0 the number of E, L and R are the same, set at 100. With these assumptions in period 0 (with stationary population), the contribution rate ( ct ) requiredto balance the PAYG system is the same as the replacement rate, 30%. This is taken to providefinancing on a sustainable basis. Then, in period 1 the working population decides to bear 20% less children than their parents. Thiscorresponds to a decline in the fertility rate from 2.1 births per woman (constant reproduction) to 1.7.All successive generations keep the fertility rate at this new level. From period 3 onwards this leadsto a steady decline in the population at a constant rate of 20 % over the unit period, or by 0.7% p.a.All calculations for technical derivation are available in Appendix1. Scenario 1 in Table 3.3 illustrates a pure PAYG system if the replacement rate is kept constant.Pension expenditure as a share of the wage bill increases to 37.5% in period 2 and then stays at thatlevel. This is also the required contribution rate. In this scenario the adult generation in period 1would pay 30% in contributions. Is this fair? Given their decision to have less children theirdescendants would therefore have to pay 37.5% of their wages in pension contributions. The workingadults in period 1 would reap the benefits at the expense of the others, while all adult generationsfrom period 2 onwards would be treated equally amongst themselves, having the same number ofchildren per capita and paying the same proportion of their wages to pensions.Table 3.3 Pension systems shifting from a steady state to a low fertility path Period 0 1 2 3 4 1 E children 100 80 64 51,2 41 2 L labour=wage bill(wb) 100 100 80 64 51,2 3 R retired 100 100 100 80 64 4 W wage bill 100 100 80 64 51,2 Scenario 1.PAYG, replacement rate constant at 30% 5 Pension expenditure 30 30 30 24 19,2 6 Contr.rate=pens.exp.,% of wb 30% 30% 37,50% 37,50% 37,50% Scenario 2. PAYG, contr.rate constant 7 Replacement rate 30% 30% 24% 24% 24% Scenario 3. Partial funding , new contribution rate 34% 8 Total contributions 30 30 27,2 21,8 17,4 9 Interest income 0 0 2 1,6 1,3 10 Pension expenditure 30 30 30 24 19,2 11 F=fund 0 4 3,2 2,6 2 12 F/W 0 4% 4% 4% 4% 13 30* F/ W 0 120% 120% 120% 120% 29
  • 30. Actuarial analysis in social securityScenario 2 illustrates a fairer solution. In the pure PAYG system, if the contribution rate is keptconstant and the replacement rate decreased correspondingly, the working adult in period 1 receivethe same treatment as the successive generations: they get a lower pension because they initiated thedecline in fertility. In a typical PAYG system this requires that the accrual rate determining howmany percentage points of pension is earned per annum be adjusted downwards according to thedecline in fertility. This change should take place already in period 1. The decrease in the replacement rate is a straightforward solution to the ageing problem within apure PAYG system. However, it is not the solution chosen in most countries, as replacement rates arenot systematically decreased. Scenario 3 therefore assumes a constant replacement rate of 30% and answers the question of howmuch the adults in period 1 should pay in order to be treated equally with all successive generations.It shows that the fixed contribution rate that must be applied from period 1 onwards is 34%. Theadults in period 1 pay into the pension system 4% of their salaries on top of current pensionexpenditure. This is put into a fund that produces interest from period 2 onwards. The newly createdfund alleviates the burden of all successive generations, which all pay 34% as contributions. The fundas a percentage of the wage bill stays constant at 4% (or 120% of annual wage bill, to keep the simplecorrespondence to annual figures). Full funding in this structure requires a fund of 20% of the wagebill in the unit period (or 600% of the annual figure).3.3 Pension financing Nearly half of the mandatory pension schemes around the globe are financed on the basis of Pay AsYou Go (PAYG). In such schemes, current workers are responsible to pay the benefits of currentpensioners. The key parameter for this sort of funding scheme is that workers contribute a fraction oftheir income which is capable to cover all the proceeds accrued toward current retirees. Thefollowing funding equation simply shows how funds are transferred directly from the income base ofemployed participants to the pockets of pensioners. It can evidently be ascertained from the above definitional equation that the financial features of apure PAYG system depends upon a five sets of variables in which some are determined exogenouslyout of the funding equation and others might be set endogenously within the equilibrium condition ofthis equation. For instance the employed population, that is the only contributor of a pure PAYGscheme, affects the system balance more than vice versa. Such a conclusion is more applicable oncethe degree of mandating the employed population is high, and the level of contribution rate is lowthat it cannot have a substantial effect on the labor market stability. Other variables such as the levelof benefits and in most often cases the contribution charges are endogenously determined by thefunding equation. For fewer burdens on the working generation and more stable benefits for the retired one, PAYGrequires a continued rapid population and wage growth rates (Davis, 1998). The system dependencyratio which is often defined as the ratio of retired population to the working one, and the systemreplacement rate which reflects the ratio of average insured income to the average pension, putsforward the stability of financing the system in a major view. The increase of either ratio impliessome extent of difficulties, unless proportionally, the increase of one is being offset by the fall ofanother. However, in a fully funded scheme, pension benefits are always financed through the pensionersown assets. Contributions are invested either individually or centrally by the scheme sponsors andafterward annuitised at the time of retirement to entirely cover the participant expected life span afterretirement. Thus, there is no explicit relation between the system dependency ratio and replacementrate on the one hand, and the level of replaced benefits. Contrary to the former mentioned scheme, afully funded scheme is financed internally via the assets that have already accumulated in the pensionfund or in the participants own account if contribution reserves are held individually. Despite the 30
  • 31. Actuarial analysis in social securityway these accounts are held, collected contributions in such a scheme are deemed as savings while inthe PAYG they are considered as transferred taxes.3.4 Benefit Calculation After the short illustration on how pension systems meet their financial obligations, a view mustbe shown on the approaches used to determine these obligations. Most commonly, PAYG schemesdepend ultimately on Defined Benefit (DB) formulas, in which an eligible retiree receives a pensionamount that is determined by a specified benefit formula which links an individual reference salaryand years of service to a payout function. In practice, there are three forms of DB plans. The firstform is the fixed fee- PAYG system, where the gross system cash proceeds are distributed equallyamong all beneficiaries. In such a plan, individuals pension salary is endogenously determined by thesystems funding equation. Consequently, the level benefits adjust periodically to ensure the exactdistribution of the system total revenues on the current retirees. The following equation indicates howthe system dependency ratio, replacement rate, and contribution rate integrate all together todetermine the level of benefits: Bt = θ t ⋅ Nct ⋅ Yct / Npt (3.4) Where B t is the flat benefit at time t, Nc t : number of contributors, Yc t : Average income ofcontributors. Np t : the number of pensioners. Assuming θ t and Yc t are constant. For example, theincrease in the number of contributors proportionally more than the increase of pensioner wouldresult in an increasing level of benefits. The second form of DB formulas is the Earnings-based PAYG system. This form works in anopposite manner of the Fixed-fee PAYG form since benefits paid to retirees are a fixed fraction (b) oftheir earnings in the preceding period. The rate of contribution, on the other hand, regardless howmuch is paid by contributors and by their employees has to adjust endogenously to ensure the systemoverall balance. In addition to the above mentioned forms of benefit determination, benefits couldalso be fixed to an absolute term. In such a case, contribution rate has to move exactly as in the lattermentioned case. Most of the funded pension schemes, on the other hand, apply another type of pension benefitformula which is known as Defined Contribution (DC) formula (Mitchell and Fields, 1996).According to such a sort of pension calculation, benefits for pensioners at the time of retirement arelinked directly to the contribution made by them and by their employers.4 In a DC plan, thesecontributions are invested, typically by professional money managers. As a result, relatively highly-paid workers who pay more into their pension accounts would have higher retirement accumulationsthan do those who earn less and consequently pay less into the plan. Also, since under a DC plan thepension benefits are linked directly to what is contributed, these plans tend not to guarantee minimumbenefits nor redistribute across pay and service categories. At retirement, the DC benefits are payablein one of two forms. Some DC plans provide for the annuitization of investment accumulations so asto guarantee retirees a steady stream of retirement payments until death. Alternatively, some systemsprovide for retirees to take some or all of their accumulations in the form of a lump sum defrayment.Finally, several systems offer a choice between the annuity and lump-sum forms (Blostin, 2003).Moreover, aside from the form benefits are paid, the present value of benefits should be close to thecorresponding value of the contributions being paid by each participant at the time of retirement.5 4 In some countries schemes, regardless how benefits are calculated, the employers do not share the contributions of their employees e.g. Croatia and Kazakhstan, Argentina, Chile. In some others, employers pay all the contribution imposed on their employees for pension insurance purposes, e.g. Lebanon, Turkmenistan, and Cuba. (ISSA, 2002; ISSA, 2003b) 5 We cannot say that the NPV of benefits and contributions exactly equals zero. it might be less or greater than zero depending on several factors in which the selection of annuity contract and the ratio of actual life span after retirement 31
  • 32. Actuarial analysis in social securityThus, the Net Present Value (NPV) of benefits and contribution for each participant at any point oftime must equal zero or at least not far from it.3.5 Rate of Return (ROR) As initially stated by Samuelson (1958) and Aaron (1966), the PAYG financed schemescompensate the participants contribution with an implicit rate of return that equals the growth rate oftheir total wage bill. However, one can show by simple mathematical instances that such a conclusionmight not always persist in the context of differently stylized PAYG schemes. For illustrativepurposes, assume that there are only two periods with two retiring and two working generations.According to the fixed- Fee PAYG system, as being clarified in advance, the total receipts collectedfrom the working generation by an exogenously determined salary fraction are distributed equallyamong pensioner. Putting that directly in our illustrative example, the working population (A) at thefirst period pays a (Cr) fraction of his salary as pension contributions that are totally and directlydistributed to the retired generation (A) in that period. Mathematically speaking, the first step of ourderivation takes the following form: TC A = CrA ⋅ NctA ⋅ YcA = NptA ⋅ YptA t t t (3.5) t t where: TC :Total contributions paid by generation A Nc : is the number of working generation A Ain period t. Yc: The working generation average Income. Np: The number of pensioners. Yp: theaverage income of pensioners. Since the average pension in a Fixed-Fee scheme is endogenously determined by the fundingequation (3.5), YP can be calculated as follows:  Nc tA  Yp = (Cr ⋅ Yc ) ⋅  t A t A  Np t t A   (3.6)  A  The last parenthesized part of the above equation represents the inverse of Dependency Ratio (DR),the fraction that indicates for the ratio of retired participants to the working generation. While the firstpart of the same equation stands for the average contribution paid by each worker of the workinggeneration A in period t. Now imagine the situation where the working generation of period (t) toretirement at period (1 + t). The pensions of this generation as our example assumes would be paid bythe new working generation (B). TPA+! = CrA ⋅ NcB+1 ⋅ YcB+1 = NctA ⋅ YptA+1 t t t t (3.7) The right side of the above equation comprises the number of contributors of generation A as theywere contributor in period t and got retired in the period directly after. The average pension of eachretiree of generation A would exactly be determined by the same way that average pension in the firstperiod is being calculated:  Nc B+1  t Yp t +1 A = (Cr ⋅ Yc ) ⋅  t A B  Nc t  t +1  (3.8)  A  To simplify the understanding of our example, let us assume that the average income of generationB in period 1 + t comprises the average income of generation A in period t indexed by its periodicalgrowth rate, and the sum of generation B is proportionally related to the sum of generation A: to the expected one are among them. If the scheme member chooses to get a lump sum amount at the time of retirement, however, NPV for benefits and contributions is likely to approach zero. 32
  • 33. Actuarial analysis in social security YcB+1 = YctA ⋅ (1 + λt ) t (3.9) NcB+1 = NctA ⋅ (1 + ρt ) t (3.10) where ρ t : The growth rate of working generation. λt : Wage growth rate. Before going through our derivations, two connotations of ROR should be distinguished in thiscontext. The first should reflect the generational rate of return that each generation gets over the totalcontributions it has paid for the retired generation one period before:  TP t +1  ROR G+,1A =  A t  − 1 t  TC  (3.11)  A  Substituting mid of equation (3.5) and right side of (3.7) considering equations (3.9) and (3.10), thegenerational ROR would take the following form: ROR G+,1A = λt + ρ t + λt ⋅ ρ t = λt + ρ t t (3.12) 132 Neglible From the above equation, one can find that the generational ROR under a fixed-Fee PAYGapproximately equals the sum growth rates of participants average wage and their size (number).This simplified conclusion seems similar to Samuelson and Aaron attribute to the ROR awardedunder a PAYG schemes. The second concept of ROR, which is also necessary to be expressed here,is the individual ROR which reflects the participant profitability when contributing to Fixed-FeePAYG scheme. Mathematically speaking, the individual ROR comprises the proportional differenceof what participant pay as contribution and the amount he gets as pension:  Yp t +1  ROR It +A =  t A t  − 1 , 1   (3.13)  CrA ⋅ Yc A  By substituting equations (3.8), (3.9) and (3.10) in the above, we get the following simplifiedexpression which symbolizes the implicit ROR awarded on the individual pension-orientedcontributions: ROR It +1 = λt + ρ t ,A (3.14) As being ascertained on the generational level, the individuals ROR that is implicitly given on hiscontribution according to such a presided scheme comprises the growth rate of contributors wage bill.From that on, it can be said that under a Fixed-Fee based PAYG system both concepts of ROR seemto be consistent with the former view about the ROR accrued on the pension contributions paid undera pure PAYG system. The next step of our analysis switches now to derive the same concepts considered for the fixed feePAYG based system to the Earning based one, where the individuals pensions are exogenouslydetermined by their own historical earning levels and the contribution rate is endogenously andperiodically adjusted to restore the equilibrium of the PAYG funding equation. To do so, we have to reformulate our illustrative example to simply perform the latter case ofPAYG system. First, let us assume that there are two generations and two periods. At the first period,the working generation B pays the benefits of the retired generation A. Thus, the funding condition inperiod 1 can be formulated as follows: TCB = Crt ⋅ YcB ⋅ NcB = NptA ⋅ YptA t t t (3.15) At the second period, generation (B) becomes retired and is paid by the subsequent workinggeneration (c) in period 2. 33
  • 34. Actuarial analysis in social security TpB+1 = Crt+1 ⋅ Ncc+1 ⋅ Ycc+1 = NcB ⋅ YpB+1 t t t t t (3.16) Consequently, the implicit ROR given on generation B contributions can be performed as follows:  Tp B+1  t ROR t +1 B  t  −1 =  (3.17)  Tc B  By substituting the right end terms of equation (3.15) and the right end in equation (3.16) inequation (3.17), the generational ROR can be expressed by the following term: AveragePen sion Growth Index 678 4 4  Nc   Yp  t t +1 (1 + θ t +1 ROR B+1 t = ⋅ B =  Np   Yp  t B t (3.18)     DRt A {A Dependency Ratio Where θ t : is the average pension growth rate in period t+1. DR t : Dependency ratio in period t. What can be followed from the above equation is that, the generational implicit rate of returndepends mainly on the lagged dependency ratio and also on the growth rate of average pensions. Thislooks a bit different than the general view about the ROR accrued on contributions that are chargedunder PAYG financed pension schemes. Regarding the individual ROR under such a scheme, one can derive it by imagining theproportional rewards on the contributions paid during his employment through the benefits he gets aspension. Simplifying that in the context of our example, each individual of generation (B) would besupplemented with an extra amount of money which comprises the difference between his averagepension in period (t+1) and the contribution he has paid to finance the pensioners of period (t). Torationally perform that, the ROR on the individuals level should be interpreted with respect to thenumber of pensioners at period (t), their average pension and the number of contributors (generationB) at period (t).  Yp B+1 t  ROR It +B =  , 1  Cr ⋅ Yc t  −1  (3.19)  t B   Np tA ⋅ Yp tA  Given that Crt ⋅ Yc B =  t  Nc t  and by substituting it in the above equation, the individual   B  ROR would take the following expression: AveragePen sion Growth Index 678 4 4  Nc   Yp  t t +1 (1 + θ t +1 ROR It +B , 1 =  Np  ⋅  Yp  =   B t B  t (3.20)     DRt A A { Dependency Ratio Equation (3.20) indicates that when the PAYG system is implementing the earning based approachfor calculating pensions, the Implicit ROR on pension contributions, either on the generational levelor on the individual one, would ultimately depend on the average pension growth and the systemdependency ratio. What is worth to mention here, is that the average pension growth rate under suchscheme, follows exogenously many factors at which the individuals historical earning profile is one.However, if the individuals benefits in a PAYG financed schemes are exogenously fixed by thescheme sponsor, then the generational and individual ROR would identically take the following form: 1 ROR It +1 , B = +G (3.21) DR t 34
  • 35. Actuarial analysis in social security If the sponsors of the latter mentioned type of PAYG index the individuals benefits with a pre-specified rate, let say for instance the cost of living index, then the generational and individual RORwould look exactly as in equation (3.20) except that θ t +1 would reflect the indexation factor insteadof average pension growth rate. As regards the awarded ROR under the Notional Defined Contribution (NDC) schemes, it can beeasily recognized that both measures of ROR, either on the individual level or on the generationalone, would follow explicitly the notional interest that the participant contributions are marginalizedwith. If for instance the notional interest rate is measured by the economic growth rate, then the RORgiven on participants contribution would mirror that rate. What is worthy to remind here, is that theROR equals the notional rate only if that rate is awarded on contributions during the accumulationphase and on the remaining balance during the withdrawing stage (retirement period). Otherwise, theimplicit rate would for most, be lower than the notional rate. Funded schemes with centralized managed reserves provide the participants with a ROR that fullyreflects the financial profitability of the contribution assets after the cost of running-out the schemeactivities is being deducted. If the participant contributions are individually invested, however, thenROR would most likely vary among the scheme participants as contributions can be invested indifferent tools and by different agents. In addition to that, the risk exposure may differ between thefunded schemes participants as well as their investment agents, making their pension assets subject todifferent rates of return.3.6 Internal Rate of Return (IRR) IRR is one of the most important money measures for pension schemes promises and contracts.This concept relates to some extent to the clear image of fairness from a pure financial point of view.The IRR is an imperative element for assessing the financial viability of pension schemes. It implies ahypothetical rate of return given on actual contributions that have been made by a participant duringhis career life, which makes the accumulated assets at the time of retirement sufficient to finance thepromised benefits when he is elderly. Of course, in a pure PAYG where benefits are awarded on afixed fee basis, fixed benefits or flat rate, no actual contribution or assets exist in reality since allproceeds from the working generations are transferred directly to pensioners. Despite the fiction of anactual contributions account, the internal rate of return is still a useful concept because it allows us tocompare social provision contracts with other types of investments that could provide retirementsupport. From the pure view of finance, IRR is the rate that makes the present value of future promisedbenefits equal to the present value of all injected contributions in the system. Mathematicallyspeaking, IRR is the discount rate (r) that solves the following equation: LE RA Bt Cr ⋅ Y ∑+1 (1 + r )t = m∑ (1 +mr )mm t = RA = EA (3.22) t m Where B t is the value of benefits at age t, RA represents the age at which the person retires, LE lifeexpectancy at the age of retirement, Cr m : the contribution rate at age m, r: the discount rate, Y m isthe level of income on which the contribution is based on and EA is the age at which the pensionerstarts his career. In view of the above equation, many factors might influence the algebraic value of our concept.Few of them are uncontrolled by the participants themselves, but others to some extent aredetermined on behavioral bases more than on institutional ones. Nonetheless, the favored value ofIRR in a pension provision differs substantially from the point of view of pensioners and theirscheme sponsors. A high IRR for the pensioner implies implicitly that benefits would be relativelyhigh, while for the provisions sponsors it means an extent of generosity and a fear of financialdifficulty. 35
  • 36. Actuarial analysis in social security Considering a benchmark for comparing returns remains a matter of debate among many pensionexperts. However, some actuaries and pension specialists often use the performance of investmentfunds, hedge funds, and the returns on pension buffer funds, among others as bases for comparison.Some others prefer to analyze returns in an international context. Anyhow, the concept regardless ofthe benchmark considered for comparison, is still valid.3.7 Net Present Value (NPV) Another approach for defining the concept of pension fairness is through estimating the presentvalue of a pensioner’s benefits that surpasses the present value of his own contributions. To clarifyfurther, the latter measure calculates the current value of all expected benefits during a person’sretirement life after the current values of all contributions made by the same person being subtracted.Although there is some extent of similarity between this measure and the IRR measure, theaggregation of NPV (social security monetary value) puts another image in our minds. The followingformula shows mathematically how NPV for pension contracts is calculated: LE RA Bt Cr ⋅ Y NPV = ∑+1 (1 + r )t m=EA (1 +mr )mm t = RA −∑ (3.23) t m Where B t is the value of benefits at age t, RA represents the age at which the person retires, LE lifeexpectancy at the age of retirement, Cr m : the contribution rate at age m, r: the discount rate, Y m isthe level of income on which the contribution is based on and EA is the age at which the pensionerstarts his career. As apparent in the above formula, the NPV is sensitive to several variables, but it is more critical tothe discount rate. This comes from the fact that contribution and benefits are both back-counted withthe discount rate, while the life expectancy only affects the amount which a pensioner takes asbenefits. Nonetheless, despite the extent of similarity between this measure and the latter used toreflect generosity (ROR), NPV can play an effective role in showing the net gains (losses) fromjoining the pension provisions. In this context, a neutral pension scheme provides its participants withlifelong retirement benefits, at which if they are discounted to their current value they will matchexactly the discounted value of the benefits they had actually paid to the scheme sponsors. Thus insuch a case, the NPV of benefits and contributions for each retiree equals zero. While a positiveNPV, means that the scheme is awarding retirement benefits that exceed contributions and implies apure gift or subsidy from the system to participants. However, if NPV is none of both cases, theprovision involves some costly measures for pensioners. Moreover, the NPV in this paper is presented as a fraction of the last salary earned by theparticipant just before his retirement, exactly like the replacement rate, except that nominator is NPVinstead of pension salary. This is done in an attempt to make the concept clearer for policy makers aswell as for foreign researchers, since absolute measures might be less understandable under theunfamiliarity of the currencies exchange rates and the real value of money for developing countries,among others. 36
  • 37. Actuarial analysis in social security4. Actuarial practice in Social Security System of Turkey During the last decade, the publicly managed pay-as-you-go (PAYG) pension (old-age insurance)system in Turkey began to face serious financial difficulties due to generosity of pension benefitsrelative to contributions, combined with unrealistically low statutory entitlement ages. When thedeficits generated by the system exceeded tolerable limits, a major pension reform bill wasprepared to set key program parameters straight. Taking 1995 as the base year, and the prevailing conditions in that year as given, several scenarioanalyses are carried out. A pension model that is based on the contribution and pensioncharacteristics of Turkey, such as the minimum retirement age, minimum contribution period,replacement ratio, contribution rate, etc., and Turkish demographic and labor market data are usedin system simulation. Scenario analysis indicates that even with scenarios, with no shocksintroduced to the system, it is financially possible for the system to be viable.4.1 Characteristics of Turkish Social Security System (TSSS) Old-age insurance operations of the publicly managed social security system in Turkey were setup in the 1940s to offer universal coverage to workers employed by public and private sectors alike.The system is made up of three different and distinct branches, each providing pension benefits inreturn for compulsory participation in retirement plans run on a pay-as-you-go (PAYG) basis. Priorto 2003, additional coverage on a voluntary basis was only available through a number of privatepension funds set up by some companies, banks etc. to provide optional coverage to their ownemployees. Following the completion of legal and regulatory framework to allow workingindividuals to voluntarily purchase optional retirement plans from private companies in 2002, mostinsurance companies began to sell optional coverage through money purchase schemes in 2003. The initial TSSS law allows providing five types of insurance: I- Insurance against natural disability old age and death.II- Insurance against work injuries and occupational diseases.III- Insurance against temporary disability due to sickness or motherhood.IV- Health insurance for the worker and his/her dependent.V- Unemployment. Although the TSSS provides only the first two types of insurance coverage, the attention towardthis corporation has increased substantially from the time it was established especially if thesubstitute provisions are absent and the private insurance system in Turkey is still immature andneeds imminent reform. According to State Planning Organization of Republic of Turkey, 48-50 percent of the workers inTurkey have social security coverage. There are three major publicly administered social securityinstitutions, with a combined pool of over 14.3 million active participants in 2006. These are theSocial Insurance Institution [Sosyal Sigortalar Kurumu (SSK)], which is open to private sectoremployees and workers in the public sector, Retirement Fund [Emekli Sandigi(ES)], which coverscivil servants, and Bag-Kur (BK), which is a fund for the self-employed. Approximately 59 percentof the insured population is covered by SSK, 17 percent by ES, and 24 percent by BK. The share ofprivately insured individuals is a trivial 0.5 percent in the population. The data in Table 1 provide additional information on the three main components, and trace outthe evolution of the system. In 1980 there were close to 1.3 million pensioners, implyingapproximately one pension recipient for 3.65 contributors to the pay-as-you-go system. In 2006 thenumber of pensioners exceeded 7.7 million, and the number of contributors per pensioner wasdown to 2. The situation is especially acute in the case of SSK and ES, where the ratio of 37
  • 38. Actuarial analysis in social security contributors to pension recipients was under 2 in 2006. To view the burden from another perspective, there were 5.1 beneficiaries per active SSK member in 1980, and 5.54 in 2006. During the same time this figure rose from 4.1 to 4.51 in the case of ES, and from 4.13 to 5.06 in the case of BK. Table 4.1 : Social Security Coverage by Status and Institution (1980-2007) INSTITUTIONS 1980… …..2004 2005 2006 2007* THE SOC AL NSURANCEI. INSTITUTION 1. Active nsured 2204807 6 033 875 6 569 159 7 351 434 7 792 521 2. Voluntary Active nsured - 328 250 269 267 264 123 260 000 3. Active nsured in Agriculture - 171 500 182 500 194 496 207 883 4. Pensioners 635815 4 032 523 4 220 454 4 388 471 4 571 430 26 143 28 202 31 067 34 444 5. Dependents 8407100 417 187 954 814 36 709 39 443 43 266 47 276Total 11247722 565 567 478 648Active insured per pensioner=(1+2+3)/4 3,47 1,62 1,66 1,78 1,81Beneficiars per activeinsured=Total/(1+2+3) 5,10 5,62 5,62 5,54 5,72II. THE RET REMENT FUND 1. Active nsured 1325000 2 234 769 2 433 022 2 722 753 2 886 119 2. Pensioners 495669 1466372 1534710,6 1595807,7 1662338,3 3. Dependents 3605604 7469547,6 7520583,2 7966142,1 8201146,1 11 170 11 488 12 284 12 749Total 5426273 688 316 703 603Active insured per pensioner=1/2 2,67 1,52 1,59 1,71 1,74Beneficiars per active insured=Total/1 4,10 5,00 4,72 4,51 4,42III. BAĞ-KUR 1. Active nsured 1100500 2320721,3 2433021,7 2625512,3 2687076 2. Voluntary Active nsured - 84166,56 69042,842 67723,734 66666,667 3. Active nsured in Agriculture - 806050 857750 914130,08 977050,49 4. Pensioners 138317 1550970,4 1623251,6 1687873,5 1758242,4 5. Dependents 3301500 12449246 12819176 12944981 13248005Total 4540317 17211154 17802242 18240221 18737041Active insured per pensioner=(1+2+3)/4 7,96 2,07 2,07 2,14 2,12Beneficiars per activeinsured=Total/(1+2+3) 4,13 5,36 5,30 5,06 5,02Total population 44737000 71152000 72065000 72974000 73875000 1. Share of all active insured 0,10 0,17 0,18 0,19 0,20 2. Share of all pensioners 0,03 0,10 0,10 0,11 0,11 3. Share of all dependents 0,34 0,50 0,58 0,65 0,68Share of all with social securitycoverage 0,47 0,77 0,86 0,95 0,99 Source: The Retirement Fund (ES), Social Insurance Institution (SSK), Bag-Kur, SPO (DPT), SIS (DIE). 38
  • 39. Actuarial analysis in social security Excluding the unemployment insurance (UI) premiums, the contribution rate for workers coveredby SSK ranges between 33.5 percent and 39 percent of insurable earnings. The variation is due todifferences in the occupational risk premium (1.5-7 percent) paid by employers, which is typicallyaround 2.5 percent. The rates are 3 percentage points higher for workers who qualify for UIbenefits. Employees contribute as much as 15 percent (5 percent for health insurance, 9 percenttowards retirement benefits, plus 1 percent for UI), while employers in the typical risk occupationcontribute as much as 22.5-27 percent (6 percent for health insurance, 11 percent towardsretirement benefits, 1.5 -7 percent towards work injury and occupational disease risks, 1 percent asmaternity benefits, plus 2 percent for UI). The effective rates depend on the income floor belowwhich a minimum tax applies, and the ceiling above which earnings are not insurable (but are stilltaxed). The nominal floor is adjusted annually by a multiplier which equals the product of theprevious years’ inflation rate (based on the CPI) and the GDP growth rate. The ceiling is set as fivetimes the base. In the case of ES, the contribution rate is about 35 percent of insurable earnings.The public servant pays 15 percent, while the State pays 20 percent. Self-employed individualscovered by BK need to contribute about 20 percent of their earnings towards their retirementpension, and 20 percent towards health insurance. A SII insured to be eligible for retirement must (a) at least be at the age of 50/55 (female/male)and have made contributions for 5000 days, or (b) have been insured for 15 years, madecontributions for at least 3600 days, and be at least 50/55 (F/M) years old, or (c) been insured for20/25 (F/M) years, and made contributions for at least 5000 days. Eligibility requirement forretirement from BK and ES is to have made contributions for 20/25 (F/M) years or be at least 50/55(F/M) years old and made contributions for at least 15 years. Despite the stricter conditions for early retirement that were introduced with the 1999 reform,more than half of the current pensioners in the system for private sector workers (SSK) are stillbelow the official retirement age (58 for women and 60 for men). Moreover, more than threequarters of the pensioners are younger than the higher benchmark of 65 years, and this percentageis expected to remain high for several decades to come. At present women are allowed to retire earlier than men and, because they live longer on average,they typically extract higher implicit rates of return on their contributions. This suggests that somesavings could be made, and some increases in female participation rates achieved, by acceleratingthe equalization of the retirement ages for women and men. At present, with a pension eligibilityage of 44, and a life expectancy (at age 44) of 76, women enjoy an average retirement period of 32years, whereas men, with a pension eligibility age of 47, enjoy an average retirement period of 28years (given life expectancy of 75 at age 47).4.2 Scheme- specific inputs, assumptions and projections The most demanding issue in this context is how the scheme financial conditions would look likeover the first half of this century if the current law remains unchanged. Without quantitativemeasures, the judgment on the future viability and appropriateness of the concerned scheme in thisstudy as well as on the implications of any reform options would be unconvincing.Many pension specialist and academics have used actuarial methodologies to outperform theirfuture forecasts regarding the financial sustainability, stability and distributional dimensions ofpension schemes over long time horizons.6 In this context, the main purposes of using actuarialmodel are manifolds. First, such a methodological approach is well thought to afford us with a clearimage about the periodical movements of the TSSSs financial receipts as well as its expenditures.The need for these estimates is to assess the financial viability of the pension system on a year-by-year basis and to appraise their distributive implications on the scheme main members as there areno reform steps taking place. Second, estimating future financial flows can even be better6 See for instance, Palacios and Rocha (1998) and Oksanen (2002). 39
  • 40. Actuarial analysis in social securityunderstood when the different stages of pension systems life cycle, particularly partially fundedones, are clearly defined.4.2.1 The population projection model As it is widely recognized, demographic parameters are among the most important factors thatformulate and respond to the economic, environmental and social changes. The future prospects ofthe population age and sex structure, beside many others, devote considerable attention of manyresearchers and academics that might benefit to a different extent by putting them in greater use.For instance, commercial institutions benefit largely from the more accurate future populationprojections classified according to the socioeconomic categories such as the individuals incomedistribution and their consumption preferences. These figures as they are actually used areemployed by this sort of institutions to shape the future of their production and marketing strategiesin such a way to maximize their profits. Governments might also be concerned with the same ordifferent types of demographic data to set up their medium-long term fiscal and development plan(ONeill et al., 2001). However, the current status of population as well as its future prospects plays a greater or a lesserrole in this context. The age and gender distribution of a population is considered as one of the mostsignificant elements that determine the future of many pension schemes around the globe. Theinteraction between some of the demographic elements and labour market parameters affect inseveral dimensions the social security schemes characteristics to which in their term they impressthe future financial viability of these schemes. Theoretically and not so far empirically, population projections can be obtained by varioustechniques and methodologies. However, most of the long term oriented projections have employedwhat is called a Cohort Component Method (CCM). This method was formerly developed by theEnglish economist Edwin Cannan (1895) and was first employed by Notestein (1945) to perform aglobal population projection.7After him, the majority of population projection literatures havehinged essentially on this method, the thing which has made it the dominant framework tospecifically project the periodical transition of the global population in the 20th century. Theprojection method according to this approach proceeds by updating the population of each sex andage specific brackets according to the periodical assumptions about the components of thepopulation change. The sources of population growth components regardless of their algebraic signcan be listed under two major groups. The first incorporates the natural changes of population sizeand structure as some people along different time intervals die and some infants are born.( Whilethe second group of transitional components deals with the future possible geographical movementsteps between the targeted population and the external ones as some inhabitants might decide topermanently go out to other countries and others might choose to immigrate into the targetedpopulation . Excluding the impact of new births, the natural periodical transition would always have a negativeimpact on the size of any population unless the number of net migrants from the outside sources isenough to offset the number of death cases at the same time interval. However, when the number ofnew births is considered, the net impact of population transitional movement over any perioddepends mainly on the force effects of all growth components. Based upon this approach, the components of population periodical movements (Fertility,Mortality and Migration) are applied separately on each age- sex brackets. Along the annual timeincrements of the simulation process, population cohorts are periodically transferred to the nextcohort group after the net natural increases is added or subtracted. The number of deaths among allcohorts can be obtained by multiplying the cohort sex groups by their parallel survival rates.Mathematically speaking: Nd it, s = N it ⋅ (1 − Srit, s ) (4.1)7 See for instance, Oksanen (2004). 40
  • 41. Actuarial analysis in social securityWhere Nd it, s denotes the number of deaths of age (i) in period tN it : Total population of age (i) in period t Srit, s : Age-Time specific survival rates: The gender status - s ∈ (male, female ) On the other hand, the number of new births is generated by applying the cohort specific fertilityrates on the female population at childbearing ages. The representative age rang for childbearingfemales as often used by corresponding literatures starts at the age of 15 and ends up at the age of49. The following formula depicts how new births are calculated in our model according to (CCM): 49 B t = ∑ N it, f ⋅ Frit (4.2) i =15Where B t : New births in year tN it, f : Female population of age (i) at time tFrit : Age-Time specific fertility rate The net count for children aged below one can be obtained via applying extra ordinary steps. First,new births are distributed among both genders by the presumed sex allocation factor of new birth.Secondly, after sexual distribution of new birth being obtained, the resulted figures are adjusted byapplying the corresponding survival and net migration rate. (Takahashi, 2002). Figure 4.1 shows ina simple manner the general methodological process for estimating the future population accordingto the (CCM): Base population in year t by sex and age Rates of survival by sex and age Population in year t+1 Net migration by sex and age Population in year t+1 Rates of fertility by sex and age by age of mothers Number of newborn Sex ratio of the newborn Number of newborn by sex Population of age 0 in year t+1 by sexSource: The international Financial and Actuarial Services (2002).Figure 4.1: The general framework of CCM 41
  • 42. Actuarial analysis in social security4.2.2 Data and assumptions As a first attempt to implement this approach to projecting the Turkish population over the entiresimulation period, the required data is being obtained from their different national and internationalsources. The initial one-year-age and gender increments of the Turkish population in 2001 wereacquired from the State Planning Organization (SPO) of Turkey. The mortality rates used in themodel are essentially based on the International Labour Organization (ILO) prospects about thefuture age- gender specific survival rates of the Turkish population. Future assumptions regardingfertility and net migration rates are based to large extent on the United Nation (UN) populationprospects country specific estimations (UN, 2000). The model relies basically on the "main variant"forecasts concerning fertility, mortality and migration rates, since they are based on the most likelyevolution of each of them in the light of the trends observed in recent years. These sources asFigure 4.2 depicts, estimate that Total Fertility Rate (TFR) will decline from currently 172% to133% by the end of this decade. Afterward, TFR continues to decline until it reaches the level of118% by the year 2050. Consequently, the average number of babies born to a Turkish womanwould almost half over the first five decades of this century. The following figure shows theestimated age specific fertility rates over the simulation period. 200,0 180,0 160,0 140,0 120,0 100,0 80,0 60,0 40,0 20,0 0,0 15-19 20-24 25-29 30-34 35-39 40-44 45-49 1995-2000 2020-2025 2045-2050Source : United Nation’s world population prospects, 2000Figure 4.2: Age specific fertility rate for 1995- 2050 As one of the consequences of improving life and health standards, the ILO vision of the futuredevelopment in mortality rates seems quit optimistic. The average mortality rate for females as theILO expect would continue its declination until it reaches half of its current level by 2050. Theaverage mortality rate for males is assumed to decrease as well but in a lower extent whencompared with their counterpart females, since that is assumed to place on 17% by 2050 which ismore than half its level in 2000 (28%). Figure 4.3 shows how the proportion of those who deceasedat a peculiar age and year would fall over the period of simulation. No less important, life expectancies for both genders at each one-year age increments arecrucially needed in this context as one of the inputs the model utilizes to canvass the implications ofreform scenarios, since they pertain directly to the estimated life expectancies. Once survival andhence mortality rates being assumed or projected, the corresponding age-sex specific lifeexpectancies can be computed accordingly. Since mortality rates at each age bracket are higher formales when compared with their counterpart females, the age specific remaining life expectancy forwomen always exceeds that of men. Aside from the sexual divergence of life expectancies, themale life expectancy at birth, as ILO projection model finds, would increase from 66.5 in 2000 upto 76 years in 2050. 42
  • 43. Actuarial analysis in social security 40% 35% 30% 25% 20% 15% 10% 5% 0% Age 0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 Age Male-2000 Male-2050 Female-2000 Female-2050Source: ILO’s prospects, 2000Figure 4.3: Age –Sex based mortality rates (2000- 2050) The female life expectancy at birth, on the other hand, most likely would jump up to 81.2 by theyear 2050, which is roughly 9.5 years above its level in 2000. By looking at Table 4.2 one canrecognize that in both terms the actual and relative ones, the life expectancies over the entireprediction period would improve for both genders but relatively larger for those of women. Thiscan be clearly attributed to the future prospects regarding the probability of dying for both genders,at which it is expected to decrease at each age after birth more proportionally for females thanmales. Concerning the remaining life expectancy at the normal age of retirement, the men whoreached the age of 60 at year 2000 are expected to live for another 19.61 years until their death,while at the same year a women who has reached this age may live for another 21.98 years. Alongthe simulation, at the age of 60, both men and women are most likely to survive longer as timepasses up. Again, the increase in the remaining life expectancies for females would surpass theirmale counterpart in absolute and proportional terms.Table 4.2 Gender life expectancy at birth and normal retirement age Year 2000 2010 2020 2030 2040 2050 At Birth Male 66,5 69,2 71,4 73,4 75 76 Female 71,7 74,4 76,6 78,3 79,9 81,2 Both sexes 68,5 71,2 73,4 75,3 76,9 78 At Normal Retirement Age, 60 for male and female Male 19,61 20 20,5 21 21,6 22 Female 21,98 22,6 23,4 24,5 25,5 26,4 Both sexes 20,3 20,9 21,5 22,3 23 23,7 The general approach of Cohort Component Method (CCM) as defined in advance, is beingsuperseded by an adjusted technical methodology. This methodology is well thought out tocontemplate the characteristic manner of the data that has been obtained from their differentsources. The model uses a one- year cohort based matrices or both genders, in an attempt to have 43
  • 44. Actuarial analysis in social securitythe needed sort of future population outcomes. The population for each gender during thesimulation time interval is modeled according to a one- year step by step transition mechanism. Themodel transmits the cohorts that have already been born in year (t) to the following estimated yearby applying the corresponding survival and migration rates. Figure 4.4 displays a general overview of the foreseeable development of the Turkish populationstructure all along the simulation period. The population of young people for those who are aged 15years and below commences to decline over the rest of the simulation period. However, theworking age population continues to increase rapidly during the coming next years and afterwardstarts to grow steadily with a few fold of decline during the early years of the first half of thesecond decade. After 2020, the aggregate population commences to decline over the rest of thesimulation period. Such an optimistic view should not continue as it is initially seen as thesimulations also depict an increasing trend of the old age population along the same interval of theincrease in working age population. The net offset of both trends on the population dependencyratio is shown clearly in Figure 4.4. The total impact of the transition process of the Turkishpopulation has resulted in the tripling of the ratio of old age people to the working one by the end ofthe simulation period. This rationalized apparently in the same figure, the concavity and convexityof the working age population and old aged population time trends, respectively, indicates that theformer is most likely to grow in decreasing rates while the growth of the latter would be inincreasing rates. Young people (0-15) Working age people (16-59) 35% 66% 30% 64% 25% 62% 20% 60% 15% 58% 10% 56% 5% 54% 0% 52% 2000 2005 2010 2015 2020 2025 2030 2035 2040 2045 2050 2000 2005 2010 2015 2020 2025 2030 2035 2040 2045 2050 Year Year Old-age population (>59) Population dependency ratio (>59/16-59) 25% 45% 40% 20% 35% 30% 15% 25% 20% 10% 15% 10% 5% 5% 0% 0% 2000 2005 2010 2015 2020 2025 2030 2035 2040 2045 2050 2000 2005 2010 2015 2020 2025 2030 2035 2040 2045 2050 Year YearFigure 4.4 The estimated development in population size and parameters The development of age and sex distribution of the whole Turkish population as shown by thepopulation pyramids in Figure 4.5 indicates a gentle transition from a classical pyramid shape thatreflects a young population to wide-top pyramid which indicates a relatively older one. This of 44
  • 45. Actuarial analysis in social security course comes to the space as the consequences of the anticipated mix of low births coinciding with continued improvements in life expectancies start to appear on the population structure. 2000 2015 M a le s Year : 2000 M a le s Year : 2015 F e ma le s F e ma le s 100+ 100+ 90-94 90-94 80-84 80-84 70-74 70-74 60-64 60-64 Age 50-54 Age 50-54 40-44 40-44 30-34 30-34 20-24 20-24 10-14 10-14 0-4 0-4 10,0% 5,0% 0,0% 5,0% 10,0% 10,0% 5,0% 0,0% 5,0% 10,0% 2030 2050 M a le s Year : 2030 M a le s Year : 2050 F e ma le s F e ma le s 100+ 100+ 90-94 90-94 80-84 80-84 70-74 70-74 60-64 60-64 Age 50-54 Age 50-54 40-44 40-44 30-34 30-34 20-24 20-24 10-14 10-14 0-4 0-4 10,0% 5,0% 0,0% 5,0% 10,0% 10,0% 5,0% 0,0% 5,0% 10,0% Figure 4.5 The development of the Turkish population pyramids Expected total population and total labor force are two important determinants of the financial projection of the system. The economically active population is determined by applying labor force participation rates to active age groups. Total employment is calculated on the basis of growth assumptions. To the employed labor force, coverage rates are applied to reflect the actual insured population under TSSS 4.2.3 Actuarial projectionsThe TSSS Pension Model, Data Sources and Assumptions The model is based on actuarial techniques and simulates the behaviour of the TSSS pensionscheme based on demographic and financial projections. While actuarial valuation assesses the long-term viability of the pension plan at a valuation date,pension projections provide insight on the expected cash flows of contribution income and benefitexpenditure based on demographic trends. The model provides deterministic projections of pensionsdetermined on a defined-benefit basis, based on a set of initial data and projection assumptions overtime. Demographic data used and assumptions made in estimating the parameters of the actuarialmodel are summarized below. 45
  • 46. Actuarial analysis in social security(a) Calculation of the value of the accrued liabilities of a pension scheme This calculation was made to calculate the total liability of TSSS for pension rights accrued at31.12.2002. Mortality rates provide the basis for aging the insured population and are very important foractuarial models. There are no officially prepared ‘Turkish Life and Mortality Tables’. Old agepensioners and survivors are assumed to experience the same mortality as the general population,whereas the mortality rates of the invalids below retirement age are assumed to be higher than thoseof the general population. The assumed annual growth rates of real pensions are calculated based on TSSS’s real pensionexpenditures between 1965 and 2004. The average growth rate of real pensions in this period is foundto be 1.84%.a.1) Assumptions male/female by age1. Investment income (Inv) – 0%-12%2. Inflation rate (Inf.) - 0%3- Technical rate of interest = (1+Inv)/ (1+inf.) -1, (0%- 12%)4- Survivor’s benefit: This liability is assumed to be a percentage of the liability for old age pension– 30%5- Retirement age: Variable (Averages depending on transition rules) Table 4.3 Mortality table used for males (All rates are per 1000 lives) Male Age l(x) q(x) D(x) N(x) 20 99690 0,00170 99 690 299 540 30 97843 0,00190 97 843 1 286 520 40 95121 0,00330 95 121 2 251 294 50 89443 0,00860 89 443 3 175 285 55 83782 0,01390 83 782 3 606 541 60 75150 0,02140 75 150 4 001 105 65 63040 0,03280 63 040 4 341 912 70 47310 0,05250 47 310 4 610 079 80 16628 0,13010 16 628 4 906 129 90 2003,4 0,27420 2 003 4 976 374 100 0,0576 1,00000 0 4 980 095wherel(x): is the number of survivors at age x of 1,000,000 birthsq(x) : is the mortality ratesD(x), N(x): are the commutation functions 46
  • 47. Actuarial analysis in social securityTable 4.4 Mortality table used for females (All rates are per 1000 lives) Female Age q(y) l(y) D(y) N(y) 0,00080 20 99 181 99 181 598 221 0,00120 30 98 207 98 207 2 571 677 0,00210 40 96 507 96 507 4 519 082 0,00480 50 92 950 92 950 6 414 988 0,00710 55 89 731 89 731 7 326 084 0,01150 60 84 948 84 948 8 196 467 0,01950 65 76 969 76 969 9 001 054 0,03490 70 65 768 65 768 9 707 327 0,10250 80 30 327 30 327 10 647 942 0,25040 90 4 941 4 941 10 936 890 100 1,00000 0 0 10 956 655a.2) Present value factorsPresent value factors are calculated on the basis of the assumptions per unit of annual benefit.Table 4.5 Present value factors Active Pensioner Age Male Female Age Male Female Ret.Age PV factor Ret. Age PV factor PV factor PV factor 20 57 0,84 55 1,20 20 15,25 15,56 30 52 2,59 49 3,74 30 14,61 15,04 40 47 7,70 48 7,73 40 13,48 14,16 50 53 8,97 57 7,00 50 11,76 12,75 60 70 2,66 68 4,43 60 9,56 10,63 65 74 2,15 74 2,82 65 8,29 9,30 70 80 1,05 81 1,20 70 6,97 7,85 80 80 4,71 92 0,10 80 4,71 5,26 90 90 2,62 92 1,04 90 2,62 2,74 100 100 100a.3) Liabilities Liabilities are calculated on the basis of the present value factors and the total pension (old age,mortality, survivors) amount by sex and age. If the interest rate increases, then total liability will bedecrease. (Table 4.6) 47
  • 48. Actuarial analysis in social securityTable 4.6 Total liability TOTAL LIABILITY PER 31-12-2001 IN TL 1.000.000 Technıcal ınterest rate 0% % 6% % 12% % Actıve insureds 346 030 144 765 69% 65 450 816 224 89% 28 686 362 148 84% Pensioners 152 573 772 622 31% 7 732 068 204 11% 5 278 595 965 16% TOTAL 498 603 917 387 100% 73 182 884 429 100% 33 964 958 112 100%Table 4.7 Liabilities by sex and age Age Actives Pensioners Male Female Total Male Female Total 1 233 856 1 901 485 20 025 645 3 135 341 669 - 9 271 971 3 090 588 30 002 636 12 362 559 638 141 303 141 303 13 026 507 1 599 810 721 382 888 40 650 644 14 626 318 294 678 059 331 1 609 442 009 2 568 154 209 969 5 589 744 1 238 50 313 959 2 778 124 272 535 716 352 6 828 460 888 72 651 12 989 3 005 460 602 60 175 629 85 640 804 332 789 225 3 608 249 557 8 013 1 252 975 736 163 70 134 361 9 265 494 364 935 193 1 139 671 557 10 355 36 99 769 21 80 202 400 10 391 603 447 895 953 121 665 401 4 182 1 90 - 350 716 368 5 898 718 100 - - 278 004 791 68 025 353 121 217 860 31 355 Total 385 381 346 030 144 765 599 912 022 152 573 772 622Note: For detailed actuarial calculations see section 1.2 (Chapter 1)(b) Projection of social insurance income and expenditure of Turkey 80 TPG t = ∑ PG x =13 t x TH t = TPG t * Contribution collection factor (82, 26%) t t S xt −1 + S xt −1 PG x = ( PEGK x )(%PO)( )( Gün x ) 2 PEGK x = ( PEGK x−1 ) (1+ π t )(1+ r t ) t t if PEGK x−1 < PEGKT t , t = ( PEGK x−1 ) (1+ π t ) t if PEGK x−1 ≥ PEGKT t , t PEGKT t = ( PEGKT t −1 )(1+ π t )(1+ r t ) r t : GDP growth rate in year t-1 and t π t : Inflation rate in year t-1 and t PEGKT t : Daily earning based on defined contribution in year t 48
  • 49. Actuarial analysis in social security tPEGK x : Earning of group at age x based on defined contribution in year t t S x : Number of population at age xGün x : Number of days of annual contribution of group at age x%PO: contribution rate, typical category of insured persons under a social insurance scheme tPG x : Insurable earnings of group at age x in year tTPG t : Total insurable earnings in year t In 2004 annual inflation rate and GDP growth rate was around accordingly 12% of CPI and 5%and expected to decrease to 5% of CPI and 2 % in year 2015, if no intervention is made.Table 4.8 Inflation and GDP growth rate 2004 2005 2006 2007 2008 2009 2010 2011 2012 2013 2014 2015Annual CPI(%) 12 10,25 8,5 6,75 5 5 5 5 5 5 5 5Annual GDPgrowth rate(%) 5 2 2 2 2 2 2 2 2 2 2 2Reserve fund income Contribution revenue accumulated at the reserve fund approximately 15 days in every month. Theinterest rate linked to the assumption made for GDP growth rate and inflation rate (CPI)F t = (TH t )(i15 ) ti15 = 24 (1 + r t )(1 + π t ) tF t : Reserve at the end of year t ti15 : Interest rate in year tTable 4.9 Active contributor / Pensioner ratio Actives/pensioner # of contributors # of pensioners Year ratio 2004 6.654.047 3.407.707 1,953 2005 6.787.087 3.504.030 1,937 2006 6.911.672 3.593.810 1,923 2007 7.004.613 3.696.338 1,895 2008 7.123.767 3.771.852 1,889 2009 7.208.110 3.863.085 1,866 2010 7.277.679 3.959.870 1,838 2011 7.392.357 4.010.998 1,843 2012 7.451.928 4.096.315 1,819 2013 7.574.706 4.128.472 1,835 2014 7.641.378 4.199.935 1,819 2015 7.716.121 4.264.991 1,809 49
  • 50. Actuarial analysis in social securityFigure 4.6 Expected total insurable earnings (2004-2015) 45 000 000 40 000 000 35 000 000 30 000 000 Billion TL 25 000 000 20 000 000 15 000 000 10 000 000 5 000 000 0 2004 2005 2006 2007 2008 2009 2010 2011 2012 2013 2014 2015 YearsFigure 4.7 Expected total insurable earnings and expenditures 45 000 40 000 35 000 30 000 Trillion TL 25 000 20 000 15 000 10 000 5 000 0 2004 2005 2006 2007 2008 2009 2010 2011 2012 2013 2014 2015 Years income expenditureiFigure 4.8 Required contribution rate keeping target balance ratio 35 34 Contribution rate (%) 32,93 32,97 33 32,81 32,27 32,84 32,67 32,78 31,84 31,81 32 32,23 32,07 31,71 31 30 2004 2005 2006 2007 2008 2009 2010 2011 2012 2013 2014 2015 Years 50
  • 51. Actuarial analysis in social security4.3 Sensitivity Analysis The aim of this sensitivity analysis is to find out how deficits of the system react when aparameter is changed or a policy intervention is introduced into the system. By studying which pureor mixed parameters or policy changes will offset deficits (no matter how unrealistic they are) theobjective is to help policy makers assess the implementability of the policies. In this respect, a Base Case which simulates the natural course of the current system is created andthen from the mildest to the most radical, pure and mixed scenarios are analised. Expenditure/revenue ratio is used as the performance measure in evaluating the performance ofthe scenarios and comparing the Base Case with some other projections. Since the overall effect of change or a policy intervention starts to emerge in 20- 30 years’ time insuch a pension model, the projections are carried out over the period 1995 and 2050. However,since the environment is very uncertain and no long-term or even medium-term official plans orprojections are available for Turkey the results of the model over the period 1995 to 2030 should betaken into account. ILO pension model, was used in the simulations. However, almost all of thedemographic and economic assumptions were updated based on SPO data. 4.3.1 Pure scenarios The scenarios in which only one parameter is changed and the other parameters and assumptionsare kept the same are called “pure” scenarios. In order to determine what is necessary to bring theratio down to 1.00 several values for certain parameters were tried, that were pointed out assymptoms of problems. In Scenarios 1-5, instead of 38/43 which are the minimum retirement ages specified for femalesand males, ages of 40/45, 45/50, 50/55, 55/60, and 60/65 (F/M) are tried. The results for selectedyears are reported in Table 4.10. The results indicate that the longer the period the higher is the impact of the minimum retirementage scenarios. It should be pointed out that the not most radical minimum retirement agearrangement, 50/55 and 55/60 are sufficient to offset the deficits in the short and medium term. Scenarios 6-10 assess the effect of replacement rates of 55%, 50%, 45%, 40% and 20%,respectively on expenditure/revenue ratio, over the years.Table 4.10 Ratios for Minimum Retirement Ages and Different Replacement Ratios Scenario 1995 2000 2010 2020 2030 2040 2050 Base Case 38/43 2,38 2,78 2,75 2,42 2,72 3,21 3,64 1 40/45 2,38 2,64 2,62 2,34 2,52 2,99 3,44 2 45/50 2,38 2,34 2,15 1,93 2,04 2,35 2,78 3 50/55 2,38 2,12 1,75 1,49 1,62 1,8 2,08 4 55/60 2,38 1,97 1,42 1,07 1,15 1,31 1,5 5 60/65 2,38 1,88 1,21 0,79 0,75 0,88 0,97 6 55% 2,38 2,74 2,67 2,34 2,62 3,09 3,5 7 50% 2,38 2,7 2,6 2,26 2,52 2,97 3,37 8 45% 2,38 2,66 2,53 2,18 2,42 2,85 3,23 9 40% 2,38 2,62 2,46 2,1 2,38 2,73 3,09 10 20% 2,38 2,52 2,23 1,85 1,99 2,32 2,62 All of the respective ratios are better (lower) than the Base Case as shown in Table 4.10. However,the ratio for Scenario 10, which is quite unrealistic, is seen to be ineffective in bringing theexpenditure/revenue ratio down to 1.00. Even with the most drastic change this parameter can only 51
  • 52. Actuarial analysis in social securitylower the ratio to 1.84. Furthermore, the additive effect of each decrement of 5% is found to bealmost the same. Scenarios 11 to 15 have contribution periods ranging between 6,000 and 10,000 days with anincrement of 1,000 days for each consecutive scenario while Scenarios 16-18 have contributionperiod of 12,000, 14,000, and 20,000 days, respectively. The ratios for the scenarios are tabulated inTable 4.11 for the selected years.Table 4.11 Ratios for Different Contribution Periods Scenario Days 1995 2000 2010 2020 2030 2040 2050 Base Case 5000 2,38 2,78 2,75 2,42 2,72 3,21 3,64 11 6000 2,38 2,63 2,65 2,33 2,6 3,08 3,5 12 7000 2,38 2,39 2,54 2,16 2,36 2,82 3,26 13 8000 2,38 2,14 2,17 1,79 2,04 2,43 2,85 14 9000 2,38 2,06 1,78 1,47 1,69 1,94 2,33 15 10000 2,38 2,01 1,6 1,35 1,45 1,68 1,97 16 12000 2,38 2 1,51 1,24 1,32 1,47 1,7 17 14000 2,38 1,99 1,48 1,2 1,25 1,39 1,61 18 20000 2,38 1,99 1,45 1,12 1,15 1,28 1,47 Even the most radical and the most unrealistic scenario, namely Scenario 18, cannot eliminate thedeficits altogether but lowers the ratio to 1.12 by year 2020. Scenario 19 assumes that contribution collection rate will increase to 95% by year 2030 whereasScenario 20 foresees that it will increase to 95% by year 2005. Especially Scenario 20 slows down the deterioration of the financial status since its impact will bein the short and medium term. However, after 2020, the ratio for this scenario increases steadily. Scenario 21 assumes that the share of the active contributors of TSSS in the total employedpopulation (the coverage rate) reaches 50% in year 2010 and increases at a rate of 0.5% per year.Scenario 22, on the other hand, envisages that the coverage rate will increase to 67% by year 2050. Scenario 22 yields results better than the Base Case for all projection years while the otherscenario produces results worse than the Base Case for the period between 2030 and early 2040salthough it has dramatic improvement in the medium term. The reason for this is that the newcontributors as a result of the sudden increase in the coverage in the early years will start to retireafter the late 2020s and hence the number of pensioners will increase dramatically in that period. Scenario 23 assumes that annual real pension growth rate (3%) is faster than annual real growthrate of wages (2.81%). Scenario 24 assumes that annual real pension and wage increase are equal(2.81%). Lastly, Scenario 25 assumes no real pension increase. As Table 4.12 implies deficits are highly sensitive to changes in both real wages and pensionssince the revenues and expenditures of the system are directly linked to these factors.Table 4.12 Ratios for Different Contribution Collection and Coverage Wage and Pension Increases Scenario 2000 2010 2020 2030 2040 Base Case 85% Forever 2,78 2,75 2,42 2,72 3,21 19 95% by 2030 2,55 2,48 2,26 2,38 2,85 20 95% by 2005 2,45 2,34 2,19 2,38 2,85 21 50% by 2010 2,57 1,89 1,99 2,79 3,37 22 67% by 2050 2,66 2,6 2,4 2,51 2,55 23 Faster pension increase 2,94 3,25 3,21 4,03 5,33 Equal wage and pension 24 increase 2,92 3,16 3,06 3,78 4,9 25 No real pension increase 2,54 2,09 1,54 1,44 1,43 52
  • 53. Actuarial analysis in social security Scenario 26 assumes that the ceiling of the contribution base equal 5 times the minimum wage.Scenario 27 envisages that the probability of taking widow(er) s’ pensions for the spouses of theinsured people will be halved by year 2050. Moreover, it assumes that the maximum number ofchildren eligible to orphans’ pension will be halved. Furthermore, the labor force participation ratefor females will increase to 70% by year 2050. Scenario 28 assumes that the State will contribute to the system regularly 1% of GDP every year.Table 4.13 Ratios for Other Parameters Scenario 2000 2010 2020 2030 2040 Base Case 1,8 Times minimum wage 2,78 2,75 2,42 2,72 3,21 26 Ceiling:5 Times min. wage 2,35 2,46 2,2 2,47 2,92 27 Social parameters changed 2,7 2,54 2,15 2,33 2,74 28 State Contribution 1%0f GDP 1,21 1,29 1,35 1,54 1,92 It is seen that Scenario 27 is better than Scenario 26 between 1995 and 2010, but the reverse is truefor 2020-2050. The improved ratio in 1995 steadily deteriorates over the period for Scenario 28. 4.3.2 Mixed scenarios Scenarios in which two or more parameters are changed are called “mixed” scenarios. To see theadditive effect of each parameter, the analysis starts with the change of two parameters and at eachstage one more parameter is changed. In mixed Scenario 1 the minimum retirement age is 50/55 (F/M) and the replacement rate is 50%.Mixed Scenario 2 is the same as Mixed scenario 1 but contribution period is 6000 days. In mixedScenario 3, as well as the assumptions in Mixed Scenario 2, contribution collection rate is assumedto increase to 95% by year 2030. Mixed Scenario 4 is the same as Mixed Scenario 3, but the ceiling of the contribution base isassumed to be 5 times the minimum wage, when the assumption that the coverage rate of TSSS willbe 50% by year 2010 is added to Mixed Scenario 4, Mixed Scenario 5 is obtained. As well as theassumptions in Mixed Scenario 5, Mixed Scenario 6 envisages that the probability of takingwidow(er) s’ pensions for the spouses of the insured people will be halvened by year 2050.Moreover, it assumes that the maximum number of children eligible to orphans’ pension will behalvened, and that the labor force participation rate for females will increase to 70% by year 2050. Mixed Scenario 7 is the same as Mixed Scenario 6 but state contribution which is 1% of GDP isintroduced. Mixed Scenario 8 is independent of Mixed Scenarios 1-7 and assumes that theminimum retirement age is 50/55 and the ceiling for the contribution base equal 5 times minimumwage. Mixed Scenario 9, is the same as Mixed Scenario 8, and assumes that the State contributes tothe system regularly by 1% of GDP annually.Table 4.14 Ratios for Mixed Scenarios Scenario 1995 2000 2010 2020 2030 2040 2050 Base Case 2,38 2,78 2,75 2,42 2,72 3,21 3,64 Mixed 1 2,38 2,09 1,69 1,43 1,54 1,7 1,97 Mixed 2 2,38 2,08 1,67 1,4 1,5 1,66 1,92 Mixed 3 2,38 2,05 1,59 1,3 1,34 1,49 1,72 Mixed 4 2,38 1,63 1,26 1,03 1,07 1,19 1,38 Mixed 5 2,38 1,51 0,87 0,85 1 1,22 1,37 Mixed 6 2,38 1,5 0,86 0,84 0,97 1,18 1,3 Mixed 7 2,38 0,83 0,57 0,58 0,72 0,89 1,04 Mixed 8 2,38 2,12 1,7 1,44 1,54 1,7 1,97 Mixed 9 2,38 0,88 0,77 0,78 0,9 1,03 1,23 53
  • 54. Actuarial analysis in social security For year 2010, the most dramatical impact of the additional parametric change is caused by bothincreasing the minimum retirement age to 50/55 (F/M) and decreasing the replacement rate to 50%as observed from Table 4.14. The impacts by Mixed Scenario 1, 4 and 5 are much more than theothers. The least additional effect is borne by the change in social parameters mentioned above. Inthe long run, the additional impact of Mixed Scenario 1, is much more than the others. The leastadditional effect is borne by the change in the social parameters. Mixed Scenario 7 enables thesystem to have surplus at the very beginning and leads to an average improvement of 72.9% overthe ratio of the Base Case for the period between years 2000 and 2030. It is important to note that itis the only scenario for which the ratio is below 1 until year 2050. The results show that regular State contribution to the system as much as 1% of the GDP annually,in any case, results in substantial improvement in the financial status of the system. Several scenario analysis are carried out and all pure and mixed scenarios are compared with theBase Case simulating the natural course of the system. Expenditure/revenue ratios are used as theperformance measures in comparing scenarios. The results indicate that among the pure scenarios, only the scenario with minimum retirement ageof 60/65 (F/M) and the one which envisages significantly higher real wage increase than realpension increase are found to bring the expenditure/revenue ratio down to 1. However, the mixedscenario which assumes minimum retirement age of 50/55 (F/M), replacement rate of 50%, 6000days of contribution, contribution collection rate of 95% until year 2030 and coverage rate of 50%until year 2010 results in the ratio to decrease below 1.00. Each added parametric change improvesthe financial status of the system. So the findings as a whole are much more optimistic than public and international financialinstitution forecasts, deeming the system financially unviable by 2025. It should be noted that whenthe policies are put into effect together with reorganization of the TSSS itself, the expected benefitswould be even higher. 54
  • 55. Actuarial analysis in social security5. Some actuarial calculations with regards to the pension system of Azerbaijan After regaining its independence in 1991, Azerbaijan experienced a difficult transition to amarket economy, marked by a steep fall in GDP, high inflation, population loss, and continuing lowfertility rates. Today the Azerbaijani demographic situation is improving, and this will probablycontinue for several years. The betterment of the social condition of the population has also endured, so that the economicgrowth rate in the country has sped up more in 2006. 35.1 % increase in the key macroeconomicindicator of economy, GDP, has happened. (In 2005 was 26%) The average monthly wage has amounted to AZN 182.8 manats, and its growth rate hasconstituted 26.4%. (Income growth was 37%) The average labor pension was around 33 percent ofthe average wage in August, 2007. The increase in the population’s income causing a raise in thepurchasing ability has been a factor paving the way for the development of the real sector. Consequently, the inflation that has started to increase since the end of 2004 had annuallyexceeded 16% in August 2007. The passing of the inflation into the double-digits course posed athreat to establishing new working places, negatively influencing the economic and non-oil sectordevelopment, and began to effect the daily life of all sections of the population. The state pension system has managed to keep the majority of pensioners above the poverty level(Poverty rate was 20% in August 2007), but the average net replacement rate – about 40 percent –is rather low in the European context, leaving the majority pensioners in the lower-middle range ofthe income continuum. In the longer time, the country faces demographic ageing, which will pose a challenge for pensionfinancing, regardless of the pension system’s design.Actuarial calculations Azerbaijan’s population stood at 7, 1 million in 1990, but had risen to 8, 5 million by 2006, thepopulation growth rate approximately 1, 1 percent a year. As UN projection model finds, totalpopulation would increase up to approximately 10, 5 million in 2050. (Figure 5.1)Figure 5.1 Total population T otal Population (1990-2050) 12 000 10 000 8 000 6 000 4 000 2 000 0 1990 1995 2000 2005 2010 2015 2020 2025 2030 2035 2040 2045 2050 Medium High Low Constant Source: UN’s World population projection model 55
  • 56. Actuarial analysis in social security The fertility rates are low by international standards. The total fertility rate dropped from 2.6 in1990 to a low point of 1.8 in 2006. As UN projection model finds, total fertility rate would increaseup to approximately 1, 94 in 2050. (Figure 5.2)Figure 5.2 Total fertility rate T otal Fertility Rate 3,0 2,5 2,0 1,5 1,0 0,5 0,0 1990- 1995- 2000- 2005- 2010- 2015- 2020- 2025- 2030- 2035- 2040- 2045- 1995 2000 2005 2010 2015 2020 2025 2030 2035 2040 2045 2050 Medium High Low Constant Source: UN’s World population projection model Life expectancy has varied considerably during recent years. Life expectancies, for the male atbirth, as UN projection model finds, would increase from 67, 2 in 2000 up to 76.2 years in 2050.The female life expectancy at birth, on the other hand, would jump up to 81.8 by the year 2050,which is roughly 7.3 years above its level in 2000Figure 5.3 Life expectancy Expected life expectancy 90 80 Male At birth 70 60 Male at age 60 50 Male at age 65 Age 40 Female At birth 30 Female at age 60 20 Female at age 65 10 0 2000 2010 2020 2030 2040 2050 Years 56
  • 57. Actuarial analysis in social security By looking at Table 5.1 one can recognize that in both terms the actual and relative ones, the life expectancies over the entire prediction period would improve for both genders but relatively larger for those of women. This can be clearly attributed to the future prospects regarding the probability of dying for both genders, at which it is expected to decrease at each age after birth more proportionally for females than males. Concerning the remaining life expectancy at the normal age of retirement, the men who reached the age of 60 at year 2000 are expected to live for another 19.7 years until their death, while at the same year a women who has reached this age may live for another 23.8 years. Along the simulation, at the age of 60, both men and women are most likely to survive longer as time passes up. At the age of 65 men are expected to live 16.7 years, but women 20.1 years. Table 5.1 Life expectancy 2000 2005 2010 2015 2020 2025 2030 2035 2040 2045 2050 At birth 67,21 68,71 69,71 70,71 71,51 72,31 73,31 74,11 74,91 75,71 76,21Male at age 60 19,7 20,2 20,5 20,9 21,2 21,5 21,9 22,3 22,6 23,0 23,2 at age 65 16,7 17,1 17,3 17,6 17,9 18,1 18,5 18,8 19,0 19,4 19,6 At birth 74,47 75,47 76,27 77,07 77,87 78,37 79,17 79,97 80,77 81,27 81,77Female at age 60 23,8 24,2 24,5 24,9 25,2 25,5 25,9 26,3 26,7 27,0 27,2 at age 65 20,1 20,4 20,7 21,0 21,3 21,5 21,9 22,2 22,6 22,8 23,1 The age and gender structures have been severely distorted, so that ageing will take place both from the bottom of the population pyramid (as a result of decreased fertility) and from the top (due to the increase in the number of elderly). 2000 2050 Population Pyramid Population Pyramid Ma le s Year : 2000 Ma le s Year : 2050 Fe ma le s Fe ma le s 100+ 100+ 90-94 90-94 80-84 80-84 70-74 70-74 60-64 60-64 Age 50-54 Age 50-54 40-44 40-44 30-34 30-34 20-24 20-24 10-14 10-14 0-4 0-4 10,0% 5,0% 0,0% 5,0% 10,0% 10,0% 5,0% 0,0% 5,0% 10,0% Figure 5.4 The development of the population pyramids Comparing 2000 and 2050 data we can see the 0-44 age groups will decline, but 45 and over age groups will increase. (Table 5.2) 57
  • 58. Actuarial analysis in social securityTable 5.2 Population breakdown by age groups Composition (as a % of total) Composition (as a % of total) 2000 2050 Age class Total Males Females Total Males Females 0-4 7,6% 7,9% 7,2% 5,2% 5,4% 4,9% 5-9 10,6% 11,1% 10,1% 5,1% 5,4% 4,9% 10-14 10,8% 11,2% 10,4% 4,9% 5,1% 4,6% 15-19 9,8% 10,2% 9,5% 4,8% 5,0% 4,5% 20-24 8,5% 8,8% 8,3% 5,1% 5,3% 4,8% 25-29 7,8% 8,3% 7,4% 5,6% 5,9% 5,4% 30-34 8,2% 8,4% 8,1% 6,0% 6,2% 5,7% 35-39 8,5% 8,1% 8,8% 5,8% 6,1% 5,6% 40-44 7,3% 7,1% 7,5% 5,3% 5,6% 5,1% 45-49 4,9% 4,8% 5,1% 5,3% 5,5% 5,1% 50-54 3,2% 3,0% 3,3% 6,3% 6,5% 6,1% 55-59 2,2% 2,1% 2,3% 8,6% 8,9% 8,4% 60-64 3,7% 3,4% 4,0% 8,4% 8,4% 8,4% 65-69 2,8% 2,5% 3,0% 7,1% 6,9% 7,2% 70-74 2,0% 1,8% 2,3% 5,5% 5,1% 5,8% 75-79 1,0% 0,7% 1,2% 4,2% 3,9% 4,5% 80-84 0,5% 0,2% 0,7% 3,3% 2,7% 3,9% 85-89 0,3% 0,2% 0,5% 2,3% 1,5% 3,0% 90-94 0,1% 0,1% 0,2% 1,0% 0,6% 1,5% 95-99 0,1% 0,0% 0,1% 0,3% 0,1% 0,4% 100+ 0,0% 0,0% 0,0% 0,1% 0,0% 0,1% Total 100,0% 49,2% 50,8% 100,0% 100,0% 100,0% The size of the Dependency Ratio (Population aged 60 and over to working-age (15-59)population) is a critical factor in the pension system. Based on UN’s projection results, theDependency ratio in Azerbaijan will increase by 2050. (Figure 5.5) However, over the 50 years, theportion of the population that is of working age has fallen from 60.5 percent (2000) to 52.8 percent(end of 2050). But the portion of population aged 60 and over has risen from 10.5 percent (2000) to32.1 percent (end of 2050).Indeed; the dependency ratio is projected to improve from 17.3 percentin 2000 to almost 60.9 percent end of 2050. The dependency ratio will be effect after 2015 year.Figure 5.5 Dependency ratio P opula tion a ge d 60 a nd o ve r / P opula tion a g e d 15-59 70,0% 60,0% 50,0% Medium High 40,0% Low 30,0% Constant 20,0% 10,0% 0,0% 2000 2005 2010 2015 2020 2025 2030 2035 2040 2045 2050 Source: UN’s World population projection model 58
  • 59. Actuarial analysis in social security Everybody understands that this degree of change in population structure must effect theeconomy in many ways. A harder question is to determine precisely what these effects will be. Wehave very little empirical data on changes in the age structure of the population. This means that,when we study this issue, we have to rely to a great extent on theoretical analysis and models. Figure 5.6 Employees vs labor pension beneficiaries in 2006* 3,34 3,97 1,19 - Employees, mln. people - Labor pension beneficiaries, mln. people* The ratio employees vs labour pension beneficiaries is equal to 3.34. As a result, today we have 334 employees per 100 retired people, and by 2050 their number willdrop to down because of population aging. Due to the unfavorable “employee-retired persons” ratio, in order to sustain financial stability theState Social Protection Fund(SSPF) should increase the retirement age in order to reduce the periodwhen labor pensions are payable, and to establish a statistically grounded duration of the periodwhen labor pensions are payable, instead of a fixed one. In accordance with ILO actuarial projection, for the current year the duration of the expectedperiod when old age labor pensions are payable should be set as equal to 21.9 years (19.7 and 24.2for men and women respectively). However, extremely low life expectancy, especially for men, makes it impossible to introducethis figure into a retirement formula. In 2006, this period was set as 12 years and this was acompelled measure. Under these conditions there is no way one can associate the pension system with insurance. Thisis why SSPF should either rebuild the system so as to base it on entirely non-insurance principles,which is on providing pension, or should implement coordinated demographic and macroeconomicmeasures which will only pay in mid-term perspective. One can quote a number of other examples of how demographic and macroeconomic factorsimpact the financial state of the SSPF, however, the key conclusion is self-evident: any publicmeasures to regulate the financial sustainability of the SSPF should not only be aimed at increasingthe birth rate, which will make it possible to improve the employment situation long-term, that is,no sooner than in 10 years time, but to also ensure sustainable positive dynamics in terms of alldemographic parameters. 59
  • 60. Actuarial analysis in social securityConclusion The study is devoted to the mechanisms of the actuarial analysis being applied in variouscountries. The objective of the study is determine how the social security system react when achange in fundamental parameters or policies occur and which policy intervention will offset ordecrease the deficits so as to aid policy makers in formulating policies that are implementable(economically and politically feasible). The influence of the mentioned parameters has been learnedin more details on the examples of the Turkish and Azerbaijan pension schemes. EU model (PRISM), ILO pension model and Turkish pension model were used for thesimulations. However, almost all of the demographic and economic assumptions were updatedbased on UN’s statistical data. A number of different actuarial calculations have been done on the effects of population ageing.One thing is however: the world is facing demographic changes that will have considerableimplications for the economy and the financial markets. Even when a common methodology hasbeen applied, differences in demographic and economic assumptions have been observed. Thechange in population structure will tend to reduce the flow of savings and the supply of finance. Atthe same time, lengthening life spans and especially more years spent in retirement will increase theneed to finance social security. The actuary retains control of the quantitative choice of theassumptions. Eve if this appears to be a logical way forward; the question arises as to whetherfuture standards or guidelines governing actuarial analysis of social security system should considerthe question of quantifying certain assumptions. Management of the economic and social consequences of population ageing will require threemutually supportive elements. In the first place, the volumes needed for financing pensions meanthe system will always have to be based on a public pay-as-you-go scheme. On top of this there willalso be a need for a solid funded element to balance out disturbances, spread the burden betweengenerations and thus help the economy adapt to the demographic changes. As a third pillar , we willalso need to provide a clear framework for private pension savings that will provide scope forpersonal planning and fill any gaps that remain in the public system. Finally, consideration should be given as to whether there should be greater integration ofdemographic and economic assumptions; in other words, should greater consideration be given totheir interdependencies since, in the long term at least, the demographic situation of a country isclosely linked to its economic situation. This thesis has been limited to several factors only and it would, of course, be interesting to widenits scope to include a comparison of how the demographic and economic assumptions of thedifferent scenarios presented within a study were arrived at. It would also be extremely interesting(and almost an obligation) to compare the different assumptions made for several successiveactuarial analysis of the same scheme. 60
  • 61. Actuarial analysis in social security Appendix Derivation of the formulas for the fair pension contribution rate and pre-funding The population is composed of children (E), adult labour (L) and retirees (R). The wage rate istaken as the unit of account. Each of these phases of an individual’s life are of equal length, whichis set as the unit period. Fairness means that all future generations are treated equally with the generation active when achange in any parameter takes place. Parameters with subscripts o refer to values until period 0 and with subscript n to those fromperiod 1 onwards. The replacement rate (p) captures both the replacement rate proper and the time spent onretirement (affected by a change in longevity. Note that the new value becomes effective in period1 if it is realized that those working in that period will live longer, or if it is decided that thereplacement rate for them is increased (even though in both cases an increase in pensionexpenditure starts from period 2 onwards).The parameters are:c = contribution rate,p = replacement rate,f = parameter such that 1-f indicates the number of children per adult labour (on a steady pathpopulation decreases at a rate of f),q = assets of the pension fund as a proportion of the wage bill, and ρ = rate of interest over the unit period.It holds E t = Lt +1 = Rt + 2 , for all periods (1) E t = (1 − f 0 ) ⋅ Lt , for t ≤ 0 (2) E t = (1 − f n ) ⋅ Lt , for t ≥ 1 (3) Any of the parameters p, f or ρ may change in period 1. For period 1, total revenue of the pensionsystem (contributions and interest income) is equal to pension expenditure and accumulation offunds, thus c n ⋅ L1 + ρ 0 q 0 L0 = p 0 R 1 + q n L1 − q 0 L0 (4) For period 2 onwards this equality reads as c n ⋅ Lt + ρ n q n Lt −1 = p n R t + q n ( Lt − Lt −1 ) (5) 61
  • 62. Actuarial analysis in social securityFrom these equations we obtain for the new contribution rate 1 fn + ρn ( f + ρ n )(1 + ρ 0 ) cn = ⋅ pn + ⋅ p0 − n ⋅q 0 (6) 1 + ρn (1 − f 0 )(1 + ρ n ) (1 − f 0 )(1 + ρ n ) and for the degree of funding 1 1− fn (1 − f n )(1 + ρ 0 ) qn = ⋅ pn − ⋅ p0 + ⋅q 0 (7) 1+ ρn (1 − f 0 )(1 + ρ n ) (1 − f 0 )(1 + ρ n ) The special case in Table 3 in the text, Scenario 3, can be obtained by setting p n = p 0 = 30%, f 0 = 0, f n = 0,2, q 0 = 0 and ρ n = ρ 0 = 50% . The case of increased longevityreferred in the text can be obtained with these same parameters except by setting p n = 33% and f0 = fn = 0 p q0 = 0 The extreme case of full funding is derived by setting the initial fund (1 + ρ 0 ) . This leadsto simple expressions for c n and q n , which do not depend on fertility. Correspondingly, it showsthat with less than full funding the contribution rate and the degree of funding should alwayschange with a change in fertility, if the current and future generations are treated equally. 62
  • 63. Actuarial analysis in social securityReferences1-Aaron, H. (1966): “The Social Insurance Paradox,” Canadian Journal of Economics2-Anderson, R. (2001): “United States Life Tables, 1998,” Centers for Disease Control andPrevention, Natural Center for Health Statistics, National Vital Statistics System, National VitalStatistics Reports3-Auerbach, A. and L. Kotlikoff (1985): “The Efficiency Gains from Social Security Benefit - TaxLinkage,” National Bureau of Economic Research4- Barr, Nicholas (2000), “Reforming Pensions: Myths, Truths, and Policy Choices”, IMFWP/00/1395-Börsch-Supan , A. (2003): “ What are NDC Pension Systems? What Do They Bring to ReformStrategies?” Mannheim Research Institute for the Economics of Aging, University of Mannheim,6-David Collinson MA FIA (2001) “Actuarial Methods and Assumptions used in the Valuation ofRetirement Benefits in the EU and other European countries” European Actuarial ConsultativeGroup, www.gcactuaries.org7-Disney, R. (1999): “Notional Accounts as a Pension Reform Strategy: An Evaluation,” TheWorld Bank, Social Protection Unit, Social Protection Discussion Paper8-Elaine Fultz (2006) “Pension Reform in the Baltic States” International Labour Office9- Feldstein, M. and Liebman J. B. (2002), "Social Security", NBER Working Papers, No.845110-Feldstein, M. and A. Samwick (1996): “The Transition Path in Privatizing Social Security,”National Bureau of Economic Research, NBER Working Papers No. 576111-Hazim Tayseer Saleh Rahahleh (2005) “The Financial Implications of Sustainable PensionReform: Theory and Scheme Specific-Options for the Jordanian Social Security Corporation”Darmstadt University of Technology12-International Monetary Fund (IMF) (2004): “World Economic Outlook, World economic andFinancial Survey: The Global Demographic Transition,” A Survey by the Staff of IMF13-International Social Security Association (ISSA) (2002): “Social Security Programs Throughoutthe World: Asia and the Pacific, 2002,”14- International Social Security Association (ISSA) (2002): “Social Security ProgramsThroughout the World: Europe, 2004,”15-International Social Security Association (ISSA) (2003a): “Social Security ProgramsThroughout the World: Africa, 2003,”16-International Social Security Association (ISSA) (2003b): “Social Security ProgramsThroughout the World: The Americas, 2003,”17-International Social Security Association (ISSA) (2007): “Demographic and economicassumptions used in actuarial valuations of social security and pension schemes”18-International Social Security Association (ISSA) (2007):”Optimizing pension financing under achanging demography and a volatile economy”19- International Social Security Association (ISSA) (2007): Projecting methods for pension andsocial security financing “20- International Social Security Association (ISSA) (2007): Methods used in drawing up mortalityprojections”21-James, E. (1999): “Pension Reform: Is There a Tradeoff between Efficiency and Equity?” TheWorld Bank, Policy Research Working Paper No. 176722-Lindbeck, A. (2002): “Pension and Contemporary Socioeconomic Change,” The NationalBureau of Economic Research23- Lindbeck, A. and M. Persson (2003): “The Gains from Pension Reform,” American EconomicAssociation, Journal of Economic Literature 63
  • 64. Actuarial analysis in social security24- Miles, D. (2000): “Funded and Unfunded Pension Schemes: Risk, Return and Welfare,” CESifoWorking Paper No. 23925- Office of Chief Actuary (2000): “The 18th Actuarial Report on Canada Pension Plan,” Officeof the Superintendent Bureau of Financial Institutions, www.osfi-bsif.gc.ca26-Oksanen, H. (2001): “A Case for Partial Funding of Pensions with an Application to the EUCandidate Countries,” European Commission Directorate-General for Economic and FinancialAffairs, Economic Papers No. 14927-Oksanen, H. (2002): “Pension Reforms: Key Issues Illustrated with an Actuarial Model,”European Commission, Directorate General for Economic and Financial Affairs, Economic Papers28-Ole Jorgensen (2003) “Demographic Uncertainty and the Risk Sharing Properties of FiscalPolicy”, Center for Economic and Business Research29-Orszag, P and J. Stiglitz (2001): " New Ideas about Old Age Security: Toward SustainablePension Systems in the 21st Century” World Bank30-Palacios, R. and M. Pallares-Miralles (2000): “International Patterns of Pension Provision,”Social Protection Discussion Paper Series, No.0009.31- Pierre Plamandon, Anne Drouin (2002) “Actuarial practice in social security”, InternationalLabour Office.32-Robert Holzmann (1997) “Fiscal Alternatives of Moving From Unfunded to Funded Pensions,Organization for Economic Co-operation and Development (OECD) Working Papers33-Samuelson, P. (1958): “An Exact Consumption-Loan Model of Interest with or without theSocial Contrivance of Money,” Journal of Political Economy34-Schmidt-Hebbel, K. (1999): “Latin America’s Pension Revolution: A Review of Approachesand Experience,” Central Bank of Chile35- Sinn, Y. (2002): “Minimum Pension Guarantees,” International Social Security Association,Seminar for Social Security Actuaries and Statisticians: Actuarial Aspects of Pension ReformMoscow, Russian Federation, July.36-Sinn, H. (2000): “Why a Funded Pension System is Useful and Why It is Not Useful,” Int. Taxand Public Finance37-State Planning Organization (2007) “2007 Annual Program, Development plan (2007-2013)” Subramaniam Iyer (1999) “Actuarial mathematics of social security pensions”, InternationalLabour Office39- Takahashi, S., A. Ishikawa, H. Kato, M. Iwasawa, R. Komatsu, R. Kaneko, M. Ikenoue, F.Mita, A. Tsuji and R. Moriizumi (2002): “ Population Projections for Japan 2001- 2050: WithLong-Range Population Projections: 2051-2100,” Journal of Population and Social Security40-Teksoz, A.T., and Sayan, S. (2002). “Simulation of Risks and Benefits from a Private PensionScheme for Turkey” Under secretariat of Treasury, Ankara41- United Nation (2004): “World Population Prospects: The 2004 Revision and WorldUrbanization Prospects,” United Nations Secretariat, Population Division, Department of Economicand Social Affairs.42-Valdes-Prieto, S. (1998): “Risks in Pensions and Annuities: Efficient Designs,” HumanDevelopment Network Social Protection Group43-Williamson, J. (2004): “Assessing the Notional Defined Contribution Model,” Boston College,Center for Retirement Research, An Issue in Brief No. 2444-Wolfgang Scholz, Krzystof Hagemeyer and Michael Chichon (2000)“ Social Budgeting”,International Labour Office.45- official site of State Statistical Committee of Azerbaijan Republic. 64
  • 65. Actuarial analysis in social security Discussion of preceding paper Anne Drouin8: Given time constraint, I only had the chance to pay attention on a few sections of your thesis.Therefore, it is difficult to write comprehensive comments on the general orientation of the paper.However, I have commented some specific aspects of the paper hoping that I could be modestlyhelpful.Chapter Two:Section 2.0, Page 13- "Productivity" and "GDP Deflator" should be added in the economic variables necessary todevelop a suitable macroeconomic frame.Section 2.2, Page 14- Participation rates projection is based on a simplistic approach, which is to keep the age-specificparticipation rates constant during the projection period. It would have been interesting to explorethe cohort approach. Indeed, the recent study of "The impact of ageing on public expenditure:projections for the EU25 Member States on pensions, health care, long-term care, education andunemployment transfers (2004-2050)" prepared by the Economic Policy Committee and theEuropean Commission (DG ECFIN) uses and explains the labour participation rate cohort approachmethodology. Given the Turkey proximity with the EU, a study with comparable methods wouldhave been appealing. Anyhow, please find attached the mentioned paper for your information.Chapter Three:Section 2.2, Page 36- Although the Net Present Value calculation based on the mathematical formula presented in thethesis provides a reasonable indicator of the NPV for pension contracts, it might be stated that moresophisticated actuarial methodologies are usually applied. The formula presented in the thesis isbased on a "Finite-Life streams". Thats it, with the remaining life expectancy at retirement age; apresent value of the benefits is calculated based on a "Certain annuity" approach. A more commonmethodology is to discount the present value of future benefits with mortality rates up to amaximum age (100 years old in your case) in order to properly assess the mortality factor.Chapter Four:Section 4.2.3, Page 47- Enhanced analysis should be provided in order to clarify present value factors results based onage, retirement age, active status and sex- Indeed, all section 4.2.3 would gain in accuracy if you add more substantial analysis. (explainwhy the PAYG rates have a parabolic curve per instead)Section 4.2.3, Page 50- It would be interesting to extend total insurable earnings, total expenditures and requiredcontribution projections up to 2050 and not only up to 2015.8 Anne Drouin is Coordinator of International Financial and Actuarial Service at International Labour Office( Social SecurityDeparment-Social Protection Sector) E-mail : 65
  • 66. Actuarial analysis in social security Finally, on a more general standpoint, I must add that the paper is well structured and welldocumented. Good job! All the best in the future. Heikki Oksanen9 : I can see from Mr.Tagiyev’s thesis that he have well understood the questions of principles ofpension systems and that he works so far can make a solid basis for further work. As said, his workis important and I hope it will proceed well. Seeing especially section 3 I feel obliged to raise a point about using material previouslypublished by other authors in an academic thesis. Mr. Tagiyev also quoted my work (which is fineas such). In my own Directorate –General for Economic and Financial Affairs we follow pensionreforms in various countries with regard to their effects on the economies in general and on publicfinance in particular. It is true that I have worked on pension systems using prototype actuarialmodels, but until now I have not been able to work with real data on individual countries and it isnot very likely that this would become possible for me. However, I am always most interested inseeing results of any such studies. I am only happy to hear that my work has been of some use for Mr. Tagiyev in preparing his ownapplied work. However, I must also recognize that there is quite some distance from my analyticalwork to building an actuarial model for a real world application and construct a pension system forAzerbaijan. I wish all the best for his thesis presentation. It will be a great opportunity for him to be able todefend his thesis and then pass on to further work. Alice H Wade 10, Milton P Glanz 11 : The thesis seems to be attempting to make generalizations that apply to any Social Securitysystem. We have interpreted Mr.Tagiyev’s thesis as an effort to state the actuarial aspects not onlyof the United States social security system, but of a broad class, meant to describe most if not allsocial security systems.1. p. 7 ff.The author seems to be saying that these are the projection technique. However, these calculationsare basically definitional. The real operations that we regard as projections are the construction ofthe matrices of transition probabilities Qt. These probabilities are constructed by a combination ofour past experience and our using our knowledge and judgment to tell us where future transitionprobabilities might differ from mechanically projected past experience. The transition factors arebased on exogenous factors as are the economic projections.2. p. 8.A transition probability over a one year time span takes one from age x to age x+1. It seems to usthat that the transition matrix needs to reflect this. We propose we refer Mr. Tagiyev to ActuarialStudy 120 for more details.9 Heikki Oksanen is Advisor of European Commission , Directorate General for Economic and Financial Affairs, E-mail :Heikki.Oksanen@ec.europa.eu10 Alice H Wade is Deputy Chief Actuary at Social Security Administration(SSA) Office of the Chief Actuary, United States, E-mail : Alice.H.Wade@ssa.gov11 Milton P Glanz is the member of Office of the Chief Actuary, Long range Legislative Team at SSA, United States, E-mail 66
  • 67. Actuarial analysis in social security3. p. 11.The D on page 11 that is an upper limit for the age variable x differs from the D that signifies acommutation function. Perhaps a different letter can be used for the upper limit for age.4. p. 13.We would like to see a definition of the expression "robust assumptions" as used here. A quicksurvey of our Economics Group yielded no one who knew of this expression.5. p. 13. Fifth paragraph.«Separation of GDP between remuneration of workers and, broadly, remuneration of capital ". Inthe U.S.A., we separate GDP into a) return to labor, and b) returns to all non-labor inputs. Thismay not reflect any real difference from what Mr. Tagiyev is saying.6. p. 13.In the U.S.A., final decisions as to economic assumptions are made by the Board of Trustees.There are no other economic projections that go out as far as the Social Security Trust Fundprojections. The trustees consult the economists and actuaries from the Treasury Department,Labor Department, and the Social Security Administration. Also, usually some trustees have strongeconomic backgrounds in their own right.7. p. 13.In the U.S.A., the interest rate used is the trust fund real interest rate.8. p. 15.The expression "dependent employed persons" is used. We prefer to say "employees".9. p 15. Second paragraph.In the U.S.A. we define labor productivity as output per hour. It seems that some differentdefinition of labor productivity is being used here. Perhaps "output per worker" can be clarified. Isthis worker count defined as: (number of workers in a month, averaged over 12 months)? (Aworker who works only two months in a year would get counted as 1/6 of a worker.) We believesome clarification would be helpful.10. p. 16. Last two sentences at the end of the second paragraph:In the United States, the major long term forecasts are done in the preparation of the OASDITrustees Report, and this is done by the Trustees and their staffs.11. p. 16. Ways of determining interest rate.Our only job is to determine the interest rate paid by Trust Fund securities, which are all U. S.Treasury issues. In the U.S.A., we simply look at decade averages of real interest rates over the last40 years and took an average as our long term real interest rate and combined this with our longterm inflation assumption. See pages 92 and 93 of the 2007 Trustees Report. Bertil Thorslund12 : I am afraid I am not in the position to provide with such scientific comments as thoseprovided by Ms. Wade and Mr. Glanz. Here are though a few observations from my readingMr.Tagiyev’s very interesting thesis.12 Bertil Thorslund is the Senior Advisor of The Swedish Social Insurance Agency, Sweden and the member of ImprovingConfidence in Forecasting (ICF) - an international collaboration. E-mail : 67
  • 68. Actuarial analysis in social security1) I think it was very easy to read and should be valuable even to less informed readers. Especiallyyour discussion on the characteristics of the elements of this matrix made up from PAYG or FF inone dimension and DC (defined contribution) and DB (defined benefit) in the other. Maybeshowing the matrix and blotting out the combination of FF and DB would make it even better.2) I much appreciated Mr.Tagiyev’s comments about what is in the role for the actuary and what isnot (The actuary looks primarily at consistency between assumptions ....). I would though havebeen a bit interested in some discussion about error estimation. It gets relevant in 1.2.2 whenMr.Tagiyev says that salary growth rate, pension indexation rate and interest rate are assumedconstant. Fair enough, if Mr.Tagiyev states that but it also calls for some consideration of how realthose assumptions are and what deviations would mean to calculated results.3) Mr.Tagiyev argues that if possible the actuary should refrain from making assumptions onparameters that could be more readily made by other. But Mr.Tagiyev also recognizes that quiteoften the situation calls for action (on page 13 "Hence, the actuary should extend financialprojections, when available, in order to satisfy the required length of time covered by an actuarialcalculation).4) On page 14 there might be an arrow missing. I would have expected an arrow from projectedactive population to projected employment.5) In 3.2.3 discussion on intergenerational redistribution Mr.Tagiyev mentions that low-incomeretirees in reality have a shorter life expectancy. I am not so sure.Maybe I am blinded by the situation in Sweden but here the life expectance for women are by farexceeding that of men. And women are still a relatively low-income group. And that leads toMr.Tagiyev’s next observation that he may set uniform parameters for different groups, like gender.That is probably the industrial standard for mandatory pension systems, is it not? We had differentparameters in the Swedish pension system until 1935 but that certainly was some time ago.6) The new Swedish system is certainly a full fledged NDC system. Whether the same is true aboutthe pension systems in Latvia and Poland could probably be argued.7) As concerns Mr.Tagiyev’s discussion in 3.2.4 on partial funding. I do not have a problem withwhy partial funding is needed But to my mind, the resources in that demographic is created duringthe start-up of the PAYG system rather than by some extra payments imposed on those generationsthat have not had enough children. That mechanism would be a rather curious thing, I think. I can only hope that this is helpful in the discussion on Mr.Tagiyev’s paper. And my maincomment is that I did find Mr.Tagiyev’s work very informative. (Author’s review of discussion) Hikmet Tagiyev13 : I would like to thank Anne Drouin, Heikki Oksanen, Alice Wade, Milton Glanz and BertilThorslund for taking the time to discuss my paper and thereby adding substantially to its value.13 Hikmet Tagiyev is the Project Assistant of the “Capacity Building for the State Social Protection Fund of Azerbaijan Republic”Project. E-mail : 68