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Consumption and “Full Wealth”
• Since Modigliani () we have known that consumption should depend on all current and future resources, including all components of wealth
• I call this PDV of all resources “full wealth” = M
HRS Data: Unprecedented Ability to Measure Full
Wealth
• Expected present value of resources deterministic for older households:
M = Human Wealth + Net Worth
• Human Wealth=Earnings+Pensions+Social Security+Other Transfers
• Net Worth = 10 categories of assets less 3 categories of debt
HRS: New Consumption Data
• 2001 & 2003 Consumption and Activities Mailout Survey (CAMS)– Covers >90% of total expenditures as measured by
the CEX
• Consumption & Full Wealth Together– enables household level analysis of the propensity
to consume using the right measure of resources
Full Wealth Looks Different
.1.2
.3.4
.5
55 60 65 70 75age_head
Consumption/Full Wealth Consumption/Net WorthConsumption/Cash-on-Hand
Age Profile of Consumption/Wealth
2000
0040
0000
6000
0080
0000
1000
000
55 60 65 70 75age_head
Full Wealth Net WorthCash-on-Hand
Age Profile of Wealth
Dispersion of Full Wealth0
.2.4
.6.8
1
0 .2 .4 .6 .8 1Cumulative population proportion
Lorenz(hhpvw_2pct_adj) Lorenz(h6atota)Cumulative population proportion
Coefficients of VariationFull Wealth 0.96 (mean $825,000)
Net Worth 1.67 (mean $322,000)
Income 1.21 (mean $61,600)
Consumption 0.77 (mean $40,300)
C/M 0.78 (mean 0.077)
Average Propensity to Consume out of Full Wealth
• Construct full wealth and total consumption measures to get C/M
• Test predictions about C/M from a simple neoclassical model
• Evaluate additions to the model
Findings – Part 1
• Given an appropriate time preference parameter, a simple neoclassical model with mortality hazard can approximately match the mean age profile of C/M
Findings Part 2: Heterogeneity
• Observed heterogeneity across households suggests heterogeneous time preferences– Time preference and C/M are tightly linked in the
model
– With identical time preferences, the model cannot explain much heterogeneity across households.
– Heterogeneous time preferences do well in explaining observed variation by level of income or wealth
– Some additions to the model matter, but still leave a role for heterogeneous preferences.
Literature• HRS wealth measures: other papers have constructed
wealth/pension measures (Gustman & Steinmeier)• Lifecycle and buffer stock: find that households
closer to retirement act more like neoclassical/certainty equivalence (Carroll ; Gourinchas&Parker 2002…)– Labor income uncertainty: many papers in this literature
focus on effects of stochastic income; not relevant here given my model and age of households
• Optimal wealth accumulation: don’t use consumption data (Engen et al1999; Scholtz et al 2002)
Neoclassical Model
• Only uncertainty in model is mortality and rate of return (Merton)
Implications:• C/M depends only on preferences, stochastic
return characteristics, and mortality. • Does not depend on level of full wealth,
income profile, or outcome of past income shocks
Neoclassical Model with Stochastic Returns
Subject to:
1)()(0
)(0
),(
1CCULetdtCUT
et
c ttEMax
dzdtCMrrMdM )(
*2
)(
rSolution for optimal portfolio share:
The value function:
2])([*),(
1max),(),(
2221
,
MCMrrMtMC
tMtM mmm
c
t VVVV
The Bellman equation:
dC
eEMaxtMVT
t
tt
c
tT
t
1
),(1
)(
},{
Estimate mortality with Gompertz function: age = 1 e(2*age)
Average Propensity to Consume
Infinite Horizon:
]2
)()[1
1()( 22
rrM
C
)1(
]21
)()[1()(
)](2
1)()[1()(
22
22
e
rr
M
CTtrr
In the special case where r, μ, and σ are constant, then α* is constant and dA/dt=0 which gives:
Finite Horizon:
Data - HRS
Health and Retirement Survey• Nationally representative panel of ages 50+ • Seven waves since 1992• Sample updated with new 51-56 year-olds in 1998• Detailed socioeconomic, income, wealth, health,
employment history, family• Some attitudes, subjective expectations, plans etc.• Complete Social Security earnings histories• Employer-reported pension formulas
Data – Human Wealth
Components Expected earnings for non-retired – projected from current earnings
based primarily on experience and tenure Present value of defined benefit and defined contribution pension plans
– HRS pension calculator with adjustments & using survey report of expected retirement age
Present value of Social Security benefits Government benefits – veterans, disability, approximate “income
floor” based on SSI
All human capital is after-tax (approximate year-specific tax rates) and discounted, including an age and gender-specific mortality hazard
Data - Consumption
2001 & 2003 Consumption and Activities Mailout Survey (CAMS)
Sent to approximately ½ of the households in the HRS sample
2001 response rate 77% = 3,866 househoId obs My sample: approx 2,000 households
• In CAMS, in the HRS or WB cohorts, Social Security match, and still in the sample for the 2002 wave
• 26 expenditure categories covering equivalent of >90% of total expenditures measured by the CEX
• I also impute rental equivalence and vehicle consumption with predicted values based on CEX
Predicted vs. Actual C/M Mean Age Profile
0.0
5.1
.15
55 60 65 70 75age_head
95% CI Predicted C/MActual C/M Median Spline of Actual
r=.02; μ=.06;σ=.2; ρ=.02; γ=2
Sequence of pictures just changing lines:
1. mean, median, predicted@rho=.02
2. “It’s all about rho” Mean & predicted@rho to match mean
3. Heterogeneity: add confidence intervals to 1st pic
Invariance
• Model implies invariance to past income shocks and C linear in M, so C/M independent of level of M.
• ∆C/M does not depend on past income shocks
• But…C/M does depend on level of wealth
C/M Varies by Income or Wealth Level
.05
.1.1
5P
red
icte
d a
nd A
ctu
al C
/M
9 10 11 12Log Income
95% CI Actual C/MPredicted C/M Median Spline of Actual
Changing ρ Doesn’t Help Unless Heterogeneous
Note: do without confidence intervals
Heterogeneous Preferences
• People’s preferences differ, not controversial
• Evidence for heterogeneous preferences (Barsky et al, others…)
• Here have enough data to make progress on time preference heterogeneity– Investigate and eliminate other possible sources of
variation within the model – Evaluate some alternatives outside the model
Few Sources of Variation Within the Model (other than preferences)
• Model allows for variation by age (through mortality) and differing rate of return expectations– Mortality: estimated with a Gomperts function based on life
tables – Returns: estimated using HRS questions on stock return
expectations
→ predicted C/M covaries only slightly with actual C/M (R2 of .02, simple correlation .20)
• Changing values of r or using actual versus optimal risky asset share doesn’t help
Measurement Error
Additions/Alternatives:Liquidity Constraints
• Common addition to a lifecycle model (although often found not binding at older ages)
• Of particular concern here since full wealth includes illiquid assets that can’t be borrowed against
• But, using full wealth, theory says the effect of liquidity constraints is unambiguous (Carroll&Kimball 2001):
push C/M ↓
No Evidence of Liquidity Constraints.0
6.0
8.1
.12
Act
ual C
/M
0 .2 .4 .6Fraction of Full Wealth in Liquid Assets
• Most common addition to lifecycle model
• Work in correct direction to help explain variation by income level
• HRS asks series of questions on probability of leaving bequests (any, >$10K, >$100K)
• Bequests matter, but can’t explain substantial portion of variation
Additions/Alternatives:Bequests
Bequests
Dependent variable: ln(C/M)-ln(predC/M)
Coefficent T-stat
Expect to leave any bequest
-0.129** -2.5
Large Bequest
(>50% Chance of leaving bequest >$100,000)
-0.151** -4.8
Means for Large Bequest=1
Apply coefficient
C/M 0.061 .061*.151=.0092
M $1,182,000
Net Worth
$534,000
Imagine Household’s Calculation:C/(M-b)=.061-.00092=.0518→ b ≈ $200,000
Fraction of Net Worth?200,000/534,000=38%
Hurd & Smith (2002) estimate actual bequests of 39% of net worth
• Recent literature questioning whether all households have the ability, financial literacy, or propensity to plan optimal savings and consumption strategies for retirement (Lusardi, Willis/Lillard, Caplin/Leahy…)
• HRS asks questions on basic cognition (recall, counting, subtraction) plus planning horizon and subjective expectations– Willis & Lillard “fraction of exact answers”; precision of
expectations formation related to financial decisions• Measures matter such that lower cognition, less
precision, and shorter planning horizons all imply higher propensities to consume
Additions/Alternatives:Cognition & Planning
Regression Results
• Note: Can’t fit on one slide – point out that complete results in paper, pick highlights
Dependent variable: ln(C/M) -ln(predC/M)
Coefficent T-stat
Additional people in household
0.067** 4.8
Subjective Life Expectancy -0.058* -1.7
Race/Ethnicity: Black or Hispanic
0.089* 1.9
Education: No HS 0.037 0.8
Education: Some College 0.020 0.8
Education: College+ -0.019 -0.2
Age of Head -0.119** -4.6
Age of Head Squared 0.001** 4.4
Fair/ Poor Health 0.067 1.5
Retired -0.098** -2.9
Widowed 0.186* 1.9
Never Married 0.269** 4.1
Entrepreneurs -0.341** -4.9
Coefficent T-stat
Word Recall Low 0.051* 1.6
Counting Backwards -0.092** -1.9
Easiest Subtraction Problem
-0.063 -1.0
Hardest Subtraction Problem
-0.077** -2.4
Fraction of Precise Answers
-0.067 -1.3
Horizon for financial planning
-0.074** -2.4
Smoker 0.077** 2.5
R2=0.272; N=1611
Survey Measure of Risk Aversion (midpoint of range)
-0.009* -1.6
Stats for OLS w/ Risk Aversion
R2=0.278 N=
1227