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