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P i S t A l iPension System Analysis:Basic Concepts and IdentitiesBasic Concepts and Identities
Tatyana BogomolovaWorld Bank, HDNSP
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OutlineOutline
General framework for quantitative analysis of pension systemspension systems
Key factors: demographic, economic, pension system designsystem design
Simple economics of PAYG DB schemes Simple economics of Funded DC schemes
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Pension system: main flowsDemography
Contributors Beneficiaries
Economy
PS revenues PS expendituresPS design
PS balance
Accumulated assets/debt
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M i f f tMain groups of factors
Demographic environment
Economic environmentEconomic environment
P i t d iPension system design
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Demographic factorsDemographic factors Population age/gender composition working Population, age/gender composition working
age and old age population , old age dependency ratioratio
Fertility (total fertility rate, replacement level) Mortality rates life expectancy life expectancy Mortality rates life expectancy, life expectancy
at retirement Disability prevalence rates Disability prevalence rates Migration flows, age and gender composition
W ld id d l i i World-wide trend – population aging decreasing fertility, increasing life expectancy
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Economic factors Macroeconomic indicators
GDPInflationInterest rates
Labor market indicators Labor market indicatorsLabor force participation ratesUnemployment ratesUnemployment ratesInformal sectorW i fil iWages, earning profile, income distribution
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P i t d iPension system design(system revenues)(system revenues)
Coverage Exemptions Exemptions Contribution rate Covered wage (ceilings/floors basic vs total Covered wage (ceilings/floors, basic vs total
compensation)
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Pension system designPension system design(system expenditures)
Coverage Coverage Eligibility criteria:
retirement age retirement age vesting period qualifying conditions for disability and qualifying conditions for disability and
survivorship benefits Rules for benefit calculationsu es o be e t ca cu at o s Indexation of post-retirement benefits
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PAYG Defined Benefit systemsPAYG Defined Benefit systems
Fi i k t ib ti t d d t Financing: workers contributions today are used to pay pensioners today; in return, workers get a
i th t th ill i i tpromise that they will receive a pension tomorrow paid for by workers tomorrow
Benefits: calculated based on a prescribed p(defined benefit) formula; normally linked to individual’s wages, years of contributions, accrual g yrate
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PAYG DB fiPAYG DB finances
Total expenditures: EXP = B*P Total revenues: REV = C*E Total revenues: REV = C E Books are balanced when B*P = C*E
hwhere:C = average contributionB = average benefit (pension)B = average benefit (pension)P = number of pensionersE = number of contributorsE = number of contributors
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PAYG DB fi ( t )PAYG DB finances (cont.)
Given that:B = RR*W; C = W*CR; and DR = P/EW; C W C ; a d /
The pension fund balance equation can be presented as: CR=RR*DR
where:CR = contribution rateCR contribution rateRR = average replacement rate (relative pension level)W = average wage g gDR = system dependency rate (the inverse – support ratio)
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How to keep the system in balance?
Adjust contribution rate (CR) Adjust replacement rate (RR) Adjust parameters/policy variables affecting the j p p y g
dependency rate (DR) Combination of the above Combination of the above More direct control of CR and RR; less control
over DRover DR
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Equilibrium contribution rateEquilibrium contribution rate
If replacement rate is fixed (target RR) Contribution rate required to finance a given q g
average replacement rate is:CR = RR*DRCR RR DR
So if the dependency rate grows the contribution rate has to be increased in order to bring therate has to be increased in order to bring the pension fund into balance
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Equilibrium replacement rateEquilibrium replacement rate
If t ib ti t i fi d If contribution rate is fixed Another way to balance the system is through the
replacement rate affordable replacement rate is:RR = CR/DR
So, if the dependency rate grows and the contribution rate remains unchanged thecontribution rate remains unchanged the replacement rate has to be reduced in order to keep the system in balancekeep the system in balance
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Key determinants of average y greplacement rate
Policy choices about target individual replacement rate Benefit formula
Policy choices about pension indexation method
Economic factors: wages, wage growth rate
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Benefit formula: typical structureBenefit formula: typical structure Accrual rate per year of service Accrual rate per year of service Min/max replacement rates, min/max pensions
f i ( f i bl Measure of income (reference wage, pensionable earning measure)
ili i bl- ceiling on pensionable wages- averaging period
valorization rules- valorization rules Penalties for early retirement, increments for late
retirementretirement
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Post-retirement pensions: indexation methods
Price indexation: pensions move with the price level; their real value remains unchangedeve ; t e ea va ue e a s u c a ged
Wage indexation: pensions move with wages; their relative value remains unchangedtheir relative value remains unchanged
Combination of price and wage indexation (e.g. S iss form la)Swiss formula)
Other indexation rules (ad hoc, fixed %, i i d i )progressive indexation, etc.)
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How to affect finances through gsystem dependency rate?
If contribution rate and replacement rate are fixed:pDR = CR/RR
Dependency rate is not a policy variable, but some li h i h itpolicy choices can change it
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Key determinants of system y ydependency rate: numerator Number of pensioners (P)
Demographic factors (old age population Demographic factors (old age population, mortality rates after retirement life expectancy at retirement)expectancy at retirement)
Policy choices in pension system (retirement age r les for earl retirement co erage in theage, rules for early retirement, coverage in the past, vesting period, eligibility criteria for receiving disability pensions survivorsreceiving disability pensions, survivors benefits)
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Key determinants of systemKey determinants of system dependency rate: denominator Number of contributors (E)
Demographic factors (working age population, fertility in the past, mortality, migration)
Economic factors (school-leaving age, labor force participation, unemployment, size of the p p p yinformal sector)
Policy choices (coverage, retirement age, rulesPolicy choices (coverage, retirement age, rules for early retirement, contribution rate (if high evasion), other)
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evasion), other)
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Retirement ageRetirement age
Q tit ti l i f i i t Quantitative analysis of various pension systems: retirement age is the most effective policy variable t dj t l d d tto adjust long run dependency rate
Changes in retirement age affect both the numerator and denominator in DR=P/E
If life expectancy increases, retirement age has to p y gbe adjusted to keep the system in balance in the long rung
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Policy choices: how much freedom?y From the basic relationship (CR=RR*DR) To
k PAYG DB fi i ll i bl limake a PAYG DB financially sustainable , policy makers can change only two of the three key parameters:parameters:- contribution rate- replacement ratereplacement rate- retirement age
Once two parameters are set the third is Once two parameters are set, the third is determined endogenously
Limits for setting exogenous parameters (e.g. g g p ( greplacement rate – social and political, contribution rate – economic, retirement age –physical social and political)
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physical, social and political)
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Funded defined contribution systems
Financing: Contributions are put into individual’s account Assets are accumulated and earnaccount Assets are accumulated and earn interest Accumulated capital used to pay for pensions
Benefits: Calculated based on accumulated capital
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Capital accumulated by the p yyear of retirement
AC = C1*(1+r)N + C2*(1+r)N-1 +…+ CN*(1+r)where
AC = accumulated capitalCt = CRt * Wt
N = number of working yearsr = rate of return (here assumed to be constant) Ct = contribution in year t, for t = 1, 2, …, NCRt = contribution rate in year t, for t = 1, 2, …, NWt = worker’s wage in year t, for t = 1, 2, …, N
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Benefit payout: annuityBenefit payout: annuity When worker retires, accumulated capital (AC) is When worker retires, accumulated capital (AC) is
turned into pension which is set so that:B + B /(1+d) + + B /(1+d)M = ACB0+ B1/(1+d) +… + BM/(1+d)M = AC
Initial benefit calculation: B0 =AC/AFhwhere
Bt = Bt -1 * indexation coefficient, t>0M = number of retirement yearsM = number of retirement yearsd = discount rate
AF = annuity factorAF annuity factor No bequest to survivors, longevity risk borne by
annuity provider25
annuity provider
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Annuity factor:Annuity factor:
If a person of certain age and gender is promised abenefit=$1 with specified indexation rules howbenefit=$1, with specified indexation rules, howmuch is such a promise worth in today’s dollars?
1+ ind1* surv1/(1+d)+(ind1* ind2 )* (surv1* surv2)/(1+d)2+…hwhere
indt = indexation coefficient in year t of retirementsurvt = probability of surviving from year t-1 to t
d = discount rate
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Benefit payout: programmed withdrawals Th t ti t i t t hil The account continues to earn interest while
pensioner withdraws funds Benefit is recalculated each year: Benefit is recalculated each year:
Bt = RCt / LEt,awherewhere
RCt = remaining capital in year tLEt,a = life expectancy at age a in year tt,a
If dies early, the remaining balance is turned over to survivors; if lives long, Bt may become very l l it i k b b i di id llow; longevity risk borne by individuals
Other payout forms (lump sums, required minimum annuity etc )
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minimum annuity, etc.)
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Main determinants of benefit levelsMain determinants of benefit levels
Contribution rate Individual’s wagesRate of return, rate of return-wage growth
gapPassivity ratio (retirement years/working
years years of service, retirement age, life expectancy)expectancy)
Administrative costsAnnuity factors (life expectancy indexationAnnuity factors (life expectancy, indexation,
single vs joint, discount rate)
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