P i S t A l iPension System Analysis:Basic Concepts and IdentitiesBasic Concepts and Identities

Tatyana BogomolovaWorld Bank, HDNSP

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)

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)

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

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.)

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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