Week 5: 08/03/21
ECN302 – Advanced Macroeconomics – Ageing & Pension Systems Sustainability
Video 1
There is an ageing population so spending on pensions is increasing.
In this topic, we will assume that in each period t, a new generation of individual is started. Each
generation only lives for 2 periods in this model – each individual is heterogeneous (different).
This is an OLG (overlapping generation) model.
The United Nations use the Old Age Dependency Ratio to measure ageing, where:
OADR2 = Pop aged 65+ / Pop aged (20-64)
OADR3 = Pop aged 70+ / Pop aged (20-69)
These allow for cross-country and intertemporal comparisons of ageing.
Trends according to OADR2:
The ratio has increased across the world from 1950-2015 and is projected to increase further in
future. This means that populations have aged overtime and are expected to get even older with
time.
The ratio has increased in the US, Europe & in EU14 countries.
EU14 countries are a sub-sample of the oldest European countries.
Therefore, ageing is a worldwide phenomenon, which is particularly significant in advanced
economies.
Trends according to OADR3:
The trends are very similar for this measure as they are for OADR2, but OADR3 shows a slightly
lower level of the dependency ratio because this is a more benign measure of the OADR.
EU14 countries:
All EU14 countries are forecasted to have an increased ageing population by 2050, according to both
OADR measures.
There is a lot of demographic uncertainty, as shown in slide 6. Demographic uncertainty is much higher in
Greece, Portugal & Spain than it is in Great Britain & US.
Video 2
The fundamental problem of ageing is that the proportion of those that benefit from the pension system
is increasing relative to the proportion of those who contribute to the pension system.
We assume that agents live for 2 periods. In the first period we call them young & in the second we call
them old. In each period there are two generations of agents: young (y) and old (o). The model begins in
t=0.
Number of young agents: Nt ; Growth rate of the population: nt.
Dependency ratio:
, Week 5: 08/03/21
The dependency ratio is the no. of old people (born in t-1) divided by the no. of young people (born in t).
This is equal to the reciprocal of the growth rate of the population because the growth rate of the
population = (Nt – Nt-1)/Nt-1
-Production
We assume there is a production sector, where a firm makes profits: πt = yt – wtht
ht is the hours of labour supply and wt is the wage received per hour of labour.
There is a technology constraint: yt = ωtht
The technology constraint tells us that each hour of labour is converted in one unit of output or the
technology rate ωt.
ωt is labour productivity. ω is Omega.
-Households
Households only work during young age, then they retire. The income they generate when young is taxed
& the tax revenue generated is used to pay pensions to old people at an exogenous rate. Therefore, the
pension that individuals receive when old is not proportional to the income they were earning when
young - it’s a flat rate.
Intertemporal preference of the HH:
The preference depends on consumption when young, consumption when old (positively) & labour
supply (negatively).
Gamma is a parameter. If gamma=1, utility is linear. Gamma=2 means utility is quadratic.
The budget constraint when the agent is young:
When young, the agent works & pays taxes. Their disposable income is used to finance consumption.
The budget constraint when the agent is old:
When the agent is old, they receive a pension, which they use to consume. υt+1 is the exogenous and fixed
transfer from the govt to the old.
There is no financial market.
-Government
ECN302 – Advanced Macroeconomics – Ageing & Pension Systems Sustainability
Video 1
There is an ageing population so spending on pensions is increasing.
In this topic, we will assume that in each period t, a new generation of individual is started. Each
generation only lives for 2 periods in this model – each individual is heterogeneous (different).
This is an OLG (overlapping generation) model.
The United Nations use the Old Age Dependency Ratio to measure ageing, where:
OADR2 = Pop aged 65+ / Pop aged (20-64)
OADR3 = Pop aged 70+ / Pop aged (20-69)
These allow for cross-country and intertemporal comparisons of ageing.
Trends according to OADR2:
The ratio has increased across the world from 1950-2015 and is projected to increase further in
future. This means that populations have aged overtime and are expected to get even older with
time.
The ratio has increased in the US, Europe & in EU14 countries.
EU14 countries are a sub-sample of the oldest European countries.
Therefore, ageing is a worldwide phenomenon, which is particularly significant in advanced
economies.
Trends according to OADR3:
The trends are very similar for this measure as they are for OADR2, but OADR3 shows a slightly
lower level of the dependency ratio because this is a more benign measure of the OADR.
EU14 countries:
All EU14 countries are forecasted to have an increased ageing population by 2050, according to both
OADR measures.
There is a lot of demographic uncertainty, as shown in slide 6. Demographic uncertainty is much higher in
Greece, Portugal & Spain than it is in Great Britain & US.
Video 2
The fundamental problem of ageing is that the proportion of those that benefit from the pension system
is increasing relative to the proportion of those who contribute to the pension system.
We assume that agents live for 2 periods. In the first period we call them young & in the second we call
them old. In each period there are two generations of agents: young (y) and old (o). The model begins in
t=0.
Number of young agents: Nt ; Growth rate of the population: nt.
Dependency ratio:
, Week 5: 08/03/21
The dependency ratio is the no. of old people (born in t-1) divided by the no. of young people (born in t).
This is equal to the reciprocal of the growth rate of the population because the growth rate of the
population = (Nt – Nt-1)/Nt-1
-Production
We assume there is a production sector, where a firm makes profits: πt = yt – wtht
ht is the hours of labour supply and wt is the wage received per hour of labour.
There is a technology constraint: yt = ωtht
The technology constraint tells us that each hour of labour is converted in one unit of output or the
technology rate ωt.
ωt is labour productivity. ω is Omega.
-Households
Households only work during young age, then they retire. The income they generate when young is taxed
& the tax revenue generated is used to pay pensions to old people at an exogenous rate. Therefore, the
pension that individuals receive when old is not proportional to the income they were earning when
young - it’s a flat rate.
Intertemporal preference of the HH:
The preference depends on consumption when young, consumption when old (positively) & labour
supply (negatively).
Gamma is a parameter. If gamma=1, utility is linear. Gamma=2 means utility is quadratic.
The budget constraint when the agent is young:
When young, the agent works & pays taxes. Their disposable income is used to finance consumption.
The budget constraint when the agent is old:
When the agent is old, they receive a pension, which they use to consume. υt+1 is the exogenous and fixed
transfer from the govt to the old.
There is no financial market.
-Government
