pay-as-you-go|a relict from the past or a promise for the future?€¦ · pay-as-you-go|a relict...

Introduction Automatic adjustment factors Demographic fluctuations Financial risk Conclusions Appendix

Pay-As-You-Go—A Relict from the Past or aPromise for the Future?

Markus Knell

Oesterreichische Nationalbank

“A Global Challenge to our Social Future”, Symposium,Austrian Academy of Sciences, Vienna,

5 May 2011

Background

Pension systems have to deal with demographic developments:

• Increase in life expectancy (one year every 6 - 8 years)

• Declines or boom-bust cycles in fertility

and with macroeconomic and financial market risk:

• “Private pension funds have been dealt a heavy blow: in thecalendar year 2008, their investments lost 23% of their valueon aggregate, or some USD 5.4 trillion”(OECD, 2009, p. 25).

Background

Objectives of pension systems

A good pension system should be able to cushion shocks, remainsustainable and to fulfill its main objectives:

• Consumption smoothing

• Providing adequate retirement incomes (poverty relief)

Among all additional (secondary?) goals I would single out thefollowing:

• Accord to generally accepted notions of intra- andintergenerational fairness

Main message

A reasonably designed pay-as-you-go (PAYG) system is capable ofdealing with demographic and macroeconomic risk without losingsight of its main objectives.

“Reasonably designed” means, e.g.:

• Lifelong assessment period

• Appropriate revaluation of past contributions

• “Actuarially fair” deductions or supplements for earlyretirement

• Built-in components that react to demographic shocks

The large and dominating PAYG pillar might be amended by a(small) funded pillar (especially to allow for individual preferences).

Main message

Structure of the argument/book/talk 1

In order to establish my argument for a dominant (reasonablydesigned) PAYG pillar I contrast it first with its main antagonist:the funded pillar. In particular I deal with three claims:

• “PAYG systems are not able to deal with demographicdevelopments”. This is shown to be wrong! There existstraightforward and intuitive adjustment factors that lead to aconstantly balanced system (chapter 2).

• “PAYG systems will cause larger adjustment swings than afunded system”. This is shown to be true only under specificassumptions. Allowing for heterogeneous agents, assets andbehavioral rules diminishes the difference between unfundedand funded systems (chapter 3).

• “PAYG systems have a lower rate of return”. This neglectsdifferences in risk. And also the advantage of PAYG systemsto fix relative incomes (chapter 4).

Chapters 2 to 4 argue for a strong PAYG pillar. Chapters 5 and 6deal with details of their design and how to choose betweendifferent feasible variants.

• If there exists more than one sustainable PAYG system (withautomatic adjustment rules) which one should be chosen? Acrucial factor in this choice should be their properties withrespect to intra- and intergenerational fairness (chapter 5).

• How to structure a workable, transparent and accepted PAYGsystem? The case of “notional defined contribution” (NDC)systems. Simple principles and important details (notionalinterest rate, concept of life expectancy, deductions etc.)(chapter 6).

Outline

I will focus on some important items and have to leave out manyaspects.

• Sustainable PAYG systems and automatic adjustment factors

• Funded vs. PAYG systems — Demographic fluctuations andadjustment swings

• Funded vs. PAYG systems — Financial market risk andpoverty

• Design details, fairness and policy conclusions

Outline

Notation and basic model

The generation born in period t has:

• cohort size Nt

• life expectancy Yt

• retirement age Xt

NOTE: The maximum age observed in period t is denoted by Ftand the retirement age by Et . In general: Yt 6= Ft and Xt 6= Et .The PAYG system stipulates the following income streams:

• Contributions: τt+a−1Wt+a−1 for 1 ≤ a ≤ Xt

• Pensions: Pt+a−1 for Xt + 1 ≤ a ≤ Yt

Furthermore:

• Pension level : qt = PtWt

• Labor force: Lt =∑Et

a=1 Nt−a+1

• Retired population: Rt =∑Ft

a=Et+1 Nt−a+1

• Dependency ratio: zt = RtLt

Notation and basic modelThe generation born in period t has:

• cohort size Nt

NOTE: The maximum age observed in period t is denoted by Ftand the retirement age by Et . In general: Yt 6= Ft and Xt 6= Et .

The PAYG system stipulates the following income streams:

Furthermore:

a=1 Nt−a+1

a=Et+1 Nt−a+1

• cohort size Nt

Furthermore:

a=1 Nt−a+1

a=Et+1 Nt−a+1

• cohort size Nt

Furthermore:

a=1 Nt−a+1

a=Et+1 Nt−a+1

Budget of the PAYG system

• The balanced budget condition is given by:

τtWtLt︸︷︷︸Income

= PtRt︸︷︷︸Expenditure

• In a “demographic steady-state”: Nt = N,Yt = Y ,Xt = X ,∀t. It holds that τ = qz .

• For examples I often use: X = 45, Y = 60 and thus z = 1/3.These values broadly conform to the case of the “standardpensioner” (start work at the age of 20, retire at 65 and die at80). Furthermore: τ = 0.25 and q = 0.75.

Budget of the PAYG system

• The balanced budget condition is given by:

τtWtLt︸︷︷︸Income

= PtRt︸︷︷︸Expenditure

• In a “demographic steady-state”: Nt = N,Yt = Y ,Xt = X ,∀t. It holds that τ = qz .

• For examples I often use: X = 45, Y = 60 and thus z = 1/3.These values broadly conform to the case of the “standardpensioner” (start work at the age of 20, retire at 65 and die at80). Furthermore: τ = 0.25 and q = 0.75.

The sustainability factor

Use changes in τt and qt if the dependency ratio zt changes.

τt = τ[1 + (1− α)

(ztz− 1)]

qt = q

[1 + α

zt− 1

• Balanced budget in every period

• Works best if life expectancy is constant (or cushioned by adifferent factor)

• Comprises a continuum of factors: DC (α = 1), DB (α = 0)and in-between. Each factor implies a different sharing of thedemographic burden of boom-and-bust-cycles. Picture

• Not just hypothetical! In Germany a similar factor wasintroduced in 2003 (with α = 0.25)

τt = τ[1 + (1− α)

(ztz− 1)]

qt = q

[1 + α

zt− 1

τt = τ[1 + (1− α)

(ztz− 1)]

qt = q

[1 + α

zt− 1

The life expectancy factor

Assume Nt is constant (or controlled by a different factor) and lifeexpectancy increases in a linear fashion: Y (t) = Y (0) + γ · t (inthe data: γ between 0.15 and 0.25). Then:

E (t) =F (t)

• Keeps dependency ratio constant. Balanced budget in everyperiod

• The required shifts in retirement age and life expectancy areequiproportionate not equal

• Uses period life expectancy not forecasted LE

• If Nt has a trend then a different formula is needed

• Not implemented in any country. NDC systems are based on adifferent LE-automatism

E (t) =F (t)

Adjustment to demographic shocks in funded andunfunded systems

• “The funded system is more stable and financially resilientbecause under Paygo the required contribution rate dependson the rate of growth of payrolls.” (Modigliani et al., 2000)

• Main argument: The possibility to accumulate anddecumulate capital smoothes the adjustment process.

• This depends, however, on many assumptions (cf., Barr andDiamond, 2009), e.g.:

• Which assets are held in the funded pillar?• Is there a homogeneous population? Or a capital-holding

“upper class” and a “normal class” that is holding houses andbonds?

• How do individuals decide on their savings? Intertemporaloptimization or behavioral rules-of-thumb?

• How large are the degrees of risk aversion and time preference?• Are demographic developments expected or unexpected?

• This depends, however, on many assumptions (cf., Barr andDiamond, 2009), e.g.:

• Which assets are held in the funded pillar?• Is there a homogeneous population? Or a capital-holding

• This depends, however, on many assumptions (cf., Barr andDiamond, 2009), e.g.:• Which assets are held in the funded pillar?• Is there a homogeneous population? Or a capital-holding

• Two assets:

• Real capital: Kt−1

• A non-produced asset in fixed supply: H (houses, gold, ...)

• Production function: Yt = (Kt−1)a1(H)a2(Lt)1−a1−a2

• Two classes:

• “Normal class”

• OLG-households that live for Y periods and have no bequestmotives

• Earn labor income and contribute to a pension system (likebefore)

• They are risk averse (Ut =∑Y

a=1 βa−1 (Ca,t+a−1)1−ρ

1−ρ)

• If they hold assets then only the non-produced asset H

• “Upper class”

• Infinitely lived “dynasties”• Hold the entire capital stock Kt−1

• Do not work but just live on capital income• They are less risk averse than the workers (in the limit: risk

neutral → constant interest rate)

Model• Two assets:

• Two classes:

• “Normal class”

a=1 βa−1 (Ca,t+a−1)1−ρ

1−ρ)

• Two classes:• “Normal class”

a=1 βa−1 (Ca,t+a−1)1−ρ

1−ρ)

• Two classes:• “Normal class”

a=1 βa−1 (Ca,t+a−1)1−ρ

1−ρ)

• “Upper class”• Infinitely lived “dynasties”• Hold the entire capital stock Kt−1

A benchmark case

Assume that:

• The funded system has the same contribution rate τ as aDC-PAYG system (or – equivalently – assume a behavioralrule-of-thumb with a fixed savings rate τ)

• The asset in limited supply does not play a role in theproduction process (gold?): a2 = 0

• There is one baby-boom cohort in t = 0 that has double size

• Question: Which generations face a higher/lower internal rateof return?

• Numerical example with: Y = 60 and X = 45 Picture

A benchmark case

Assume that:

• The funded system has the same contribution rate τ as aDC-PAYG system (or – equivalently – assume a behavioralrule-of-thumb with a fixed savings rate τ)

• The asset in limited supply does not play a role in theproduction process (gold?): a2 = 0

• There is one baby-boom cohort in t = 0 that has double size

• Question: Which generations face a higher/lower internal rateof return?

• Numerical example with: Y = 60 and X = 45 Picture

Alternative assumptions

I analyze the consequences of changeing crucial assumptions(one-by-one):

• Different annuitization rules

• The asset in fixed supply plays a role in production (houses?),a2 6= 0

• Individuals use intertemporal optimization to determine theirsavings behavior Picture

• There is no “upper class”, all households are identical (excepttheir age) and they accumulate capital (“standard model”)

Picture

Alternative assumptions

I analyze the consequences of changeing crucial assumptions(one-by-one):

• Different annuitization rules

• The asset in fixed supply plays a role in production (houses?),a2 6= 0

• Individuals use intertemporal optimization to determine theirsavings behavior Picture

• There is no “upper class”, all households are identical (excepttheir age) and they accumulate capital (“standard model”)

Picture

Risk and returns in funded and unfunded systems

• A funded system has both higher returns and higher risk thana PAYG system.

• Averages for 16 countries from 1900-2000:

• Funded system:Average return (stock market): 5.1%Standard deviation: 22.7%

• PAYG system:Average return (earnings growth): 2.1%Standard deviation: 5.2%

• Averages for 16 countries from 1900-2000:

• Funded system:Average return (stock market): 5.1%Standard deviation: 22.7%

• Averages for 16 countries from 1900-2000:• Funded system:

Average return (stock market): 5.1%Standard deviation: 22.7%

Important property of PAYG systems

• For a “reasonable”, “best practice” PAYG system it holdsthat:

• The fluctuations in the absolute pension are less severe• The relative pension level (qt = Pt

Wt) is (almost or completely)

constant

• “Best practice” PAYG system means:

• Strong link between contributions and benefits• Long (lifelong) assessment period, not just the last/best 15

years• Notional interest rate is based on wages• Crucial property: Even if the calculation of the pension

benefits is backward-looking (e.g. 80% of lifetime earnings),the actual pension will be closely tied to current wages.

• This subsumes systems like the NDC systems (Sweden etc.)and “quasi-NDC systems” (e.g. German earnings pointssystem, Austrian individual accounts system)

• For a “reasonable”, “best practice” PAYG system it holdsthat:• The fluctuations in the absolute pension are less severe• The relative pension level (qt = Pt

constant

• “Best practice” PAYG system means:

• Strong link between contributions and benefits• Long (lifelong) assessment period, not just the last/best 15

• For a “reasonable”, “best practice” PAYG system it holdsthat:• The fluctuations in the absolute pension are less severe• The relative pension level (qt = Pt

constant

• “Best practice” PAYG system means:• Strong link between contributions and benefits• Long (lifelong) assessment period, not just the last/best 15

Main argument

• Two main objectives: “prevention of destitution in old age[. . .] and maintain living standards” (OECD, 2005)

• But people care about their relative standing. This is onereason why poverty (“destitution in old age”) is mostlydefined as a relative concept.

• PAYG systems become more attractive since they involve lessrisk in absolute and in relative terms

• Question: In which proportions should one mix the two pillars?

Main argument

• Two main objectives: “prevention of destitution in old age[. . .] and maintain living standards” (OECD, 2005)

• But people care about their relative standing. This is onereason why poverty (“destitution in old age”) is mostlydefined as a relative concept.

• PAYG systems become more attractive since they involve lessrisk in absolute and in relative terms

• Question: In which proportions should one mix the two pillars?

Results

• Theoretical:

• I work with a model where people care about their relativestanding

• The (period) utility function is: 11−ρ

(Ca,t+a−1 − θCt+a−1

)1−ρ

• θ measures the importance of social comparisons• It can be shown that the “optimal mix” λ∗ decreases in θ

• Empirical:

Results• Theoretical:

)1−ρ

• Empirical:

Results• Theoretical:

)1−ρ

• Empirical:

Implementation

• The stylized models suggest a dominating PAYG pillar whichcan be constructed in a way that resists demographicfluctuations.

• Often there exists more than one way to construct the system.Principles of choice:

• Respect historic contingencies and peculiarities (NDC,quasi-NDC etc.)

• Take the issue of intra- and intergenerational fairness intoaccount. Example: Is an equal or smooth sharing of anadjustment need “fair” or should one also consider who is“responsible” for the drop or increase in cohort size? Picture

• Apparent details often matter a lot and must not be neglected.In NDC systems, e.g.:

• Notional interest rate (wage-sum, average wage growth)• Concept of life expectancy to calculate the annuity (period or

forecasted)• Adjustment of existing pensions

Implementation

• The stylized models suggest a dominating PAYG pillar whichcan be constructed in a way that resists demographicfluctuations.

• Often there exists more than one way to construct the system.Principles of choice:• Respect historic contingencies and peculiarities (NDC,

quasi-NDC etc.)• Take the issue of intra- and intergenerational fairness into

account. Example: Is an equal or smooth sharing of anadjustment need “fair” or should one also consider who is“responsible” for the drop or increase in cohort size? Picture

• Apparent details often matter a lot and must not be neglected.In NDC systems, e.g.:• Notional interest rate (wage-sum, average wage growth)• Concept of life expectancy to calculate the annuity (period or

forecasted)• Adjustment of existing pensions

Conclusions 1

• A well-designed PAYG pillar bears the promise to dealsuccessfully with demographic developments andmacroeconomic and financial market risks

• The results of “realistic” models suggest that one can useautomatic demographic adjustment factors to keep PAYGsystems in balance. The resulting adjustments are notnecessarily larger (and possibly smaller) than in a fundedpillar. Furthermore, the adequacy of pensions is more easilyguaranteed by the use of an unfunded pillar.

• There is no ready-made pension design. Various frameworkcan lead to similar achievments. Important general features:

• Lifelong assessment period• Appropriate revaluation of past contributions• Automatic demographic adjustment mechanisms?• Enough room for individual decisions (retirement age, “pension

corridor”) with correct deductions/supplements• Transparent and forward-looking communication

Conclusions 1

• A well-designed PAYG pillar bears the promise to dealsuccessfully with demographic developments andmacroeconomic and financial market risks

• The results of “realistic” models suggest that one can useautomatic demographic adjustment factors to keep PAYGsystems in balance. The resulting adjustments are notnecessarily larger (and possibly smaller) than in a fundedpillar. Furthermore, the adequacy of pensions is more easilyguaranteed by the use of an unfunded pillar.

• There is no ready-made pension design. Various frameworkcan lead to similar achievments. Important general features:• Lifelong assessment period• Appropriate revaluation of past contributions• Automatic demographic adjustment mechanisms?• Enough room for individual decisions (retirement age, “pension

corridor”) with correct deductions/supplements• Transparent and forward-looking communication

Conclusions 2

Open issues:

• Socio-demographic differences in life expectancy.Could/should this be taken into account by the adjustmentregime?

• Occupation-specific individualization of the pension system?

• Valuation of non-contributory periods (childcare etc.)

• Minimum pension entitlement before early retirement isallowed

• Organization of the funded pillar

Conclusions 2

Open issues:

• Socio-demographic differences in life expectancy.Could/should this be taken into account by the adjustmentregime?

• Occupation-specific individualization of the pension system?

• Valuation of non-contributory periods (childcare etc.)

• Minimum pension entitlement before early retirement isallowed

• Organization of the funded pillar

Appendix

The IRR for a PAYG pension systems and four differentvalues of α

The IRR with a2 = 0 and a fixed contribution rate

The IRR with a2 = 0 and a fixed contribution rateBack

The IRR with a2 = 0 and optimal savings decisionsBack

The IRR with accumulation in real capitalBack

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