70
AEA Papers and Proceedings 2023, 113: 70–75
https://doi.org/10.1257/pandp.20231027
The Trickling Up of Excess Savings
†
By A A, M R, L S*
In the wake of the COVID pandemic, house-
holds accumulated a very large stock of “excess
savings,” which they have only recently begun to
deplete. Figure1, panel A shows that the US per-
sonal savings rate rst rose very rapidly in 2020,
more than doubling relative to its long-term
average, then started falling below that average
in late 2021. Figure1, panel B shows an esti-
mate of the resulting stock of excess savings by
the Federal Reserve Board (Aladangady et al.
2022). This stock has only modestly fallen from
its peak. In mid-2022, it still stood at $1.7 tril-
lion, or 6.7 percent of GDP.
Because excess savings and their distribu-
tion across the population intuitively matter for
aggregate demand, economists have paid a con-
siderable amount of attention to estimating both.
In this paper, we provide a tractable heteroge-
neous agent New Keynesian model that explic-
itly maps the distribution of excess savings to
the path of output, and that explains the process
by which their effect dissipates. We use this
framework to estimate the likely contribution
of excess savings to aggregate spending in the
coming years under various assumptions about
the marginal propensities to consume (MPCs)
of agents holding the savings and scenarios for
monetary policy.
Our framework recognizes that one person’s
spending is another person’s income. As we
show, taking this fact into account implies that
excess savings from debt-nanced transfers
have much longer-lasting effects than a naive
calculation would suggest. In a closed economy,
unless the government pays down the debt used
to nance the transfers, excess savings do not go away as households spend them down. Instead,
the effect of excess savings on aggregate demand
slowly dissipates as they “trickle up” the wealth
distribution to agents with lower MPCs. Tight
monetary policy speeds up this process, but this
effect is likely to be quantitatively modest.
I. Model
We consider a continuous time model
with N types of households, i = 1, … N .
* Auclert: Stanford University and NBER (email:
Straub: Harvard University and NBER (email: ludwigstraub@
fas.harvard.edu). We thank S¸ebnem Kalemli-Özcan and our
discussant Fabrizio Perri for helpful comments.
†
Go to https://doi.org/10.1257/pandp.20231027 to visit
the article page for additional materials and author disclo-
sure statement(s).
F1. US P S R E S
Sources: The personal savings rate is from the Bureau of
Economic Analysis (FRED code: PSAVERT). The estimated
stock of excess savings is from Aladangady etal. (2022).
2014 2015 2016 2017 2018 2019 2020 2021 2022
5
10
15
20
25
30
35
Percent of GDP
US personal savings rate
2020:1 2020:7 2021:1 2021:7 2022:1
0
500
1,000
1,500
2,000
Billions of USD
Estimated stock of excess savings
Actual
2014–2019 average
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THE TRICKLING UP OF EXCESS SAVINGS
Agents with higher i have lower instantaneous
MPCs m
i
, with agent N having an MPC of 0,
m
1
> m
2
> ⋯ > m
N
= 0 . Motivated by
the empirical evidence on the negative correla-
tion between MPCs and wealth, we think of
agents with higher i as being initially richer,
with agent N being the richest. While this is a
useful interpretation, it is not strictly necessary:
what is important is the distribution of m
i
across
types i .
At t = 0 , the government distributes a trans-
fer a
i0
to households, issuing debt B =
∑
i=1
N
a
i0
to nance the transfer and maintaining a con-
stant debt level thereafter. We rst consider an
“easy monetary policy” scenario in which the
central bank responds by holding constant the
real interest rate at its steady-state level of 0,
r = 0 . This implies, in particular, that the addi-
tional debt requires no change in taxes.
Each type’s behavior is described by a utility
function over consumption and assets. Agents
understand the central bank’s announcements
of future real interest rates r
t
(here, r = 0 ),
but they assume that future aggregate income
Y
t
remains permanently at its steady-state lev-
el.
1
Agent type i earns a xed proportion θ
i
∈
(
0, 1
)
of total income Y
t
.
We linearize this model around the steady
state where each agent type owns a certain stock
of assets (with higher-type agents plausibly
holding more wealth). This delivers the follow-
ing equations:
(1) c
it
= m
i
a
it
, a
˙
it
= θ
i
Y
t
− c
it
, Y
t
=
∑
i=1
N
c
it
,
where Y
t
is aggregate demand and income, c
it
is
type i ′s consumption, a
it
his asset holdings (all
relative to their steady-state level), and m
i
∈
[
0, ∞
)
his instantaneous MPC out of liquid
assets. The θ ’s, which satisfy
∑
i=1
N
θ
i
= 1 , are
the income shares across the types. The equa-
tions in (1) give a tractable version of the inter-
temporal Keynesian cross (Auclert, Rognlie,
and Straub 2018).
An unconventional feature of our model is
that it assumes the presence of agents with zero
MPC. One can interpret these type N agents as
standard permanent-income agents, in the limit
1
In the words of Farhi and Werning (2019), agents have
level k thinking, with k = 1 . This makes the model par-
ticularly tractable. We later consider the case with rational
expectations.
where their discount rate goes to zero, but alter-
native interpretations are possible. First, they
could stand in for the rest of the world. Second,
they could represent the government receiving
a fraction of aggregate income via taxation and
using it to pay down the debt. Finally, they could
represent zero-MPC nancial accounts, such
as retained earnings saved by rms or pension
funds.
One natural objection to the model in (1) is
that it assumes that monetary policy maintains
an easy stance of r = 0 in the face of high
demand. To address this, we extend our model
by assuming that monetary policy tightens
as it sees higher demand, reacting with a rule
r
t
= ϕ Y
t
.
2
Since higher demand will naturally
be associated with higher ination, an alterna-
tive interpretation of this rule is that monetary
policy tightens in reaction to the ination gen-
erated by excess savings. Online Appendix A
derives the equations characterizing the model
in this case.
Another objection to the model in (1) is that
it relies on imperfect foresight by agents. Online
Appendix A also derives the equations charac-
terizing the model when agents have rational
expectations about interest rates r
t
as well as
income Y
t
.
Partial Equilibrium Analysis.—A naive par-
tial equilibrium approach to calculating the
effect of excess savings on spending would be to
ignore the endogeneity of output, instead assum-
ing that Y
t
remains at its normalized steady-state
level of 0 forever. Solving out for (1) in this
case, we nd that aggregate demand is given by
(2) C
t
=
∑
i=1
N−1
m
i
e
− m
i
t
a
i0
.
Equation (2) delivers a simple way to map a
distribution of MPCs and excess savings by
type into an effect on aggregate spending: take
type i ’s initial stock of savings, and apply to it
an exponential distribution for spending with
2
To neutralize the income effects of changing interest
rates, in this extension we assume that all agents types start
with a steady-state level of wealth of 0. We think of this as
proxying for the presence of long duration assets, which
hedge agents against interest rate risk.
MAY 202372
AEA PAPERS AND PROCEEDINGS
mean 1/ m
i
.
3
A simple back-of-the-envelope
calculation using this equation suggests that for
the United States, the remaining excess savings
might only affect aggregate demand for a few
quarters (see Table 1).
This approach, however, fails to recognize that
one agent’s spending is another agent’s income.
Ignoring this fact has important consequences:
if agents simply spent down their excess savings
without raising anyone else’s income, then no
one would be purchasing the assets they sold
in the process. But this is inconsistent with the
government keeping its debt constant. As we
show next, recognizing this fact implies a much
greater persistence of excess savings and output
than equation (2) suggests.
II. The Trickling-Up Effect
We now explicitly solve the dynamical sys-
tem in (1). We begin with a simple observation
about the steady state of this system.
PROPOSITION 1 ( Long-Run Trickling Up): In
the long run, type N owns all the debt: lim
t→∞
a
Nt
= B .
This result follows immediately from the fact
that type N has m
N
= 0 , so that its asset dynam-
ics are given by a
˙
Nt
= θ
N
(
∑
i=1
N−1
m
i
a
it
)
. Hence,
as long as other agents have excess savings, they
spend them down, increasing the income and
3
This functional form characterizes the intertemporal
MPCs of agents with assets in the utility; once multiple types
of such agents are mixed together, the model’s aggregate
dynamics are similar to those of alternative heterogeneous
agent models. See Auclert, Rognlie, and Straub (2018).
therefore the savings of the richest type. Since
the government keeps its debt position constant
(
∑
i=1
N
a
it
= B at all times), in the long run all
types have zero assets except for type N , which
owns all of B . At this point, excess savings have
“trickled up” to agents with the highest i . Given
our interpretation of type N as being initially the
richest agent, we see that any initial transfer, no
matter how targeted it is to the poor, eventually
ends up raising wealth inequality.
PROPOSITION 2 ( Trickling-Up Dynamics):
Assume that m
i
a
i0
/ θ
i
decreases in i . Then the
distribution of assets across types i at any later
date t′ rst-order stochastically dominates the
distribution at any earlier date t < t′ :
∑
i=1
n
a
it′
<
∑
i=1
n
a
it
for all n < N .
This result, proved in online Appendix B,
shows the exact sense in which excess savings
trickle up: no matter where we look in the dis-
tribution of excess savings, as time passes, the
wealth held by all lower types is falling, and the
wealth held by all higher types is rising. The
only necessary condition is that excess savings
initially cause a larger percentage increase in
spending among poorer agents, which is easily
satised since they have higher MPCs.
PROPOSITION 3 (Slow Dissipation): In the
long run, Y
t
∼ e
−λt
: aggregate demand and
excess savings dissipate at rate λ , where λ <
m
N−1
. Hence, excess savings have a strictly
longer-lasting effect on demand than the naive
partial equilibrium calculation in (2) would
suggest.
T1—D O E S T A S ( )
Duration of output and excess savings
Scenario
Output Y Middle-class a
1
Rich a
2
Partial equilibrium 3 2 4
Benchmark 20 19 22
Lower MPCs ( mp c
1
= 0.3 , mp c
2
= 0.1 )
38 34 43
More excess savings to rich ( a
10
= a
20
= 0.45B )
21 20 22
More earnings to rich ( θ
1
= 0.3, θ
2
= 0.55 )
23 19 26
Rational expectations 8 6 10
Tight monetary policy ( ϕ = 1.5 )
8 7 11
Notes: The time unit is a quarter. Given that r = 0 , the duration of a variable X
t
is dened as
∫
t X
t
dt/
∫
X
t
dt . Our benchmark
calibration has mp c
1
= 0.4 , mp c
2
= 0.2 , with m
i
= − log
(
1 − mp c
i
)
; income shares θ
1
= 0.47, θ
2
= 0.38, θ
3
= 0.15 ;
and initial assets a
10
= 0.6 · B , a
20
= 0.3 · B , with B = 6.7% of GDP. For the monetary response scenario, we assume that
agents have an elasticity of intertemporal substitution of 1/2.
VOL. 113
73
THE TRICKLING UP OF EXCESS SAVINGS
In the partial equilibrium calculation from
equation (2), spending eventually becomes
dominated by type N − 1 agents, decaying at
rate m
N−1
. Proposition 3 shows that general equi-
librium spending dissipates strictly more slowly
than this. Intuitively, this is because the spending
from any type sustains income from any other
type as the wealth of all agents goes to zero.
Figure 2 illustrates the adjustment process
characterized by Propositions 1–3. Dark arrows
ow from agent types to aggregate demand Y
t
via their spending ( m
i
), with lower types spend-
ing down their assets faster. Gray arrows ow
from aggregate demand to the income of these
agents, and they are more equally distributed
across the population ( θ
i
), with type N agents
receiving a signicant share. Running this sys-
tem forward, we see that excess savings slowly
trickle up the wealth distribution, until type N
agents own all of the assets.
Three-Type Example.—We now specialize
the model to a case with N = 3 types. This case
is simple to analyze graphically, and provides
additional analytical insights into the trickling
up of excess savings. We think of type 1 as rep-
resenting the poor and the middle class, type 2
as representing the rich, and type 3 as represent-
ing the superrich. Manipulating the equations in
(1), we see that the dynamics of excess savings
for the rst two types satisfy
(
a
˙
1
a
˙
2
)
=
(
− m
1
(
1 − θ
1
)
θ
1
m
2
θ
2
m
1
− m
2
(
1 − θ
2
)
)
(
a
1
a
2
)
.
Once we have solved for
(
a
1t
, a
2t
)
, it is easy to
back out a
3t
= B −
(
a
1t
+ a
2t
)
.
Figure 3 visualizes this dynamical system
using a phase diagram for
(
a
1
, a
2
)
. The locus
for a
˙
1
= 0 is given by a
2
=
θ
2
+ θ
3
_
1 −
(
θ
2
+ θ
3
)
m
1
_
m
2
a
1
;
to the right of this locus, the assets of type 1
agents decline. The locus for a
˙
2
= 0 is atter, at
a
2
=
θ
2
_
1 − θ
2
m
1
_
m
2
a
1
; to the right of this locus, type
2 assets increase. The dynamics of the wealth
distribution are then given by the arrows on the
graph, splitting the positive quadrant into three
regions: two regions close to the axes in which
agents’ assets move in opposite directions, and
a middle cone in which both agents’ assets
decline together. In the scenario where initial
a
2
is low relative to a
1
, type 2 agents initially
increase their assets, as the spending by type 1
agents initially boosts their incomes and savings
before reaching a second phase in which both
types’ assets decline as the superrich accumu-
late. We formalize this situation in the following
proposition:
PROPOSITION 4: Assume that type 1 agents
initially own a sufciently large share of assets,
θ
2
m
1
a
10
>
(
1 − θ
2
)
m
2
a
20
. Then, type 2
agents rst accumulate assets before spending
them down.
The hump-shaped response of savings of type
2 agents is a simple manifestation of the trick-
ling-up effect from Proposition 2.
F2. T T-U E
Top
1%
Rich
Poor and
middle class
Aggregate
demand
Poor and middle
class spend
down the fastest
Top 1%
earn income but
don’t spend much
Excess savings slowly
“trickle up” toward the top 1%
˙a
2
= 0
a
1
a
2
˙a
1
= 0
F3. P D N = 3 C
MAY 202374
AEA PAPERS AND PROCEEDINGS
III. Application to the United States
We use our model to quantify the likely
impact of the stock of excess savings esti-
mated by Aladangady etal. (2022) on aggregate
demand and its likely duration. We follow the
three-type classication outlined in Section II.
We set the time units so that t = 1 corresponds
to a quarter. The parameters of the model are θ
i
,
m
i
, and a
i0
for each i .
We interpret types as follows: type 1 is the
bottom 80 percent of the US wealth distribution,
type 2 is the next 19 percent, and type 3 is the
top 1 percent. In the 2019 Survey of Consumer
Finances, the bottom 80 percent of the US
wealth distribution earns 47 percent of income,
the next 19 percent earns 38 percent, and the
top 1 percent earns 15 percent. We assume that
marginal income is distributed like average
income; this implies our θ
i
’s. Next, we assume
realistically high quarterly MPCs for the middle
class and the rich: mp c
1
= 0.4 and mp c
2
= 0.2
, respectively. We then convert these num-
bers to instantaneous MPCs using the formula
1 − e
− m
i
= mp c
i
. Finally, we assume that the
excess savings have only started to trickle up
the wealth distribution, with the middle class
owning 60 percent and the rich owning 30 per-
cent of the stock of excess savings. Finally, we
take the total stock to be B = 6.7% of GDP, as
estimated by Aladangady et al. (2022). While
the exact numbers entering our calculations are
highly uncertain, Table 1 shows that our results
are robust to reasonable alternative calibrations.
Figure4 reports the evolution of the distribu-
tion of savings across types in three alternative
scenarios. The top panel shows the outcome of a
partial equilibrium analysis: all types except the
rst quickly run down their excess savings, and
after a few years, only 10 percent of the US debt
is held by superrich US residents. The second
panel from the top shows our general equilib-
rium benchmark instead, in which the debt is
continuously held domestically.
4
This visual-
izes the trickling-up phenomenon: the share of
wealth held by the rich initially rises (the para-
metric restriction for a hump shape is satised),
4
Aggarwal et al. (2022) consider an intermediate
case where the United States is a partially open economy.
With home bias in spending, the outcome is similar to our
closed-economy simulations, except that we can interpret
the top 1 percent as the foreigners.
and the superrich keep accumulating assets
until they hold all of the excess savings. The
third panel from the top shows what happens
under a tight monetary policy scenario, with
ϕ = 1.5 . The qualitative trickling-up patterns
are unchanged, but the monetary response does
speed up the adjustment process. The bottom
F4. D E D
E S C
0
0.5
1
1. 5
2
2.5
Percent of GDP
Consumption
0 5 10 15 20 25 30 35 40
Quarters
Partial equilibrium
Easy monetary policy
Tight monetary policy
0
2
4
6
Percent of GDP
Excess savings: Tight monetary policy
0 5 10 15 20 25 30 35 40
Quarters
0 5 10 15 20 25 30 35 40
Quarters
0
2
4
6
Percent of GDP
Excess savings: Partial equilibrium
Bottom 80%
Next 19%
Top 1%
0 5 10 15 20 25 30 35 40
Quarters
0
2
4
6
Percent of GDP
Excess savings: Easy monetary policy
VOL. 113
75
THE TRICKLING UP OF EXCESS SAVINGS
panel summarizes the effect of excess sav-
ings on aggregate consumption. These effects
are long-lasting and signicant. In addition
to speeding up the adjustment, the monetary
response brings down the level of demand.
Table1 summarizes our results by display-
ing the duration of output and excess savings
for the middle class and the rich under each of
our scenarios. The partial equilibrium scenario
summarizes the conventional wisdom, accord-
ing to which the effect of excess savings will
dissipate in a few quarters. By contrast, our
benchmark scenario suggests that these effects
will stick around for roughly ve years. These
numbers are larger if MPCs are lower, and they
are robust to plausible alternative calibrations.
Rational expectations about the future boom
make the response much larger on impact due
to current spending out of anticipated income,
which turns out to speed up the trickling-up
process. Tight monetary policy, on the other
hand, also speeds up trickling up, but it does
so by mitigating the effects of excess savings
on demand. In either case, however, the dura-
tion of excess savings and output remains more
than twice as long as the conventional wisdom
suggests.
REFERENCES
Aggarwal, Rishabh, Adrien Auclert, Matthew
Rognlie, and Ludwig Straub.
2022. “Excess
Savings and Twin Decits: The Transmission
of Fiscal Stimulus in Open Economies.” In
NBER Macroeconomics Annual 2022, Vol. 37,
edited by Martin Eichenbaum, Erik Hurst, and
Valerie A. Ramey.
Aladangady, Aditya, David Cho, Laura Feiveson,
and Eugenio Pinto.
2022. “Excess Savings
during the COVID-19 Pandemic.” FEDS
Notes, Board of Governors of the Federal
Reserve System, October 21. https://doi.
org/10.17016/2380-7172.3223.
Auclert, Adrien, Matthew Rognlie, and Ludwig
Straub.
2018. “The Intertemporal Keynesian
Cross.” NBER Working Paper 25020.
Farhi, Emmanuel, and Iván Werning. 2019.
“Monetary Policy, Bounded Rationality, and
Incomplete Markets.” American Economic
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