Pension System Analysis:

Basic Concepts and Identities

Tatyana Bogomolova

World Bank, HDNSP

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Outline

General framework for quantitative analysis of

pension systems

Key factors: demographic, economic, pension

system design

Simple economics of PAYG DB schemes

Simple economics of Funded DC schemes

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Demography

Contributors Beneficiaries

PS revenues PS expenditures

Economy

PS balance

Pension system: main flows

PS design

Accumulated assets/debt

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Main groups of factors

Demographic environment

Economic environment

Pension system design

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Demographic factors

Population, age/gender composition working

age and old age population , old age dependency ratio

Fertility (total fertility rate, replacement level)

Mortality rates life expectancy, life expectancy at retirement

Disability prevalence rates

Migration flows, age and gender composition

World-wide trend – population aging decreasing fertility, increasing life expectancy

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Economic factors

Macroeconomic indicators

GDP

Inflation

Interest rates

Labor market indicators

Labor force participation rates

Unemployment rates

Informal sector

Wages, earning profile, income distribution

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Pension system design

(system revenues)

Contributor coverage

Exemptions

Contribution rate

Covered wage (ceilings/floors, basic vs total compensation)

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Pension system design

(system expenditures)

Beneficiary coverage

Eligibility criteria:

retirement age, early retirement

vesting period

qualifying conditions for disability and survivorship benefits

Rules for benefit calculations

Indexation of post-retirement benefits

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PAYG Defined Benefit systems

Financing: workers contributions today are used to

pay pensioners today; in return, workers get a

promise that they will receive a pension tomorrow

paid for by workers tomorrow

Benefits: calculated based on a prescribed

(defined benefit) formula; normally linked to

individual’s wages, years of contributions, accrual

rate

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PAYG DB finances

Total expenditures: EXP = B*P

Total revenues: REV = C*E

Books are balanced when B*P = C*E

where:

C = average contribution

B = average benefit (pension)

P = number of pensioners

E = number of contributors

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PAYG DB finances (cont.)

Given that:

B = RR*W; C = W*CR; and DR = P/E

The pension fund balance equation can be presented as: CR=RR*DR

where:

CR = contribution rate

RR = average replacement rate (relative pension level)

W = average wage

DR = system dependency rate (the inverse – support ratio)

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How to keep the system in balance?

Adjust contribution rate (CR)

Adjust average replacement rate (RR)

Adjust parameters/policy variables affecting the

dependency rate (DR)

Combination of the above

More direct control of CR and RR; less control

over DR

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Equilibrium contribution rate

If average replacement rate is fixed (target RR)

Contribution rate required to finance a given

average replacement rate is:

CR = RR*DR

So if the dependency rate grows the contribution

rate has to be increased in order to bring the

pension fund into balance

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Equilibrium replacement rate

If contribution rate is fixed

Another way to balance the system is through the

average replacement rate affordable

replacement rate is:

RR = CR/DR

So, if the dependency rate grows and the

contribution rate remains unchanged the average

replacement rate has to be reduced in order to

keep the system in balance

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Key determinants of average

replacement rate

Policy choices about target individual replacement

rate (individual pension/individual wage)

Benefit formula (entry pensions)

Policy choices about pension indexation method

(post-retirement pensions)

Economic factors: wages, wage growth rate

Behavior: contribution density years of

contributions at retirement

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Benefit formula: typical structure

Accrual rate per year of service

Min/max replacement rates, min/max pensions

Measure of income (reference wage, pensionable earning measure)

- ceiling on pensionable wages

- averaging period

- valorization rules

Penalties for early retirement, increments for late retirement

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Post-retirement pensions:

indexation methods

Price indexation: pensions move with the price

level; their real value remains unchanged

Wage indexation: pensions move with wages;

their relative value remains unchanged

Combination of price and wage indexation (e.g.

Swiss formula)

Other indexation rules (ad hoc, discretional, fixed

%, progressive indexation, etc.)

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How to affect finances through

system dependency rate?

If contribution rate and replacement rate are fixed:

DR = CR/RR

Dependency rate is not a policy variable, but some

policy choices can change it

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Key determinants of system

dependency rate: numerator

Number of pensioners (P)

Demographic factors (old age population,

mortality rates after retirement life

expectancy at retirement)

Policy choices in pension system (retirement

age, rules for early retirement, beneficiary

coverage rate, vesting period, eligibility criteria

for receiving disability pensions, survivors

benefits)

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Key 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

informal sector)

Policy choices (contributor coverage,

retirement age, rules for early retirement, built-

in incentives (e.g. contribution rate), other)

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Retirement age

Average retirement age Normal retirement age

and early retirement arrangements

Quantitative analysis of various pension systems:

retirement age is the most effective policy variable

to 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

be adjusted to keep the system in balance in the

long run

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Policy choices: how much freedom?

Basic relationship (CR=RR*DR) To make a PAYG DB financially sustainable, policy makers can change only two of the three key parameters:

- contribution rate

- average replacement rate

- retirement age

Once two parameters are set, the third is determined endogenously

Limits for setting exogenous parameters (e.g. replacement rate – social and political, contribution rate – economic, retirement age – physical, social and political)

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Funded defined contribution systems

Financing: Contributions are put into individual’s account 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

year of retirement

AC = C1*(1+r)N + C2*(1+r)N-1 +…+ CN*(1+r)

where

AC = accumulated capital

Ct = CRt * Wt

N = number of working years

r = rate of return (here assumed to be constant)

Ct = contribution in year t, for t = 1, 2, …, N

CRt = contribution rate in year t, for t = 1, 2, …, N

Wt = worker’s wage in year t, for t = 1, 2, …, N

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Benefit payout: annuity

When worker retires, accumulated capital (AC) is turned into pension which is set so that:

B0+ B1/(1+d) +… + BM/(1+d)M = AC Initial benefit calculation: B0 =AC/AF

where

Bt = Bt -1 * indexation coefficient, t>0

M = number of retirement years

d = discount rate

AF = annuity factor

No bequest to survivors, longevity risk borne by annuity provider

Variety of annuity products

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Annuity factor:

If a person of certain age and gender is promised a

benefit=$1, with specified indexation rules, how

much is such a promise worth in today’s dollars?

1+ ind1* surv1/(1+d)+(ind1* ind2 )* (surv1* surv2)/(1+d)2+…

where

indt = indexation coefficient in year t of retirement

survt = probability of surviving from year t-1 to t

d = discount rate

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Benefit payout:

programmed withdrawals

The account continues to earn interest while pensioner withdraws funds

Benefit is recalculated each year:

Bt = RCt / LEt,a

where

RCt = remaining capital in year t

LEt,a = life expectancy at age a in year t

If dies early, the remaining balance is turned over to survivors; if lives long, Bt may become very low; longevity risk borne by individuals

Other payout forms (lump sums, required minimum annuity, etc.)

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Main determinants of benefit levels

Contribution rate

Individual’s wages

Rate of return, rate of return-wage growth gap

Passivity ratio (retirement years/working years years of service, retirement age, life expectancy)

Administrative costs

Annuity factors (life expectancy, indexation, single vs joint, discount rate)

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