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 [email protected]2 European Central Bank [email protected]3 Ministry of Finance, Japan [email protected]4 University of Delaware [email protected]“Serious” Microfoundations ⇒ High MPC Defining ‘the MPC’ (≡ κ)? If households receive a surprise extra 1 unit of income, how much will be in aggregate spent over the next year? Elements that interact with each other to produce the result: I Households are heterogeneous I Wealth is unevenly distributed I c function is highly concave I ⇒ Distributional issues matter for aggregate C Giving 1 to the poor 6= giving 1 to the rich Consumption Concavity and Wealth Heterogeneity 0.00 0.05 0.10 0.15 0.20 ConsumptionHquarterlyL perm income ratio Hleft scaleL fl m t Rep agent's ratio of M to HquarterlyL perm income fi Histogram: empirical HSCF2004L density of m t Hright scaleL fl 0 5 10 15 20 0.0 0.5 1.0 1.5 Why Worry About the MPC (≡ κ)? Nobody trying to make a forecast in 2008–2010 would ask: I Big ‘stimulus’ tax cuts I Keynesian multipliers should be big in liquidity trap I Crude Keynesianism: Transitory tax cut multiplier is 1/(1 - κ) - 1 I 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 ≈ 0.05 I This is about the size of κ in Rep Agent and KS models
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The Distribution of Wealth andthe Marginal Propensity to Consume
Christopher Carroll1 Jiri Slacalek2 Kiichi Tokuoka3 Matthew N. White4
If households receive a surprise extra 1 unit of income,how much will be in aggregate spent over the next year?
Elements that interact with each other to produce the result:
I Households are heterogeneous
I Wealth is unevenly distributed
I c function is highly concave
I ⇒ Distributional issues matter for aggregate CGiving 1 to the poor 6= giving 1 to the rich
Consumption Concavity and Wealth Heterogeneity
0.00
0.05
0.10
0.15
0.20
Consumption�HquarterlyL perm
income ratio Hleft scaleL¯
mt
Rep agent's ratio of
M to HquarterlyL perm income ®
Histogram: empirical HSCF2004Ldensity of mt Hright scaleL
¯
0 5 10 15 200.0
0.5
1.0
1.5
Why Worry About the MPC (≡ κ)?
Nobody trying to make a forecast in 2008–2010 would ask:
I Big ‘stimulus’ tax cuts
I Keynesian multipliers should be big in liquidity trapI Crude Keynesianism: Transitory tax cut multiplier is
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 Rep Agent and KS models
Microeconomics of Consumption
Since Friedman’s (1957) PIH:
I c chosen optimally:Goal: smooth c in light of beliefs about y fluctuations
I Single most important thing to get right is income dynamics!I With smooth c , income dynamics drive everything!
I Saving/dissaving: Depends on whether E[∆y ] ↑ or E[∆y ] ↓I Wealth distribution depends on integration of saving
I Cardinal sin: Assume crazy income dynamicsI Throws out the defining core of the intellectual framework
Our Goal: “Serious” Microfoundations
Requires three changes to well-known Krusell–Smith (1998) model:
1. Sensible microeconomic income process: Friedman
2. Finite lifetimes: Blanchard
3. Match wealth distributionI Here, achieved by preference heterogeneityI View it as a proxy for many kinds of heterogeneity
I AgeI Optimism/Pessimism about GrowthI Risk aversionI Rate of ReturnI . . .
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 Question:Does a model that matches micro facts about income dynamicsand wealth distribution give different (and more plausible) answersthan KS to macroeconomic questions (say, about the response ofconsumption to fiscal ‘stimulus’)?
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 todynamic stochastic optimization problem of impatientconsumers with geometric discounting under CRRA utilitywith uninsurable idiosyncratic risk calibrated using these microincome dynamics (!)
Our (Micro) Income Process
Idiosyncratic (household) income process is logarithmic Friedman:
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 (2014))
I Aggregate MPC Increases Substantially: 0.23 ↑ 0.43
β-DistNet Worth Liq Fin and Ret Assets
Overall average 0.23 0.44
By wealth/permanent income ratioTop 1% 0.05 0.12Top 20% 0.06 0.13Top 40% 0.08 0.2Top 60% 0.12 0.28Bottom 1/2 0.35 0.59
Notes: Annual MPC is calculated by 1− (1−quarterly MPC)4.
Distribution of MPCs
Wealth heterogeneity translates into heterogeneity in MPCs
Annual MPC
KS-JEDC
KS-Hetero
Matching net worth
Matching liquid financial + retirement assets
0 0.25 0.5 0.75 10
25
50
75
100Percentile
Typology of Our Models—Four Dimensions
1. Discount Factor β
I ‘β-Point’ model: Single discount factorI ‘β-Dist’ model: Uniformly distributed discount factor
2. Aggregate Shocks
I (No)I Krusell–SmithI Friedman/Buffer Stock
3. Empirical Wealth Variable to Match
I Net WorthI Liquid Financial Assets
4. Life Cycle
I Perpetual Youth (a la Blanchard)I Overlapping Generations
Dimension 4: Overlapping Generations
Realistic Life-Cycle Model
I Three education levels: e ∈ {D,HS ,C}I Age/education-specific income profiles
yt = 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
Macro Dynamics
I Population growth N, technological progress Γ
I Tax rate to finance social security and unemployment benefits:τ = τSS + τU
I τSS =
∑e∈{D,HS,C}
[θepppe0
∑384t=164
(((1+Γ)(1+N))−t
∏ts=0(ψes�Des)
)]∑
e∈{D,HS,C}
[θepppe0
∑163t=0
(((1+Γ)(1+N))−t
∏ts=0(ψes�Des)
)]I τU = uµ
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: Annual MPC is calculated by 1− (1−quarterly MPC)4.
Results: MPC by Age
Most patient
Most impatient
Population average
30 40 50 60 70 80 90 100Age0
0.25
0.5
0.75
1MPC
I Initial drop in MPC: Build-up of buffer stock
I Rise while rapid income growth, fall before retirement, then incrsing mortlty risk
Conclusions
I Definition of “serious” microfoundations: Model that matchesI Income DynamicsI Wealth Distribution
I The model produces more plausible implications about:I Aggregate MPCI Distribution of MPC Across Households
I Version with more plausible aggregate specification issimpler, faster, better in every way!
References I
Blundell, Richard, Luigi Pistaferri, and Ian Preston (2008): “Consumption Inequality and PartialInsurance,” 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): “RisingInequality: Transitory or Persistent? New Evidence from a Panel of U.S. Tax Returns,” Brookings Papers onEconomic Activity, Spring, 67–122.
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 (2014): “A Model of the Consumption Response to Fiscal StimulusPayments,” Econometrica, 82(4), 1199–1239.
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 LifeCycle,” American Economic Review, 100(4), 1432–1467.
Meghir, Costas, and Luigi Pistaferri (2004): “Income Variance Dynamics and Heterogeneity,” Journal ofBusiness and Economic Statistics, 72(1), 1–32.
Storesletten, Kjetil, Chris I. Telmer, and Amir Yaron (2004): “Cyclical Dynamics in IdiosyncraticLabor-Market Risk,” Journal of Political Economy, 112(3), 695–717.