The Distribution of Wealth and the Marginal Propensity to Consume Christopher Carroll 1 Jiri Slacalek 2 Kiichi Tokuoka 3 Matthew N. White 4 1 Johns Hopkins University and NBER 2 European Central Bank 3 Ministry of Finance, Japan 4 University of Delaware Household Wealth Data and Public Policy IFS/Public Economics UK Conference
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The Distribution of Wealth and the Marginal Propensity to Consume · 2015-03-17 · The Distribution of Wealth and the Marginal Propensity to Consume Christopher Carroll1 Jiri Slacalek2
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The Distribution of Wealth andthe Marginal Propensity to Consume
Christopher Carroll1 Jiri Slacalek2 Kiichi Tokuoka3 Matthew N. White4
1Johns Hopkins University and NBER
2European Central Bank
3Ministry of Finance, Japan
4University 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 MPC reflects size of economy’s response to fiscal stimulusI Crude Keynesianism: Transitory tax cut multiplier = 1
1−κ − 1I If κ = 0.75, then multiplier is 4− 1 = 3
I Some micro estimates of κ are this large
I If κ = 0.05, then multiplier is only ≈ 0.05I 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 CGiving EUR 1 to the poor 6= giving EUR 1 to the rich
Concavity of Consumption Function and Wealth Heterogeneity
Consumption�HquarterlyL permanentincome ratio Hleft scaleL¯
mt�HptWtL
Histogram: empirical HSCF1998L density ofmt�HptWtL Hright scaleL
¯
0 5 10 15 200.0
0.5
1.0
1.5
0.
0.05
0.1
0.15
0.2
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:
yyy t+1 = pt+1ξt+1W
pt+1 = ptψt+1
pt permanent income ψt+1 permanent shockξt transitory income W aggregate wage rate
I ξt incorporates unemployment insurance (Carroll (1992)):
ξt = µ with probability u
= (1− τ)¯̀θt with probability 1− u
µ UI when unemployedτ rate of tax collected for the unemployment benefits
Decision Problem
v(mt) = max{ct}
u(ct) + β�DEt
[ψ1−ρt+1v(mt+1)
]s.t.
at = mt − ct
at ≥ 0
kt+1 = at/(�Dψt+1)
mt+1 = (k + r)kt+1 + ξt+1
r = αZ (KKK/¯̀LLL)α−1
Variables normalized by ptW
Parameter Values
I β, ρ, α, δ, ¯̀, µ , and u taken from JEDC special volume
I Key new parameter values:
Description Param Value Source
Prob of Death per Quarter D 0.00625 Life span of 40 yearsVariance of Log ψt σ2
ψ 0.016/4 Carroll (1992); SCFDeBacker et al. (2013)
Variance of Log θt σ2θ 0.010× 4 Carroll (1992)
Annual Income, Earnings, or Wage Variances
σ2ψ σ2
ξ
Our parameters 0.016 0.010
Carroll (1992) 0.016 0.010Storesletten, Telmer, and Yaron (2004) 0.008–0.026 0.316Meghir and Pistaferri (2004)? 0.031 0.032Low, Meghir, and Pistaferri (2010) 0.011 −Blundell, Pistaferri, and Preston (2008)? 0.010–0.030 0.029–0.055DeBacker, Heim, Panousi, Ramnath, and Vidangos (2013) 0.007–0.010 0.15–0.20
Implied by KS-JEDC 0.000 0.038Implied by Castaneda et al. (2003) 0.03 0.005
?Meghir and Pistaferri (2004) and Blundell, Pistaferri, and Preston (2008) assume that the transitory component is serially correlated (an MA
process), and report the variance of a subelement of the transitory component. σ2ξ for these articles are calculated using their MA estimates.
2. Empirical Wealth Variable to MatchI Net WorthI Liquid Financial Assets
3. Life CycleI Perpetual Youth (a la Blanchard)I Overlapping Generations
Dimension 3: Overlapping Generations
Realistic Life-Cycle Model
I Three education levels: e ∈ {D,HS ,C}I Age/education-specific income profiles
yyy t = ξtpppt = (1− τ)θtpppt ,
pppt = ψtψespppt−1
I Age-specific variances of income shocksI Transitory unemployment shock with prob u
I Household-specific mortality Des
Household Decision Problem
ves(mt) = maxct
u(ct) + β�DesEt
[ψ1−ρt+1ves+1(mt+1)
]s.t.
at = mt − ct ,
kt+1 = at/ψt+1,
mt+1 = (k + r)kt+1 + ξt+1,
at ≥ 0
Calibration
Description Parameter Value
Coefficient of relative risk aversion ρ 1Effective interest rate (r − δ) 0.01Population growth rate N 0.0025Technological growth rate Γ 0.0037Rate of high school dropouts θD 0.11Rate of high school graduates θHS 0.55Rate of college graduates θC 0.34Average initial permanent income, dropout pppD0 5000Average initial permanent income, high school pppHS0 7500Average initial permanent income, college pppC0 12000Unemployment insurance payment µ 0.15Unemployment rate u 0.07Labor income tax rate τ 0.0942
Notes: The figure shows the range of aggregate MPCs spanned by the estimates based on the distribution of net wealth (lower bound) and of liquidassets (upper bound).
Wealth Inequality and MPCI W inequality implies higher MPC, especially for liquid assets
ALL
AT
BE
CY
DE
ES FIFR
GR
IT LUMT NLPTSISK
ALLAT
BECYDE
ES
FIFR
GR
IT
LU
MTNL
PT
SI
SK
00.
10.
20.
30.
40.
5A
ggre
gate
MP
C
0.4 0.5 0.6 0.7 0.8Gini Coefficient
Net Wealth Liquid Assets
Conclusions
What We Do
I We solve a model that matchesI Income dynamicsI Wealth distribution
Results
I The model produces more plausible implications aboutI Aggregate MPCI 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 EconomicActivity, 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 orPermanent? 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 WorkingPaper 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 PoliticalEconomy, 112(3), 695–717.
I Micro data: Friedman description of income shocks works well
I Math: Friedman’s words well describe optimal solution to dynamic stochasticoptimization problem of impatient consumers with geometric discounting underCRRA utility with uninsurable idiosyncratic risk calibrated using these microincome dynamics (!)
Our (Micro) Income Process
Idiosyncratic (household) income process is logarithmic Friedman: