The Distribution of Wealth and
the Marginal Propensity to Consume
Christopher Carroll1
Jiri Slacalek2
1 Johns
Kiichi Tokuoka3
Matthew N. White4
Hopkins University and NBER
2 European
3 Ministry
Central Bank
of Finance, Japan
4 University
of Delaware
Household Wealth Data and Public Policy
IFS/Public Economics UK Conference
Marginal Propensity to Consume
The Question: How Large Is the MPC (≡ κ)?
If households receive a surprise one-off EUR 1 in income,
how much more will be in aggregate spent over the next year?
Why Do We Care?
I
I
MPC reflects size of economy’s response to fiscal stimulus
1
Crude Keynesianism: Transitory tax cut multiplier = 1−κ
−1
I
If κ = 0.75, then multiplier is 4 − 1 = 3
I
If κ = 0.05, then multiplier is only ≈ 0.05
I
I
Some micro estimates of κ are this large
This is about the size of κ in RBC models
Our Claim: Heterogeneity Is Key To Modeling the MPC
Need to Consider:
I
Households are heterogeneous
I
Wealth is unevenly distributed
I
C function is highly concave
I
⇒ Distributional issues matter for aggregate C
Giving EUR 1 to the poor 6= giving EUR 1 to the rich
Concavity of Consumption Function and Wealth Heterogeneity
0.2
1.5
ConsumptionHquarterlyL permanent
income ratio Hleft scaleL
¯
1.0
0.15
0.1
Histogram: empirical HSCF1998L density of
mt Hpt Wt L Hright scaleL
0.05
¯
0.5
0.0
0
5
10
15
20
mt Hpt Wt L
0.
To-Do List
1. Calibrate realistic income process
2. Match empirical wealth distribution
3. Back out optimal C and MPC out of transitory income
4. Is MPC in line with empirical estimates?
Our (Micro) Income Process
I
Motivated by Friedman’s (1957) Permanent Income Hypothesis
I
Idiosyncratic (household) income process:
y t+1 = pt+1 ξt+1 W
pt+1 = pt ψt+1
pt permanent income
ξt transitory income
I
ψt+1 permanent shock
W aggregate wage rate
ξt incorporates unemployment insurance (Carroll (1992)):
ξt
= µ with probability u
¯ t with probability 1 − u
= (1 − τ )`θ
µ UI when unemployed
τ rate of tax collected for the unemployment benefits
Decision Problem
v(mt )
=
h
i
1−ρ
max u(ct ) + β DEt ψt+1
v(mt+1 )
{ct }
s.t.
at
=
mt − ct
at
≥
0
kt+1
=
at /(Dψt+1 )
mt+1
=
r
=
(k + r )kt+1 + ξt+1
¯L)α−1
K /`L
αZ (K
Variables normalized by pt W
Parameter Values
I
¯ µ , and u taken from JEDC special volume
β, ρ, α, δ, `,
I
Key new parameter values:
Description
Param
Value
Source
Prob of Death per Quarter
Variance of Log ψt
D
σψ2
0.00625
0.016/4
Variance of Log θt
σθ2
0.010 × 4
Life span of 40 years
Carroll (1992); SCF
DeBacker et al. (2013)
Carroll (1992)
Annual Income, Earnings, or Wage Variances
?
Our parameters
σψ2
0.016
σξ2
0.010
Carroll (1992)
Storesletten, Telmer, and Yaron (2004)
Meghir and Pistaferri (2004)?
Low, Meghir, and Pistaferri (2010)
Blundell, Pistaferri, and Preston (2008)?
DeBacker, Heim, Panousi, Ramnath, and Vidangos (2013)
0.016
0.008–0.026
0.031
0.011
0.010–0.030
0.007–0.010
0.010
0.316
0.032
−
0.029–0.055
0.15–0.20
Implied by KS-JEDC
Implied by Castaneda et al. (2003)
0.000
0.03
0.038
0.005
Meghir and Pistaferri (2004) and Blundell, Pistaferri, and Preston (2008) assume that the transitory component is serially correlated (an MA
2
process), and report the variance of a subelement of the transitory component. σξ
for these articles are calculated using their MA estimates.
Typology of Our Models—Three Dimensions
1. Discount Factor β
I
I
‘β-Point’ model: Single discount factor
‘β-Dist’ model: Uniformly distributed discount factor
2. Empirical Wealth Variable to Match
I
I
Net Worth
Liquid Financial Assets
3. Life Cycle
I
I
Perpetual Youth (a la Blanchard)
Overlapping Generations
Dimension 1: Estimation of β-Point and β-Dist
‘β-Point’ model
I ‘Estimate’ single β̀ by matching the capital–output ratio
‘β-Dist’ model—Heterogenous Impatience
I Assume uniformly distributed β across households
I Estimate the band [β̀ − ∇, β̀ + ∇] by
minimizing distance between model (w ) and data (ω) net worth
held by the top 20, 40, 60, 80%
X
min
(wi − ωi )2
{β̀,∇}
i=20,40,60,80
s.t. aggregate net worth–output ratio matches steady-state value from the perfect foresight model
Results: Wealth Distribution
F
1
0.75
US data HSCFL
KS-JEDC
Β-Point
Β-Dist
0.5
0.25
0
0
25
50
75
100
Percentile
Results: Wealth Distribution
Micro Income Process
Friedman/Buffer Stock
Point
Discount
Factor‡
Top 1%
Top 20%
Top 40%
Top 60%
Top 80%
KS-Orig
KS-JEDC
Our solution
β-Point
Uniformly
Distributed
Discount
Factors?
β-Dist
8.6
54.3
76.6
90.
97.5
28.4
83.4
93.8
97.4
99.3
3.
39.5
65.4
83.6
95.1
Hetero
U.S.
Data∗
3.0
35.0
Y t = 10.3.
Notes: ‡ : β̀ = 0.9894. ? : (β̀, ∇) = (0.9867, 0.0067). Bold points are targeted. K t /Y
24.0
88.0
29.6
79.5
92.9
98.7
100.4
Marginal Propensity to Consume and Net Worth
ct
1.5
f
0.6
Most Impatient Hleft scaleL ¯
Identical Patience
Hleft scaleL ¯
1.0
0.4
­ Most Patient Hleft scaleL
0.3
0.2
Representative agent's net worth ®
Histogram: empirical density of
net worth Hright scaleL
¯
0.5
0.0
0.5
0
5
10
15
0.1
mt
20
0.
Results: MPC (in Annual Terms)
Micro Income Process
Friedman/Buffer Stock
Overall average
By wealth/permanent income ratio
Top 1%
Top 20%
Top 40%
Top 60%
Bottom 1/2
By employment status
Employed
Unemployed
Notes: Annual MPC is calculated by 1 − (1−quarterly MPC)4 .
KS-JEDC
β-Point
β-Dist
Our solution
0.1
0.23
0.05
0.06
0.06
0.06
0.07
0.13
0.05
0.06
0.08
0.12
0.35
0.04
0.04
0.04
0.04
0.05
0.09
0.23
0.2
0.54
0.05
0.06
Estimates of MPC in the Data: ∼0.2–0.6
Consumption Measure
Authors
Nondurables
Blundell et al. (2008b)‡
0.05
Coronado et al. (2005)
Hausman (2012)
Johnson et al. (2009)
∼ 0.25
Lusardi (1996)‡
0.2–0.5
Parker (1999)
0.2
Parker et al. (2011)
0.12–0.30
Sahm et al. (2009)
Shapiro and Slemrod (2009)
Souleles (1999)
0.045–0.09
Souleles (2002)
0.6–0.9
Notes: ‡ : elasticity.
Durables
Total PCE
0.36
0.6–0.75
0.29–0.54
0.50–0.90
∼ 1/3
∼ 1/3
0.34–0.64
Horizon
1 Year
1 Year
3 Months
3
3
1
1
3
1
Months
Months
Year
Year
Months
Year
Event/Sample
Estimation Sample: 1980–92
2003 Tax Cut
1936 Veterans’ Bonus
2003 Child Tax Credit
Estimation Sample: 1980–87
Estimation Sample: 1980–93
2008 Economic Stimulus
2008 Economic Stimulus
2008 Economic Stimulus
Estimation Sample: 1980–91
The Reagan Tax Cuts
of the Early 1980s
Typology of Our Models—Three Dimensions
1. Discount Factor β
I
I
‘β-Point’ model: Single discount factor
‘β-Dist’ model: Uniformly distributed discount factor
2. Empirical Wealth Variable to Match
I
I
Net Worth
Liquid Financial Assets
3. Life Cycle
I
I
Perpetual Youth (a la Blanchard)
Overlapping Generations
Dimension 2: Matching Net Worth vs. Liquid Financial Assets
f
0.6
ct
1.5
­ Most impatient Hleft scaleL
Most patient Hleft scaleL
¯
1.0
0.4
0.3
¬ Histogram: empirical density of
liquid financial asset + retirement assets
Hright scaleL
Histogram: empirical density of
net worth Hright scaleL
¯
0.5
0.0
0.5
0
5
10
15
mt
Liquid Assets ≡ transaction accounts, CDs, bonds, stocks, mutual funds
0.2
0.1
20
0.
Matching Net Worth vs. Liquid Financial Assets
I
Buffer stock saving driven by accumulation of liquidity
I
May make more sense to match liquid (and retirement) assets
(Hall (2011), Kaplan and Violante (2011))
I
Aggregate MPC Increases Substantially: 0.23 ↑ 0.43
Overall average
By wealth/permanent income ratio
Top 1%
Top 20%
Top 40%
Top 60%
Bottom 1/2
Notes: Annual MPC is calculated by 1 − (1−quarterly MPC)4 .
Net Worth
β-Dist
Liq Fin and Ret Assets
0.23
0.43
0.05
0.06
0.08
0.12
0.35
0.12
0.13
0.2
0.28
0.59
Distribution of MPCs
Wealth Heterogeneity Translates into Heterogeneity in MPCs
Percentile
100
75
50
KS-JEDC
25
Matching net worth
Matching liquid financial + retirement assets
0
0
0.25
0.5
0.75
1
Annual MPC
Typology of Our Models—Three Dimensions
1. Discount Factor β
I
I
‘β-Point’ model: Single discount factor
‘β-Dist’ model: Uniformly distributed discount factor
2. Empirical Wealth Variable to Match
I
I
Net Worth
Liquid Financial Assets
3. Life Cycle
I
I
Perpetual Youth (a la Blanchard)
Overlapping Generations
Dimension 3: Overlapping Generations
Realistic Life-Cycle Model
I
Three education levels: e ∈ {D, HS, C }
I
Age/education-specific income profiles
yt
pt
I
I
I
= ξt p t = (1 − τ )θt p t ,
= ψt ψ es p t−1
Age-specific variances of income shocks
Transitory unemployment shock with prob u
Household-specific mortality Des
Household Decision Problem
ves (mt )
=
h
i
1−ρ
max u(ct ) + β Des Et ψt+1
ves+1 (mt+1 )
ct
s.t.
at
=
mt − ct ,
kt+1
=
at /ψt+1 ,
mt+1
=
(k + r )kt+1 + ξt+1 ,
at
≥
0
Calibration
Description
Coefficient of relative risk aversion
Effective interest rate
Population growth rate
Technological growth rate
Rate of high school dropouts
Rate of high school graduates
Rate of college graduates
Average initial permanent income, dropout
Average initial permanent income, high school
Average initial permanent income, college
Unemployment insurance payment
Unemployment rate
Labor income tax rate
Parameter
Value
ρ
(r − δ)
N
Γ
θD
θHS
θC
p D0
p HS0
pC0
µ
u
τ
1
0.01
0.0025
0.0037
0.11
0.55
0.34
5000
7500
12000
0.15
0.07
0.0942
Results: Wealth Distribution in Life Cycle Model
F
1
0.75
US data HSCFL
KS-JEDC
Β-Point
Β-Dist
0.5
0.25
0
0
25
50
75
100
Percentile
Results: MPC (in Annual Terms)
Micro Income Process
Wealth Measure
KS-JEDC
Our solution
NW
FBS
β-Dist
NW
Overall average
0.05
0.23
By wealth/permanent income ratio
Top 1%
0.04
0.05
Top 20%
0.04
0.06
Top 40%
0.04
0.08
Top 60%
0.04
0.12
Bottom 1/2
0.05
0.35
By employment status
Employed
0.05
0.2
Unemployed
0.06
0.54
Notes: Annual MPC is calculated by 1 − (1−quarterly MPC)4 .
Life-Cycle Model
β-Point
NW
β-Dist
NW
β-Dist
Liquid
0.11
0.29
0.42
0.08
0.09
0.08
0.08
0.13
0.07
0.07
0.07
0.10
0.49
0.07
0.07
0.11
0.20
0.70
0.10
0.13
0.28
0.39
0.42
0.56
Results: MPC by Age
MPC
1
0.75
Most impatient
0.5
Population average
0.25
Most patient
0
30
40
50
60
70
80
90
Age
100
I Initial drop in MPC: Build-up of buffer stock
I Rise while rapid income growth, fall before retirement, then increasing mortality risk
Empirical Wealth Distribution Across Countries
Eurosystem Household Finance and Consumption Survey (HFCS)
I
Detailed wealth data from 15 euro area countries
I
Ex ante harmonized, country-representative
I
62,000 households
I
First wave released in April 2013, second planned for 2016
I
http://www.ecb.europa.eu/home/html/researcher_hfcn.en.html
st
Be ria
lg
iu
m
C
yp
G rus
er
m
an
y
Sp
ai
Fi n
nl
an
Fr d
an
c
G e
re
ec
e
Lu
xe Ital
m y
bo
ur
g
M
N
al
et
he ta
rla
n
Po ds
rtu
Sl gal
ov
e
Sl nia
ov
ak
ia
Au
0
Wealth-Income Ratios (Quarterly)
100
150
50
European Evidence—Wealth Distribution
excludes outside values
Net Wealth
Liquid Assets
e
Au s
st
Be ria
lg
iu
m
C
yp
G rus
er
m
an
y
Sp
a
Fi in
nl
an
Fr d
an
c
G e
re
ec
e
Lu
xe Ital
m y
bo
ur
Th
g
e
M
N
al
et
he ta
rla
n
Po ds
rtu
Sl gal
ov
e
Sl nia
ov
ak
ia
nt
ri
ou
lC
Al
0
0.1
Aggregate MPC
0.3
0.2
0.4
0.5
MPC Across European Countries—A bit Lower than US
Wealth Inequality and MPC
0.4
0.5
W inequality implies higher MPC, especially for liquid assets
ES
Aggregate MPC
0.2
0.3
GR
PT
IT
DE
SKLU
MT
FR
SI
FI
BE
ALL
CY
AT
DE
NL
AT
0.1
ES
SK
SIGR
IT
MT
BE
PT
FR
CYFI
ALL
LU
NL
0
I
0.4
0.5
0.6
Gini Coefficient
0.7
0.8
Conclusions
What We Do
I
We solve a model that matches
I
I
Income dynamics
Wealth distribution
Results
I
The model produces more plausible implications about
I
I
Aggregate MPC
Distribution of MPC across households
References I
Blundell, Richard, Luigi Pistaferri, and Ian Preston (2008): “Consumption Inequality and Partial Insurance,” American Economic Review,
98(5), 1887–1921.
Carroll, Christopher D. (1992): “The Buffer-Stock Theory of Saving: Some Macroeconomic Evidence,” Brookings Papers on Economic
Activity, 1992(2), 61–156, http://econ.jhu.edu/people/ccarroll/BufferStockBPEA.pdf.
Castaneda, Ana, Javier Diaz-Gimenez, and Jose-Victor Rios-Rull (2003): “Accounting for the U.S. Earnings and Wealth Inequality,”
Journal of Political Economy, 111(4), 818–857.
DeBacker, Jason, Bradley Heim, Vasia Panousi, Shanthi Ramnath, and Ivan Vidangos (2013): “Rising Inequality: Transitory or
Permanent? New Evidence from a Panel of US Tax Returns,” mimeo.
Friedman, Milton A. (1957): A Theory of the Consumption Function. Princeton University Press.
Hall, Robert E. (2011): “The Long Slump,” AEA Presidential Address, ASSA Meetings, Denver.
Kaplan, Greg, and Giovanni L. Violante (2011): “A Model of the Consumption Response to Fiscal Stimulus Payments,” NBER Working
Paper Number W17338.
Krusell, Per, and Anthony A. Smith (1998): “Income and Wealth Heterogeneity in the Macroeconomy,” Journal of Political Economy, 106(5),
867–896.
Low, Hamish, Costas Meghir, and Luigi Pistaferri (2010): “Wage Risk and Employment Over the Life Cycle,” American Economic Review,
100(4), 1432–1467.
Meghir, Costas, and Luigi Pistaferri (2004): “Income Variance Dynamics and Heterogeneity,” Journal of Business and Economic Statistics,
72(1), 1–32.
Storesletten, Kjetil, Chris I. Telmer, and Amir Yaron (2004): “Cyclical Dynamics in Idiosyncratic Labor-Market Risk,” Journal of Political
Economy, 112(3), 695–717.
Friedman (1957): Permanent Income Hypothesis
Yt
= Pt + Tt
Ct
= Pt
Progress since then
I
Micro data: Friedman description of income shocks works well
I
Math: Friedman’s words well describe optimal solution to dynamic stochastic
optimization problem of impatient consumers with geometric discounting under
CRRA utility with uninsurable idiosyncratic risk calibrated using these micro
income dynamics (!)
Our (Micro) Income Process
Idiosyncratic (household) income process is logarithmic Friedman:
y t+1 = pt+1 ξt+1 W
pt+1 = pt ψt+1
pt = permanent income
ξt = transitory income
ψt+1 = permanent shock
W = aggregate wage rate
Further Details of Income Process
Modifications from Carroll (1992)
Transitory income ξt incorporates unemployment insurance:
ξt
= µ with probability u
¯ t with probability 1 − u
= (1 − τ )`θ
µ is UI when unemployed
τ is the rate of tax collected for the unemployment benefits
What Happens After Death?
I
You are replaced by a new agent whose permanent income is equal to the
population mean
I
Prevents the population distribution of permanent income from spreading out
What Happens After Death?
I
You are replaced by a new agent whose permanent income is equal to the
population mean
I
Prevents the population distribution of permanent income from spreading out
Ergodic Distribution of Permanent Income
Exists, if death eliminates permanent shocks:
DE[ψ 2 ] < 1.
Holds.
Population mean of p 2 :
M[p 2 ] =
D
1 − DE[ψ 2 ]
Dimension 2.a: Adding KS Aggregate Shocks
Model with KS Aggregate Shocks: Assumptions
I Only two aggregate states (good or bad)
I Aggregate productivity Zt = 1 ± 4Z
I Unemployment rate u depends on the state (u g or u b )
Parameter values for aggregate shocks from Krusell and Smith (1998)
Parameter
Z
4
ug
ub
Agg transition probability
Value
0.01
0.04
0.10
0.125
Dimension 2.b: Adding FBS Aggregate Shocks
Friedman/Buffer Stock Shocks
I Motivation:
More plausible and tractable aggregate process, also simpler
I Eliminates ‘good’ and ‘bad’ aggregate state
I Aggregate production function: K α
Lt )1−α
t (L
I L t = Pt Ξt
I Pt is aggregate permanent productivity
I Pt+1 = Pt Ψt+1
I Ξt is the aggregate transitory shock.
I Parameter values estimated from U.S. data:
Description
Variance of Log Ψt
Variance of Log Ξt
Parameter
Value
2
σΨ
σΞ2
0.00004
0.00001
Dimension 2.b: Adding FBS Aggregate Shocks
Friedman/Buffer Stock Shocks
I Motivation:
More plausible and tractable aggregate process, also simpler
I Eliminates ‘good’ and ‘bad’ aggregate state
I Aggregate production function: K α
Lt )1−α
t (L
I L t = Pt Ξt
I Pt is aggregate permanent productivity
I Pt+1 = Pt Ψt+1
I Ξt is the aggregate transitory shock.
I Parameter values estimated from U.S. data:
Description
Variance of Log Ψt
Variance of Log Ξt
Parameter
Value
2
σΨ
σΞ2
0.00004
0.00001
Results
Our/FBS model
I
A few times faster than solving KS model
I
The results are similar to those under KS aggregate shocks
Results: MPC Over the Business Cycle
Model: β-Dist
Krusell–Smith (KS)
Friedman/Buffer Stock (FBS)
Scenario
Base
Expnsn
Base
Large Bad
Perm Shock
Large Bad
Trans Shock
0.25
0.21
0.20
0.20
0.21
0.05
0.06
0.06
0.08
0.10
0.12
0.38
0.05
0.06
0.06
0.08
0.09
0.11
0.32
0.05
0.06
0.06
0.06
0.06
0.09
0.32
0.05
0.06
0.06
0.06
0.06
0.09
0.32
0.05
0.06
0.06
0.06
0.09
0.09
0.32
0.20
0.56
0.20
0.51
0.19
0.41
0.19
0.41
0.19
0.41
Recssn
Overall average
0.23
By wealth/permanent income ratio
Top 1%
0.05
Top 10%
0.06
Top 20%
0.06
Top 40%
0.08
Top 50%
0.09
Top 60%
0.12
Bottom 50%
0.35
By employment status
Employed
0.20
Unemployed
0.54
Results: MPC Over the Business Cycle
Krusell–Smith
I
Aggregate and idiosyncratic shocks positively correlated
I
Higher MPC during recessions, especially for the unemployed
Friedman/Buffer Stock
I
Shocks uncorrelated
I
MPC essentially doesn’t vary over BC
Macro Dynamics in Life-Cycle Model
I
Population growth N, technological progress Γ
I
Tax rate to finance social security and unemployment benefits: τ = τSS + τU
h
i
P384
Qt
P
I
τSS =
e∈{D,HS,C }
P
e∈{D,HS,C }
I
τU = uµ
θe p e0
h
θe p e0
t=164
P163
t=0
((1+Γ)(1+N))−t
((1+Γ)(1+N))
s=0 (ψ es Des )
Qt
−t
i
Des )
s=0 (ψ es