Pensions
• Population is ageing in all countries. What policy reforms can gov use to ensure strong incentives to work and
save and have enough funds for retirement. How to fund pension schemes
• In 2000, 10% above 60, by 2050 forecast as 21.3% in world. UK 20.8% above 60 in 2000, forecast to be 31.5%
• 2 causes: falling fertility rates (avg births per women) and increased life expectancy.
• Most recently due to increases in life expectancy in old age.
- Since 1905s, life expectancy conditional on being 65 has risen from around 10 extra years to 20
• Old age dependency ratio (number of people aged 65 & over / number of people aged 15-64)
• Migration brings new young people but not enough to offset the changes in fertility and longevity
• Employment rate for women risen, fallen for men
- Employment rate of men 65+ has fallen over the last 100 years: enjoy leisure
• Issue about labour supply: can elderly work to older ages or does their productivity decline.
- To what extent does productivity decline with age?
• Trends: retire earlier, live longer, fewer kids and until recently, state pensions were becoming more generous
- Pension costs are projected to rise for many European countries inc UK
• Pension replacement rate (pension income relative to average income when working)
- Tends to be relatively low for the UK, 30%.
• There has been reductions in benefit generosity & increases in the official retirement age
Pension Finance
• Individual cares about the replacement rate RR=b/Y
- Where b=benefits, t=pay roll tax rate, Y= wage income when working. Sometimes RR=b/Y(1-t).
• RR in UK was 30% but falling. Private pensions get RR near 60%. Europe total is 80%
• In a pay as you go (PAYG) system, bR=tYL (total pension expenditure=tax revenue)
• R= no of retirees, L=no workers, b=benefits, w=wages of current workers
• tY= taxes raised per worker. tYL= total taxes raised. Can rearrange to find the tax rate
• Number of retirees relative to workers has risen (R/L) so tax t must rise or benefits fall
- How to fund a long retirement (20 years) relative to a short working life
• Moreover, expenditure on health and social services must also rise with more elderly.
Generational Accounts
• Measure overall inter-temporal liabilities in fiscal policy in the face of changing population structure
- Gov spending= Gov tax revenue over time. We focus on all tax and spending, not just pensions
• PV future government consumption+ public debt = PV net taxes of currently
alive generation + PV net taxes of future generations
• D=age of oldest person/generation alive; Nt,t-s = remaining net tax payment
at time t for an individual of generation t-s; Pt,t-s = population of generation t-s alive at time t; Gt+s = value
of government consumption; Dt = current net debt
- 2nd term on RHS looks at those who aren’t born yet
• We compare the generational account of a current newborn (age 0 in time t) and a future newborn to measure
the generational imbalance.
• We have to forecast lots of things, assuming current gov policy runs forever, forecast growth and wages, life
expectancy, demographics
• If gov transfers fell 7% then UK would have generational balance, for Italy it’s over 40%
, Pensions
UK
• UK has a lower replacement rate and pensions as a share of GDP
• Beveridge Pension Design: provide a universal floor called a first tier. Introduce a 2nd tier called an earnings
related benefit, mostly for lower life-time income individuals. Most 2nd tier benefits are provided by a private
pension. Third tier is private savings. Seen in UK, US, Australia, NZ
• Bismark: government does 1st & 2nd tier for both low and high income people.
- Benefits are linked to life-time earnings e.g. France, Germany, Italy
• Basic state pension is also known as the minimum income guarantee. Can leave SSP for a private pension
• Minimum income guarantee is flat benefit- given to rich and poor. Around 20% of median earnings.
• UK public pensions have become less generous and state pension age is likely to rise
- Increase in use of private pensions and reduction of work disincentives
• State pension funded by National Insurance Contrition on earnings between lower and upper limit.
- Reduced rate above the upper limit
• 2 components of pension are the Minimum income guarantee which is flat rate (basic state pension)
• Then State Second Pension (S2P). Age is 65 for men, 60 for women. Rise to 66 and 65
• State second pension (SSP): could contract out (leave it) and join a private pension scheme
2 types of Private Pensions
• Defined Benefit (DB): Employer pays contributions into a pension fund while employee is working.
• Once retired, employee gets pension benefits, depending on years of service for employer and final (or
weighted average of) salary
- Risk on mostly on the employer side. But not portable across employers: bad for worker mobility
• State pension= defined benefit as benefit is defined by amount put in and years of service
• Defined Contribution: employee and/or employer contributes into a fund. When you retire you get the value
of the fund. DC works like a saving’s account except only tax on withdrawal
• Risk on individual- will not be bailed out if you lose the funds in the pot. Can move pot to different providers
• Private pensions have favourable tax status: EET(exempt contributions, exempt accumulations, taxable
withdrawals). Savings plan are the opposite
Why we need government pension
• 1) Redistributing Income: Income tax is imperfect in redistributing from rich to poor because of transitory
variations in income (sometimes high, other low). Social security implicitly taxes life-time earnings
• 2) Correct market failure: absence of real annuities (due to adverse selection) and absence of insurance against
risks of varying length of working life (disability insurance). High transaction costs and individual info costs
• 3) Paternalism: individuals will not save enough since age of death is uncertain. Can outlive retirement savings
• Solution is annuity: a stream of income lasting from today until death, from gov or private
- Save up in a pension pot and when you retire, convert pot into an annuity to get a guaranteed income for as
long as you live.
• Private Annuity a fixed lump sum payment in return for a stream of income lasting from today until death.
• Can be nominal or real (keep up with inflation).
• Were mandatory in UK up to last year: much of the value of a DC pension fund must be annuitised on
retirement. Now voluntary: buy annuities on the market
Redistribution in State Pension
• Within cohort redistribution (rich to poor members of a cohort): low income members have a bigger
replacement ratio. No within cohort redistribution in privately funded schemes.
• Between cohort redistribution: Transfers from rich to poor cohorts (e.g., transfers to Depression Era cohorts
from richer younger cohorts whose pension performs better). Not in a private pension.
• If redistribution is not done by the government pensions, it can still be done by government somewhere else
(through taxes and transfers) . But this will have other deadweight losses associated.
, Pensions
Adverse Selection argument for government pensions
• Gov pensions take in taxes and pay out an annuity. Private market has adverse selection
• Individuals differ in their value of P2
• Private firms have incentives to screen out high P2 types, but high P2 types might be the only ones to buy
insurance
Annuities
• Often single priced i.e. price is a function of age
• Single price annuities’ redistribute from short-lived to long-lived i.e. poor to rich, unhealthy to healthy, men to
women, smokers to non-smokers. Since men live less than women so get same annuity but for fewer years
- Some annuity prices may be linked to individual characteristics: smokers get better rates
• EU: prices can’t be based on gender. US: prices depend on gender and age
- UK has a bigger market for annuities than US but still not that big
• Why few people purchase annuities: may have enough annuitised wealth and may leave some wealth
- unannuitised for bequest reasons and maybe contingencies e.g. medical expenses
• Studies suggest that annuities appear to be a bad deal & there is a lot of heterogeneity in prices.
Expected Present Discounted Value of an Annuity (nominal annuity stream)
• aj=annuity income paid in month j, Pj=probability of being alive in month j (survivor probability), ik=nominal
interest rate month k. We use cumulative for IR as interest rate varies
- So if IR was constant then denominator would be (1+i)j
• The ‘money’s worth” refers to the ratio of expected present discounted value of annuity stream Vb to the
price of the annuity. I.e. Vb/q1. If actuarially fair then ratio is 1.
• The money’s worth will usually be less than 1 due to : loaded factors (admin costs, corporate taxes)
- Mortality rates typically lower for annuitants: active selection from people who expect to live longer buying
annuities as they get a good deal. Also passive selection on attributes correlated with mortality
- rich people live longer, believe in the system & have lower replacement rates so bigger demand for
annuities
• Poterba (1999): when we use population mortality, money’s worth is low. When using life table for annuitants,
money’s worth is almost one. Money’s worth ratio falls faster for population than annuitants.
- Tells us there’s adverse selection as more healthy tend to purchase annuity
• Until recently, in UK annuity purchase is partly mandatory (3/4 of pot annuitised).
• The compulsory annuity market was large relative to the voluntary annuity market. In US, it’s entirely voluntary
• Poterba (2002) looked at the annual payout from £10,000 spent on an annuity and found the annual payment
was lower in nominal and real terms for the voluntary market than the compulsory market.
- Annual payment lower in real than nominal terms and higher for men than women
• Poterba then subbed into survival probabilities into equation: found adverse selection matters
• There is adverse selection in the UK annuities market, but not as bad relative to US
- Mandatory purchase of annuities seems to alleviate adverse selection
• Other key source of adverse selection: disability insurance (have to stop working): provided by gov or
employer in US
• UK new law: decline in amount purchased and possible price rise due to increased adverse selection
• Paternalism: use as people don’t save enough for retirement
- Due to a lack of info and myopia ( difficulty in making decisions or lack of ability to plan)
• Myopia causes: before social security, few people retired as they kept working so little need to save.
• As SS spending rises, elderly poverty rate has fallen. Also consumption tends to fall on retirement
• Graph: as SS spending goes up, elderly poverty rate falls
• Population is ageing in all countries. What policy reforms can gov use to ensure strong incentives to work and
save and have enough funds for retirement. How to fund pension schemes
• In 2000, 10% above 60, by 2050 forecast as 21.3% in world. UK 20.8% above 60 in 2000, forecast to be 31.5%
• 2 causes: falling fertility rates (avg births per women) and increased life expectancy.
• Most recently due to increases in life expectancy in old age.
- Since 1905s, life expectancy conditional on being 65 has risen from around 10 extra years to 20
• Old age dependency ratio (number of people aged 65 & over / number of people aged 15-64)
• Migration brings new young people but not enough to offset the changes in fertility and longevity
• Employment rate for women risen, fallen for men
- Employment rate of men 65+ has fallen over the last 100 years: enjoy leisure
• Issue about labour supply: can elderly work to older ages or does their productivity decline.
- To what extent does productivity decline with age?
• Trends: retire earlier, live longer, fewer kids and until recently, state pensions were becoming more generous
- Pension costs are projected to rise for many European countries inc UK
• Pension replacement rate (pension income relative to average income when working)
- Tends to be relatively low for the UK, 30%.
• There has been reductions in benefit generosity & increases in the official retirement age
Pension Finance
• Individual cares about the replacement rate RR=b/Y
- Where b=benefits, t=pay roll tax rate, Y= wage income when working. Sometimes RR=b/Y(1-t).
• RR in UK was 30% but falling. Private pensions get RR near 60%. Europe total is 80%
• In a pay as you go (PAYG) system, bR=tYL (total pension expenditure=tax revenue)
• R= no of retirees, L=no workers, b=benefits, w=wages of current workers
• tY= taxes raised per worker. tYL= total taxes raised. Can rearrange to find the tax rate
• Number of retirees relative to workers has risen (R/L) so tax t must rise or benefits fall
- How to fund a long retirement (20 years) relative to a short working life
• Moreover, expenditure on health and social services must also rise with more elderly.
Generational Accounts
• Measure overall inter-temporal liabilities in fiscal policy in the face of changing population structure
- Gov spending= Gov tax revenue over time. We focus on all tax and spending, not just pensions
• PV future government consumption+ public debt = PV net taxes of currently
alive generation + PV net taxes of future generations
• D=age of oldest person/generation alive; Nt,t-s = remaining net tax payment
at time t for an individual of generation t-s; Pt,t-s = population of generation t-s alive at time t; Gt+s = value
of government consumption; Dt = current net debt
- 2nd term on RHS looks at those who aren’t born yet
• We compare the generational account of a current newborn (age 0 in time t) and a future newborn to measure
the generational imbalance.
• We have to forecast lots of things, assuming current gov policy runs forever, forecast growth and wages, life
expectancy, demographics
• If gov transfers fell 7% then UK would have generational balance, for Italy it’s over 40%
, Pensions
UK
• UK has a lower replacement rate and pensions as a share of GDP
• Beveridge Pension Design: provide a universal floor called a first tier. Introduce a 2nd tier called an earnings
related benefit, mostly for lower life-time income individuals. Most 2nd tier benefits are provided by a private
pension. Third tier is private savings. Seen in UK, US, Australia, NZ
• Bismark: government does 1st & 2nd tier for both low and high income people.
- Benefits are linked to life-time earnings e.g. France, Germany, Italy
• Basic state pension is also known as the minimum income guarantee. Can leave SSP for a private pension
• Minimum income guarantee is flat benefit- given to rich and poor. Around 20% of median earnings.
• UK public pensions have become less generous and state pension age is likely to rise
- Increase in use of private pensions and reduction of work disincentives
• State pension funded by National Insurance Contrition on earnings between lower and upper limit.
- Reduced rate above the upper limit
• 2 components of pension are the Minimum income guarantee which is flat rate (basic state pension)
• Then State Second Pension (S2P). Age is 65 for men, 60 for women. Rise to 66 and 65
• State second pension (SSP): could contract out (leave it) and join a private pension scheme
2 types of Private Pensions
• Defined Benefit (DB): Employer pays contributions into a pension fund while employee is working.
• Once retired, employee gets pension benefits, depending on years of service for employer and final (or
weighted average of) salary
- Risk on mostly on the employer side. But not portable across employers: bad for worker mobility
• State pension= defined benefit as benefit is defined by amount put in and years of service
• Defined Contribution: employee and/or employer contributes into a fund. When you retire you get the value
of the fund. DC works like a saving’s account except only tax on withdrawal
• Risk on individual- will not be bailed out if you lose the funds in the pot. Can move pot to different providers
• Private pensions have favourable tax status: EET(exempt contributions, exempt accumulations, taxable
withdrawals). Savings plan are the opposite
Why we need government pension
• 1) Redistributing Income: Income tax is imperfect in redistributing from rich to poor because of transitory
variations in income (sometimes high, other low). Social security implicitly taxes life-time earnings
• 2) Correct market failure: absence of real annuities (due to adverse selection) and absence of insurance against
risks of varying length of working life (disability insurance). High transaction costs and individual info costs
• 3) Paternalism: individuals will not save enough since age of death is uncertain. Can outlive retirement savings
• Solution is annuity: a stream of income lasting from today until death, from gov or private
- Save up in a pension pot and when you retire, convert pot into an annuity to get a guaranteed income for as
long as you live.
• Private Annuity a fixed lump sum payment in return for a stream of income lasting from today until death.
• Can be nominal or real (keep up with inflation).
• Were mandatory in UK up to last year: much of the value of a DC pension fund must be annuitised on
retirement. Now voluntary: buy annuities on the market
Redistribution in State Pension
• Within cohort redistribution (rich to poor members of a cohort): low income members have a bigger
replacement ratio. No within cohort redistribution in privately funded schemes.
• Between cohort redistribution: Transfers from rich to poor cohorts (e.g., transfers to Depression Era cohorts
from richer younger cohorts whose pension performs better). Not in a private pension.
• If redistribution is not done by the government pensions, it can still be done by government somewhere else
(through taxes and transfers) . But this will have other deadweight losses associated.
, Pensions
Adverse Selection argument for government pensions
• Gov pensions take in taxes and pay out an annuity. Private market has adverse selection
• Individuals differ in their value of P2
• Private firms have incentives to screen out high P2 types, but high P2 types might be the only ones to buy
insurance
Annuities
• Often single priced i.e. price is a function of age
• Single price annuities’ redistribute from short-lived to long-lived i.e. poor to rich, unhealthy to healthy, men to
women, smokers to non-smokers. Since men live less than women so get same annuity but for fewer years
- Some annuity prices may be linked to individual characteristics: smokers get better rates
• EU: prices can’t be based on gender. US: prices depend on gender and age
- UK has a bigger market for annuities than US but still not that big
• Why few people purchase annuities: may have enough annuitised wealth and may leave some wealth
- unannuitised for bequest reasons and maybe contingencies e.g. medical expenses
• Studies suggest that annuities appear to be a bad deal & there is a lot of heterogeneity in prices.
Expected Present Discounted Value of an Annuity (nominal annuity stream)
• aj=annuity income paid in month j, Pj=probability of being alive in month j (survivor probability), ik=nominal
interest rate month k. We use cumulative for IR as interest rate varies
- So if IR was constant then denominator would be (1+i)j
• The ‘money’s worth” refers to the ratio of expected present discounted value of annuity stream Vb to the
price of the annuity. I.e. Vb/q1. If actuarially fair then ratio is 1.
• The money’s worth will usually be less than 1 due to : loaded factors (admin costs, corporate taxes)
- Mortality rates typically lower for annuitants: active selection from people who expect to live longer buying
annuities as they get a good deal. Also passive selection on attributes correlated with mortality
- rich people live longer, believe in the system & have lower replacement rates so bigger demand for
annuities
• Poterba (1999): when we use population mortality, money’s worth is low. When using life table for annuitants,
money’s worth is almost one. Money’s worth ratio falls faster for population than annuitants.
- Tells us there’s adverse selection as more healthy tend to purchase annuity
• Until recently, in UK annuity purchase is partly mandatory (3/4 of pot annuitised).
• The compulsory annuity market was large relative to the voluntary annuity market. In US, it’s entirely voluntary
• Poterba (2002) looked at the annual payout from £10,000 spent on an annuity and found the annual payment
was lower in nominal and real terms for the voluntary market than the compulsory market.
- Annual payment lower in real than nominal terms and higher for men than women
• Poterba then subbed into survival probabilities into equation: found adverse selection matters
• There is adverse selection in the UK annuities market, but not as bad relative to US
- Mandatory purchase of annuities seems to alleviate adverse selection
• Other key source of adverse selection: disability insurance (have to stop working): provided by gov or
employer in US
• UK new law: decline in amount purchased and possible price rise due to increased adverse selection
• Paternalism: use as people don’t save enough for retirement
- Due to a lack of info and myopia ( difficulty in making decisions or lack of ability to plan)
• Myopia causes: before social security, few people retired as they kept working so little need to save.
• As SS spending rises, elderly poverty rate has fallen. Also consumption tends to fall on retirement
• Graph: as SS spending goes up, elderly poverty rate falls
