The Average Propensity to
Consume Out of Full Wealth:
Testing a New Measure
Full Wealth: The Right Measure of
Wealth for Consumption
Lifecycle/PIH theory since Modigliani says
consumption should depend on all current and
future resources (including financial and
human wealth.)
• Essentially a stock value of permanent income
from today forward
• I call this PDV of all resources:
“Modigliani full wealth” = M
Unprecedented Ability to Measure Full Wealth
Health and Retirement Study
Expected present value of resources:
M = Net Worth + Human Wealth
• Net Worth = 10 categories of assets less 3 categories
of debt
• Human Wealth=
Earnings+Pensions+Social Security+Other Transfers
(deterministic for older households)
Outline
• Full wealth: How it’s different
– by age profile, variance, and distribution
• The APC out of full wealth: C/M
(Comparing C/M to C/NetWorth and C/Income)
– What to expect from C/M theoretically
• More tightly distributed
• More consistent over time
• Relatively invariant to circumstances and shocks
– Empirical Results
Full Wealth is Not Just Scaled-Up
Net Worth
200,000 400,000 600,000 800,000
1000000
Age Profile of Wealth
Full Wealth
Net worth
55
60
Full Wealth
65
Age of Household Head
Cash-on-Hand
70
75
Net Worth
Full Wealth Has Less Variance…
Coefficients of Variation
CV
Mean
Full Wealth
0.96
$825,000
Net Worth
1.67
$322,000
Income
1.21
$61,600
Consumption
0.77
$40,300
…and is more equally distributed
1
Lorenz Curves
.4
.6
.8
Full Wealth
0
.2
Net worth
0
.2
.4
.6
Cumulative population proportion
Lorenz Curve Full Wealth
.8
Lorenz Curve Net Worth
1
The Average Propensity to Consume
Out of Full Wealth
Neoclassical model:
• C proportional to M
• Very limited sources of variation in C/M
across households
• C/M changes only slowly over time (from
mortality, changes in returns expectations, or
changes in preferences)
• C/M does not change with income shocks if
consumption responds quickly
Which Implies…
C/M relative to C/NetWorth or C/Income Should Have:
• Lower variance
• Higher covariance over time
• Lower correlation with “circumstances” such as:
– Having a pension or the generosity of pension and social security benefits
(income replacement rate in retirement)
– Earnings profile over lifetime
– Having children
– Income Shocks
Also ∆(C/M) Should Have:
• Lower correlation with income shocks (also proxied by
employment and health shocks)
And the data says…
Lower and more consistent variance
Std. Dev.
Mean
Median
CV
C/M 2001
.058
.078
.060
0.74
C/M 2003
.062
.084
.067
0.74
C/NW 2001
3.26
1.05
.221
3.10
C/NW 2003
12.56
2.59
.256
4.85
C/I 2001
1.47
1.22
.828
1.20
C/I 2003
Higher covariance over time
Covariance
2001&2003
C/M
0.70
C/NW
0.37
C/I
Circumstances
• Traditional savings or consumption rates (C/I)
have “noise” from circumstances, both crosssectionally and longitudinally
• Examples:
– Households expecting generous DB pension
income will save less than otherwise identical
households with little or no DB pension
– Households experiencing a temporary positive
income shock will save more that period
How much of C/I is explained by
circumstances?
If C/M is a cleaner measure of true consumption rates…
Then a low covariance between C/I and C/M means a lot of
noise in C/I from circumstances
Scatter Plot of Consumption Rates:
.14
Income vs. Full Wealth
.02
.06
C/M
.1
Cov = 0.31
.5
1
1.5
C/Income
2
2.5
Cross-Section or Level of C/M:
Less Correlated with Many Circumstances
• Circumstance: Generosity of retirement benefits (DB
pension and Social Security)
• Measure: RetRatio: Ratio of PV(Pension+Social
Security) to Average Earnings Over Ages 45-55
• Outcome: C/M is less correlated
Bivariate OLS
Coefficient & T-stat
R2
Const
ln(C/M) 2001 on RetRatio
.0032**
(2.4)
.004
-2.86
ln(C/NW) 2001 on RetRatio
.0159*** (6.0)
.025
-1.58
ln(C/M) 2003 on RetRatio
.0014
(0.9)
.001
-2.79
ln(C/NW) 2003 on RetRatio
.0154*** (5.0)
.025
-1.52
…Cont
Income Profile
• Circumstance: Income Profile
• Measure: Average slope of household earnings during
30s, 40s, 50s & early 60s
• Outcome: C/M uncorrelated; C/NW & C/I have some
significant correlation
Dependent Variable→
ln(C/M)
ln(C/NW)
ln(C/I)
-.067 (-1.3) -.267** (-2.2)
-.111* (-1.9)
Independent Variables↓
2001 Earning slope 30s
Earning slope 40s
.059 (1.3)
.220** (2.4)
-.001
(-0.1)
Earning slope 50s
.060 (1.1)
.049
(0.4)
-.073
(-1.2)
-.049 (-0.6)
.029
(0.2)
-.222** (-2.2)
-.074 (-1.4) -.050
(-0.5)
Earning slope early 60s
Separate Regressions:
2003 Earning slope 30s
Earning slope 40s
.037 (0.8) .238*** (2.8)
Earning slope 50s
.019 (0.4)
Earning slope early 60s
.187* (1.7)
-.022 (-0.2) -.183
(-0.8)
…Cont
Having Children
• Circumstance: Children
• Measure: Dummy variable for having any children
• Outcome: C/M less correlated for 2001; both
uncorrelated in 2003
OLS
ln(C/M) 2001 on Children
ln(C/NW) 2001 on Children
ln(C/M) 2003 on Children
ln(C/NW) 2003 on Children
Coefficient
T-stat
R2
Const
-0.102*
-1.73
.002
-2.73
-0.302**
-2.32
.005
-1.16
0.064
0.94
.001
-2.83
-0.109
-0.73
.001
-1.22
…Cont
Income Shocks
• Circumstance: Past Income Shock
• Measure: Change in Earnings over previous years
• Outcome: C/M less correlated than C/I; results mixed
comparing C/M with C/NW
Dependent Variable→
ln(C/M)
ln(C/NW)
ln(C/I)
Independent Variables↓
2001
Y Shock 2000-2001
Y Shock 1999-2000
.086** (2.0)
-.034
(-0.7)
.138* (1.6) -.141*** (-3.2)
-.086 (-0.8) -.168*** (-3.3)
Separate Regressions:
2003
Y Shock 2000-2001
.076
(1.3) -.069 (-0.6)
Y Shock 1999-2000
.014
(0.2)
.088
(0.7)
Time-Series: Change in C/M
• Previous tables showed relative invariance of
the level of C/M to circumstances, including
income shocks
• The change in C/M should also be invariant to
income shocks if C responds relatively quickly
to new information.
Change in C/M Less Correlated With
Shocks
Dependent Variable→
∆(C/M)
∆(C/NW)
Independent Variables↓
Y Shock 2000-2001
Y Shock 1999-2000
-.050 (-1.3) -.175** (-2.0)
.001 (0.0)
.044
(0.4)
Separate Regressions:
Recent Past Negative
Employment Shock
-.132 (-1.5) -.429** (-2.3)
∆(C/I)
Instrument that affects M ex-post:
Show it does not affect C/M
• Note: Not sure about this, still working on it.
• I’ve thought about employment shock
(unexpected retirement between 2001 & 2003 or
unemployment in 2002) but survey timing of C
and M makes this difficult
• Rate of return shock problematic b/c can’t
separate portfolio changes from returns –
especially relevant in 2000-2003 when people
probably changed their portfolio
Conclusion
Full Wealth and the APC out of Full Wealth:
• Empirically match expected distribution
characteristics
• The level of C/M has less correlation with
circumstances than either C/NW or C/I
• The change in C/M is relatively invariant to recent
shocks when compared to C/NW or C/I