MBA Thesis by Hikmet Tagiyev


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Actuarial analysis in Social Security

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MBA Thesis by Hikmet Tagiyev

  1. 1. AZERBAIJAN REPUBLIC KHAZAR UNIVERSITY School : Economics & Management Major : Finance Student : Hikmet Tagiyev SakhavetSupervisor: Dr. Oktay Ibrahimov Vahib BAKU 2007
  2. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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