Week 7:
22/03/21
ECN302 – Advanced Macroeconomics – Secular Stagnation
Video 1
Required reading: Eggertsson, Mehrotra and Robbins. 2019. A Model of Secular Stagnation: Theory and
Quantitative Evaluation.
-Long term stagnation
There has been a long term decline in the nominal IR (particularly since the 1980s).
The short term nominal IR has reached the zero lower bound (ZLB) for a prologue period of time. (The
nominal IR can’t be negative – 0 is the limit).
There’s been a long term reduction in the growth rate of advanced economies (particularly since the
1980s).
The secular stagnation hypothesis says that the natural IR (the real IR consistent with output at full
potential) can be permanently negative.
Slide 3 shows that post 1980s, the growth rate has declined to a very low level.
Slide 4 shows that the nominal T-bill rate reached a ZLB in 1940 and then increased up until 1980. Since
1980 it has decreased and since 2008 it has stayed at/close to the ZLB.
If the real nominal IR is close to 0 and there is inflation, then the real IR will be negative, since r ≈ i−π t
Slide 5 shows the real T-bill IR (when inflation has been taken away). Because inflation was very high in
1920, the real IR was negative. During the 1930s-40s, the nominal rate was on average close to 0 so the
real IR was negative. The 2008 recession reduced the nominal IR to the ZLB, causing the real IR to become
negative for a prolonged period of time. The COVID shock has caused the nominal IR to reach the ZLB
once again since Jan 2020, causing a negative real IR.
-Modelling Secular Stagnation
We need a model in which the LR IR can be negative.
This is an infinitely-lived agent model (DGE/DSGE).
We think of the LR as the steady state equilibrium condition.
The key equation of this model is the Euler equation:
U’(ct) = βu’(ct+1) (1+rt+1) for t ≥ 0.
This in an equil condition which holds throughout the entire time horizon of the model.
In the steady state, consumption is constant at ct = ct+1 = c. therefore, the equil condition is that he
product between the individual discount factor and gross IR is equal to 1 in the LR. That is:
1 = β (1 + rt+1) for t ≥ 0.
, Week 7:
22/03/21
Since β=1/(1+ ρ ), you can solve the above expression which implies that the LR IR is always equal to the
rate of time preference which is non-negative. That is:
rt+1 = ρ ≥ 0 for t ≥ 0.
A negative IR cannot be a LR equilibrium in a DGE model. Therefore, we need to move away from this
model.
We need to use the Overlapping Generational (OLG) model to derive a model of the economy that is
consistent with the secular stagnation hypothesis.
Video 2
In this OLG, there are 3 periods. In each period, there are 3 generations of agents young (y), middle aged
(m), and old (o).
-Demographics
Number of young: Nt.
Growth rate of the population: gt
We assume a closed, endowment economy.
There is a total amount of resources in any given period t, Yt , which is fixed. This is distributed across the
3 generations alive in that period.
-Environment
Preferences:
Lifetime utility of a young person in period t:
Budget constraints:
Young agent:
Young agents don’t receive any endowment income so their only way to finance consumption in the first
period is by borrowing. Therefore, total endowment income, Yt, is distributed between middle and old
age agents.
Middle age agent:
Old age agent:
A positive B means debt. A negative B means savings.
22/03/21
ECN302 – Advanced Macroeconomics – Secular Stagnation
Video 1
Required reading: Eggertsson, Mehrotra and Robbins. 2019. A Model of Secular Stagnation: Theory and
Quantitative Evaluation.
-Long term stagnation
There has been a long term decline in the nominal IR (particularly since the 1980s).
The short term nominal IR has reached the zero lower bound (ZLB) for a prologue period of time. (The
nominal IR can’t be negative – 0 is the limit).
There’s been a long term reduction in the growth rate of advanced economies (particularly since the
1980s).
The secular stagnation hypothesis says that the natural IR (the real IR consistent with output at full
potential) can be permanently negative.
Slide 3 shows that post 1980s, the growth rate has declined to a very low level.
Slide 4 shows that the nominal T-bill rate reached a ZLB in 1940 and then increased up until 1980. Since
1980 it has decreased and since 2008 it has stayed at/close to the ZLB.
If the real nominal IR is close to 0 and there is inflation, then the real IR will be negative, since r ≈ i−π t
Slide 5 shows the real T-bill IR (when inflation has been taken away). Because inflation was very high in
1920, the real IR was negative. During the 1930s-40s, the nominal rate was on average close to 0 so the
real IR was negative. The 2008 recession reduced the nominal IR to the ZLB, causing the real IR to become
negative for a prolonged period of time. The COVID shock has caused the nominal IR to reach the ZLB
once again since Jan 2020, causing a negative real IR.
-Modelling Secular Stagnation
We need a model in which the LR IR can be negative.
This is an infinitely-lived agent model (DGE/DSGE).
We think of the LR as the steady state equilibrium condition.
The key equation of this model is the Euler equation:
U’(ct) = βu’(ct+1) (1+rt+1) for t ≥ 0.
This in an equil condition which holds throughout the entire time horizon of the model.
In the steady state, consumption is constant at ct = ct+1 = c. therefore, the equil condition is that he
product between the individual discount factor and gross IR is equal to 1 in the LR. That is:
1 = β (1 + rt+1) for t ≥ 0.
, Week 7:
22/03/21
Since β=1/(1+ ρ ), you can solve the above expression which implies that the LR IR is always equal to the
rate of time preference which is non-negative. That is:
rt+1 = ρ ≥ 0 for t ≥ 0.
A negative IR cannot be a LR equilibrium in a DGE model. Therefore, we need to move away from this
model.
We need to use the Overlapping Generational (OLG) model to derive a model of the economy that is
consistent with the secular stagnation hypothesis.
Video 2
In this OLG, there are 3 periods. In each period, there are 3 generations of agents young (y), middle aged
(m), and old (o).
-Demographics
Number of young: Nt.
Growth rate of the population: gt
We assume a closed, endowment economy.
There is a total amount of resources in any given period t, Yt , which is fixed. This is distributed across the
3 generations alive in that period.
-Environment
Preferences:
Lifetime utility of a young person in period t:
Budget constraints:
Young agent:
Young agents don’t receive any endowment income so their only way to finance consumption in the first
period is by borrowing. Therefore, total endowment income, Yt, is distributed between middle and old
age agents.
Middle age agent:
Old age agent:
A positive B means debt. A negative B means savings.
