Risk Aversion Heterogeneity, Risky Jobs and the
Distribution of Wealth
Marco Cozzi
Queen’s University
Mar 13th - Bank of Lithuania
Cozzi (Queen’s University)
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Motivation
Understanding the determinants of saving behavior is key: design of
…scal (stimulus) policies and income redistribution schemes.
U.S. Data: wealth is highly concentrated, Gini index 0.78-0.82.
Empirical challenges: matching the top and bottom quintiles.
Successful quantitative answers for the top: entrepreneurship,
uninsurable income risk (with large shocks), and inter-vivos transfers.
The role of preference heterogeneity (i.e. di¤erent attitudes towards
risk) has not been studied carefully.
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Research Questions
1
Is (measurable) heterogeneity in risk aversion quantitatively important
in accounting for the U.S. wealth distribution?
2
Does it matter for Macroeconomic outcomes?
3
Is the measurement of precautionary savings a¤ected?
4
How much does it matter for the evaluation of Macroeconomic
policies (e.g. Fiscal stimulus)?
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Related Literature
Cagetti and De Nardi (JPE 06), Castaneda, Diaz-Gimenez, and
Rios-Rull (JPE 03), De Nardi (REStud 04), Quadrini (RED 00).
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Related Literature
Cagetti and De Nardi (JPE 06), Castaneda, Diaz-Gimenez, and
Rios-Rull (JPE 03), De Nardi (REStud 04), Quadrini (RED 00).
Cagetti (JBES 03), Coen-Pirani (MD 05), Guvenen (JME 06),
Hendricks (JEDC 07), Krusell and Smith (JPE 98).
Cozzi (Queen’s University)
CRRA Heterogeneity and Wealth
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Related Literature
Cagetti and De Nardi (JPE 06), Castaneda, Diaz-Gimenez, and
Rios-Rull (JPE 03), De Nardi (REStud 04), Quadrini (RED 00).
Cagetti (JBES 03), Coen-Pirani (MD 05), Guvenen (JME 06),
Hendricks (JEDC 07), Krusell and Smith (JPE 98).
Barsky, Juster, Kimball, and Shapiro (QJE 97), Chiappori and Paiella
(JEEA 11), Harrison, Lau, and Rutstrom (SJE 07), Hryshko,
Luengo-Prado and Sorensen (QE 11), Kimball, Sahm, and Shapiro
(JASA 08 - AER P&P 09), von Gaudecker, van Soest, and
Wengstrom (AER 10).
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Ingredients
Incomplete Markets and Borrowing Constraint (self-insurance through
a riskless asset to smooth income ‡uctuations).
Heterogeneity: Assets, Productivity (Ex-post).
Heterogeneity: Risk Aversion Preference Parameter (Ex-ante).
! Empirically grounded, unlike unobserved heterogeneity.
Self-selection into risky careers.
GE.
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Preview of the Results
Observable preference heterogeneity goes a long way in accounting for
several features of the U.S. wealth distribution.
Both the wealth Gini index and the quintiles implied by the model
approximate well the actual ones.
The results are robust wrt both the labor income process and
preference heterogeneity speci…cations.
The allocations in the economy with preference heterogeneity di¤er
substantially from the ones in its representative agent counterpart.
Models without risk aversion heterogeneity heavily underestimate the
size of precautionary savings (up to 40 p.p.).
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Heterogeneous RA and the Wealth Distribution: Intuition
0.25
γ
γHigh
γLow
0.2
0.15
0.1
0.05
0
-4
-2
0
2
4
6
8
10
Asset
Figure: Heterogenous Risk Aversion and the Wealth Distribution
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Risk Aversion Heterogeneity
What do the data say?
Robust …nding: across individuals the relative risk aversion is highly
heterogeneous.
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Risk Aversion: Estimated Densities (Survey Data)
Kimball, Sahm and Shapiro (2009)
Chiappori and Paiella (2011)
1
0.8
0.6
0.4
0.2
0
0
2
4
6
R
i
8
s
k
A
10
v
e γ )r
s
i
12
o
n
14
(
Figure: US PSID Survey Data - 5,622 obs; ITA SHIW Data - 2,785 obs.
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Risk Aversion: Estimated Densities (Experimental Data)
Figure: Danish Experimental Data - 273 obs
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Risk Aversion: Estimated Densities (Exp. Data - Non EU)
Figure: Dutch Experimental Data - 1,422 and 178 obs
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Risk Aversion: Estimated Densities (Survey Data)
Figure: Italian Panel Data on Portfolio Composition, SHIW
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Eliciting Risk Preferences (US Data: HRS and PSID)
Advantage of PSID: several obs, reliable question, representative of
the whole US population, consistent with income dynamics sample.
Risk tolerance parameter
Risk aversion parameter
τ
γ
Simple relationship between the two: γ =
1
τ
For the CRRA case risk tolerance and elasticity of intertemporal
substitution coincide.
Property of LN distribution: if τ
Cozzi (Queen’s University)
LN (µ, σ2 ) ! γ
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LN
µ, σ2
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Eliciting Risk Tolerance (HRS and PSID)
1. Survey Question:
Suppose that you are the only income earner in the family, and you
have a good job guaranteed to give you your current (family) income every year for life.
You are given the opportunity to take a new and equally good job, with a 50–50 chance it
will double your (family) income and a 50–50 chance that it will cut your (family)
income by a third. Would you take the new job?
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Eliciting Risk Tolerance (HRS and PSID)
1. Survey Question:
Suppose that you are the only income earner in the family, and you
have a good job guaranteed to give you your current (family) income every year for life.
You are given the opportunity to take a new and equally good job, with a 50–50 chance it
will double your (family) income and a 50–50 chance that it will cut your (family)
income by a third. Would you take the new job?
2.a If yes ! lottery with higher risk:
Suppose the chances were 50–50 that it
would double your (family) income, and 50–50 that it would cut it in half. Would you
still take the new job?
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Eliciting Risk Tolerance (HRS and PSID)
1. Survey Question:
Suppose that you are the only income earner in the family, and you
have a good job guaranteed to give you your current (family) income every year for life.
You are given the opportunity to take a new and equally good job, with a 50–50 chance it
will double your (family) income and a 50–50 chance that it will cut your (family)
income by a third. Would you take the new job?
2.a If yes ! lottery with higher risk:
Suppose the chances were 50–50 that it
would double your (family) income, and 50–50 that it would cut it in half. Would you
still take the new job?
2.b If no ! lottery with lower risk:
Suppose the chances were 50–50 that it would
double your (family) income and 50–50 that it would cut it by 20 percent. Would you
then take the new job?
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Eliciting Risk Tolerance (HRS and PSID)
1. Survey Question:
Suppose that you are the only income earner in the family, and you
have a good job guaranteed to give you your current (family) income every year for life.
You are given the opportunity to take a new and equally good job, with a 50–50 chance it
will double your (family) income and a 50–50 chance that it will cut your (family)
income by a third. Would you take the new job?
2.a If yes ! lottery with higher risk:
Suppose the chances were 50–50 that it
would double your (family) income, and 50–50 that it would cut it in half. Would you
still take the new job?
2.b If no ! lottery with lower risk:
Suppose the chances were 50–50 that it would
double your (family) income and 50–50 that it would cut it by 20 percent. Would you
then take the new job?
3.a If yes ! lottery with higher risk:
50–50 double, and 50–50 that it would cut it
by 75 percent.
3.b If no ! lottery with lower risk:
50–50 double, and 50–50 that it would cut it
by 10 percent.
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Estimating Risk Tolerance from PSID data
Make the structural assumption that the utility function is CRRA (CP
JEEA 11 test for it, and do not reject).
From the survey answers the respondents fall into six possible RT
intervals.
Make the assumption that preferences are log-normally distributed in
the population.
We are left with an ordered probit, with known thresholds: estimate it
with MLE (KSS, JASA 08 and AER P&P 09).
I’ve redone it because of di¤erent sample selection rules in the PSID
(results are similar to KSS 09).
Adjust the variances for measurement error and status quo bias.
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Eliciting Risk Tolerance (Status Quo Bias Free)
1. Survey Question:
Suppose that you are the only income earner in the family. Your
doctor recommends that you move because of allergies, and you have to choose between
two possible jobs. The …rst would guarantee your current total family income for life. The
second is possibly better paying, but the income is also less certain. There is a 50–50
chance the second job would double your total lifetime income and a 50–50 chance that it
would cut it by a third. Which job would you take— the …rst job or the second job?
2.a If yes ! lottery with higher risk.
2.b If no ! lottery with lower risk.
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The Benchmark Model (One Risky Job)
A version of Aiyagari (QJE 94) with preference heterogeneity.
The per-period utility function is de…ned over consumption c but
1 γ
depends on CRRA γi as well: u (ct ; γi ) =
ct i 1
1 γi .
γi > 0 is a permanent characteristic, and there is an exogenous
distribution of workers types.
Agents face uninsurable idiosyncratic income risk: their productivity ε
follows a …rst order Markov process.
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The Benchmark Model - Workers
V (ε, a; γ) = max0 u (c; γ) + βEε0 jε V (ε0 , a0 ; γ)
c ,a
s.t.
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The Benchmark Model - Workers
V (ε, a; γ) = max0 u (c; γ) + βEε0 jε V (ε0 , a0 ; γ)
c ,a
s.t.
c + a 0 = (1 + r ) a + w ε
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The Benchmark Model - Workers
V (ε, a; γ) = max0 u (c; γ) + βEε0 jε V (ε0 , a0 ; γ)
c ,a
s.t.
c + a 0 = (1 + r ) a + w ε
log ε0 = ρy log ε + η 0 , η
a0 given,
Cozzi (Queen’s University)
c
0,
iid N (0, σ2y )
a0 >
CRRA Heterogeneity and Wealth
b
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The Benchmark Model - Firms
Cobb-Douglas Aggregate Production Function:
Y = F (K , L) = K α L1
In a steady-state:
L=
Z
α
εd µε (ε)
Equilibrium prices:
r
w
Cozzi (Queen’s University)
= α
= (1
L
K
α)
1 α
δ
K
L
CRRA Heterogeneity and Wealth
α
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Equilibrium (Recursive Stationary)
A recursive stationary equilibrium is a set of decision rules fc (ε, a; γ),
a0 (ε, a; γ), k = KL , value functions V (ε, a; γ), prices fr , w g a set of
stationary distributions µ(ε, a; γ) such that:
Agents and Firms Optimize.
Markets Clear.
The measure of agents in each state is time invariant and consistent
with individual decisions.
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Parameterization - US
Parameter
Model Period
b - Borrowing limit
δ - Capital deprec.
α - Capital share
β - Discount factor
ε - Productiv. values
γ - CRRA
Value
Yearly
0
0.08
0.36
0.87 0.89
See Table 2
See Table 3
Target
No borrowing
Investment/Output ratio
25%
Capital share of output
Annual interest rate r = 3.5%
AR(1) process for earnings
Risk tolerance from PSID data
Table: Benchmark Calibration - US
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Parameterization - Earnings Processes
Income Process
Source
ρy
σy
(1) FLIN
Floden-Linde (2001)
0.92
0.21
(2) FREN
French (2005)
0.977
0.12
(3) GRIP
Guvenen (2009)
0.988
0.122
Table: Labor Market Risk - AR(1) Productivity Processes
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Parameterization - Risk Aversion Heterogeneity
Case
Distribution
µγ
σγ
KSS (PSID data)
LN µγ , σ2γ
1.07
0.87
CP ( γMed =1.7, γ0.75 =3.0)
Beta µγ , σγ
0.48
4.04
Table: Preference Heterogeneity
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Risk Aversion Densities: Percentiles
Case
KSS
γ < 0.5
2.3%
Avg
Med
γ<1
10.8%
4.28
2.91
γ < 1.5
22.0%
γ < 2.0
33.0%
γ < 5.0
72.9%
Table: Percentiles of the CRRA distributions
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Risk Aversion Densities: Percentiles
Case
KSS
γ < 0.5
2.3%
Avg
Med
CP
Avg
Med
γ<1
10.8%
4.28
2.91
27.5%
2.21
1.70
γ < 1.5
22.0%
γ < 2.0
33.0%
γ < 5.0
72.9%
44.7%
57.6%
92.5%
Table: Percentiles of the CRRA distributions
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Risk Aversion Vs. Elasticity of Intertemporal Substitution
Average risk aversion: 4.28.
Potential issue: implication for the EIS?
The EIS is what is typically estimated (with consumption growth
data).
d 2 [0.33, 1.5]
EIS
EIS = 1/γ but E [1/γ] = 0.498
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1/E [γ] = 0.23.
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0
.2
.4
.6
.8
1
Results: Lorenz Curves for Wealth
0
.2
.4
.6
.8
1
p
CRRA=4.2
PSID99
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KSS FL
45 line
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Wealth Distribution - Data Vs. Model
Q1
Data:
U.S. - SCF98
U.S. - PSID99
Models:
KSS (FLIN)
KSS (FREN)
KSS (GRIP)
γ = 4.28 (FLIN)
γ = 4.28 (FREN)
γ = 4.28 (GRIP)
.3
.8
.00
.00
.00
2.0
0.6
0.6
Q2
Q3
Q4
Q5
10-5%
5-1%
1%
1.3
0.8
5.0
4.2
12.2
12.6
81.7
83.2
11.3
14.0
23.1
23.7
34.7
30.8
0.1
.01
.00
7.3
4.9
4.1
3.4
0.2
0.01
14.2
12.1
10.3
16.8
9.7
7.7
24.7
24.0
21.7
79.6
90.1
92.2
51.8
58.4
63.3
20.3
22.5
21.5
13.0
14.5
15.2
26.4
31.7
33.7
14.2
16.7
19.2
10.8
14.4
17.6
5.5
6.9
9.1
Table: Data Vs. Equilibria - Statistics of the Wealth Distribution.
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Wealth Distribution - Data Vs. Model
Q1
Data:
U.S. - SCF98
U.S. - PSID99
Models:
KSS (FLIN)
KSS (FREN)
KSS (GRIP)
γ = 4.28 (FLIN)
γ = 4.28 (FREN)
γ = 4.28 (GRIP)
.3
.8
.00
.00
.00
2.0
0.6
0.6
Q2
Q3
Q4
Q5
10-5%
5-1%
1%
1.3
0.8
5.0
4.2
12.2
12.6
81.7
83.2
11.3
14.0
23.1
23.7
34.7
30.8
0.1
.01
.00
7.3
4.9
4.1
3.4
0.2
0.01
14.2
12.1
10.3
16.8
9.7
7.7
24.7
24.0
21.7
79.6
90.1
92.2
51.8
58.4
63.3
20.3
22.5
21.5
13.0
14.5
15.2
26.4
31.7
33.7
14.2
16.7
19.2
10.8
14.4
17.6
5.5
6.9
9.1
Table: Data Vs. Equilibria - Statistics of the Wealth Distribution.
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Wealth Distribution - Data Vs. Model
Q1
Data:
U.S. - SCF98
U.S. - PSID99
Models:
KSS (FLIN)
KSS (FREN)
KSS (GRIP)
γ = 4.28 (FLIN)
γ = 4.28 (FREN)
γ = 4.28 (GRIP)
.3
.8
.00
.00
.00
2.0
0.6
0.6
Q2
Q3
Q4
Q5
10-5%
5-1%
1%
1.3
0.8
5.0
4.2
12.2
12.6
81.7
83.2
11.3
14.0
23.1
23.7
34.7
30.8
0.1
.01
.00
7.3
4.9
4.1
3.4
0.2
0.01
14.2
12.1
10.3
16.8
9.7
7.7
24.7
24.0
21.7
79.6
90.1
92.2
51.8
58.4
63.3
20.3
22.5
21.5
13.0
14.5
15.2
26.4
31.7
33.7
14.2
16.7
19.2
10.8
14.4
17.6
5.5
6.9
9.1
Table: Data Vs. Equilibria - Statistics of the Wealth Distribution.
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Wealth Distribution - Data Vs. Model
Q1
Data:
U.S. - SCF98
U.S. - PSID99
Models:
KSS (FLIN)
KSS (FREN)
KSS (GRIP)
γ = 4.28 (FLIN)
γ = 4.28 (FREN)
γ = 4.28 (GRIP)
.3
.8
.00
.00
.00
2.0
0.6
0.6
Q2
Q3
Q4
Q5
10-5%
5-1%
1%
1.3
0.8
5.0
4.2
12.2
12.6
81.7
83.2
11.3
14.0
23.1
23.7
34.7
30.8
0.1
.01
.00
7.3
4.9
4.1
3.4
0.2
0.01
14.2
12.1
10.3
16.8
9.7
7.7
24.7
24.0
21.7
79.6
90.1
92.2
51.8
58.4
63.3
20.3
22.5
21.5
13.0
14.5
15.2
26.4
31.7
33.7
14.2
16.7
19.2
10.8
14.4
17.6
5.5
6.9
9.1
Table: Data Vs. Equilibria - Statistics of the Wealth Distribution.
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Wealth Distribution & Average RA - Data Vs. Model
Q1
Data:
U.S. - SCF98
U.S. - PSID99
Models:
KSS (FLIN)
Average γ
.3
.8
.00
1.32
Q2
Q3
Q4
Q5
1.3
0.8
5.0
4.2
12.2
12.6
81.7
83.2
0.1
1.88
3.4
3.18
16.8
4.76
79.6
9.12
Table: Data Vs. Equilibria - Statistics of the Wealth Distribution.
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Intuition
From the Euler Equation:
ct
γ
h
i
= β (1 + r ) Eε0 jε ct +γ1
1
E ε 0 j ε [ ct + 1 ]
[ β (1 + r )] γ
=
ct
η (γ)
with 0 < η (γ) < 1, η 0 (γ) < 0
η (γ) is a term that takes care of Jensen’s inequality: consumption
growth is highly non-linear in γ.
Expected consumption growth increases in γ because of higher
precautionary savings.
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Results - Inequality Measures: Gini Index, CV
RRA Heterogeneity :
Case
Yes - KSS:
FLIN
FREN
GRIP
FLIN
FREN
GRIP
No - γ = 4.28 :
Asset
Gini, CV
Income
Gini, CV
Consumption
Gini, CV
0.50, 0.99
0.57, 1.20
0.62, 1.42
Table: Equilibrium - Inequality Measures in the one job model: Gini Index and
Coe¢ cient of Variation. An asterisk denotes that all the parameters are the same
as in the corresponding heterogeneous preferences economy.
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Results - Inequality Measures: Gini Index, CV
RRA Heterogeneity :
Case
Yes - KSS:
FLIN
FREN
GRIP
FLIN
FREN
GRIP
No - γ = 4.28 :
Asset
Gini, CV
0.76, 1.87
0.83, 2.32
0.85, 2.62
0.50, 0.99
0.57, 1.20
0.62, 1.42
Income
Gini, CV
Consumption
Gini, CV
Table: Equilibrium - Inequality Measures in the one job model: Gini Index and
Coe¢ cient of Variation. An asterisk denotes that all the parameters are the same
as in the corresponding heterogeneous preferences economy.
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Results - Inequality Measures: Gini Index, CV
RRA Heterogeneity :
Case
Yes - KSS:
FLIN
FREN
GRIP
FLIN
FREN
GRIP
No - γ = 4.28 :
Asset
Gini, CV
0.76, 1.87
0.83, 2.32
0.85, 2.62
0.50, 0.99
0.57, 1.20
0.62, 1.42
Income
Gini, CV
0.39, 0.82
0.44, 0.98
0.51, 1.22
0.33, 0.62
0.38, 0.75
0.47, 1.02
Consumption
Gini, CV
0.28, 0.52
0.33, 0.63
0.43, 0.91
0.25, 0.47
0.32, 0.62
0.43, 0.92
Table: Equilibrium - Inequality Measures in the one job model: Gini Index and
Coe¢ cient of Variation. An asterisk denotes that all the parameters are the same
as in the corresponding heterogeneous preferences economy.
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Aggregate Allocations
Case
FLIN
FREN
GRIP
RRA Heterogeneity
Yes - KSS
No - CRRA=4.28
Yes - KSS
No - CRRA=4.28
Yes - KSS
No - CRRA=4.28
r (%)
3.51
Y
1.79
C
1.34
K /Y
3.13
3.51
1.82
1.36
3.13
3.50
2.12
1.59
3.13
Table: Comparison of Equilibria: Homogeneous Vs. Heterogeneous Preferences
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Aggregate Allocations
Case
FLIN
FREN
GRIP
RRA Heterogeneity
Yes - KSS
No - CRRA=4.28
Yes - KSS
No - CRRA=4.28
Yes - KSS
No - CRRA=4.28
r (%)
3.51
5.12
3.51
6.16
3.50
7.24
Y
1.79
1.67
1.82
1.62
2.12
1.81
C
1.34
1.30
1.36
1.29
1.59
1.46
K /Y
3.13
2.74
3.13
2.54
3.13
2.36
Table: Comparison of Equilibria: Homogeneous Vs. Heterogeneous Preferences
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The Model with Endogenous Sorting into Risky Jobs
Guiso, Jappelli, and Pistaferri (JBES 02), Schulhofer-Wohl (JPE 11)
Two jobs j = h, l (h riskier than l).
p death probability, χ altruism parameter.
n
o
e (ε, a; γ) = max V h (εh0 , a; γ), V l (εl0 , a; γ)
V
V j (ε, a; γ) = max0 u (c; γ) + β(1
c ,a
o
e (ε0 , a0 ; γ)
βpχEε0 V
p )Eε0 jε V j (ε0 , a0 ; γ)+
s.t.
log εj0 = mj + ρy ,j log εj + η j0 , η
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iid N (0, σ2y ,j ), j = h, l
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Why Do Agents Observe the Two Initial Shocks?
Percentile
Exp. 8
γ:
γ:
8 < Exp. 14
γ:
γ:
14 < Exp. 19
γ:
γ:
19 < Exp. 25
γ:
γ:
75th
90th
95th
99th
Obs
.347
.391
.553
.593
.683
.732
.985
1.02
2193
2724
.291
.323
.514
.544
.684
.697
1.07
1.20
2697
3032
.258
.282
.497
.568
.683
.738
1.26
1.18
2320
2283
.273
.308
.527
.580
.749
.741
1.48
1.16
2235
1760
Table: Selected Statistics of Residual Earnings by Potential Labor Market
Experience (Exp.)
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Calibration
Parameter
ρy ,h
ρy ,l
β
mh
σy ,l = σy ,h
Value
.9662
.9177
.9094
.0012
.1363
Targets
Earn. autocor for types γ γMedian
Earn. autocor for types γ < γMedian
Annual interest rate
Ratio of avg earnings by RA groups
S.d. of persistent shocks from PSID
Data
.9475
.9353
.0350
1.009
-
Model
.9440
.9384
.0351
1.009
-
Table: Two Risky Jobs Model with Endogenous Sorting (ES), Calibration - U.S.
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Wealth Distribution - Data Vs. Model
Q1
Data:
U.S. - SCF98
U.S. - PSID99
Exog. Earnings:
KSS (FLIN)
Endo. Sorting:
KSS (ES)
γ = 4.28 (ES)
Q2
Q3
Q4
Q5
10-5%
5-1%
1%
1.3
0.8
5.0
4.2
12.2
12.6
81.7
83.2
11.3
14.0
23.1
23.7
34.7
30.8
.00
0.1
3.4
16.8
79.6
20.3
26.4
10.8
.00
1.3
.01
6.7
1.6
14.2
12.7
25.4
85.7
52.4
20.0
13.3
30.6
14.2
15.2
5.2
.3
.8
Table: Data Vs. Equilibria - Statistics of the Wealth Distribution.
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0
.2
.4
.6
.8
1
Lorenz Curves for Wealth
0
.2
.4
.6
.8
1
p
KSS ES
PSID99
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CRRA Heterogeneity and Wealth
KSS FL
45 line
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PSID Evidence
First stage regression: log yit = βt Xit + εit , t = 1968
1993
Xit = age, edu, state, race, gender , children
AR(1) panel regression on earnings residuals
(RA = risk aversion category ):
eitRA
log εRA
it
RA group
γlow
γhigh
b
ρ
.947
.935
RA
= fi RA + log εRA
it + vit
RA
= ρRA log εRA
it 1 + η it
b2y
σ
.018
.018
b2f
σ
.061
.074
b2v
σ
.099
.079
Individuals
560
569
Table: Estimates of the Labor Earnings Shocks Variance and Persistence by two
Risk Aversion Categories in the PSID (1968-1993).
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Other Results
Prec. Savings
K IM
K CM
PS (%)
KSS (ES)
γ = 4.28 (ES)
5.477
4.273
2.731
2.660
100.59
60.63
Consumption
Model ES
PSID Food
C for γ < γMed
1.117
$7, 457
C for γ
1.533
$7, 661
γMed
∆PS
39.96
∆%
37.32%
2.74%
Table: Precautionary Savings and Consumption Comparisons.
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Aggregate Allocations
Case
FLIN
FREN
GRIP
ES
RRA Heterogeneity
Yes - KSS
No - CRRA=4.28
Yes - KSS
No - CRRA=4.28
Yes - KSS
No - CRRA=4.28
Yes - KSS
No - CRRA=4.28
r (%)
3.51
5.12
3.51
6.16
3.50
7.24
3.50
5.26
Y
1.79
1.67
1.82
1.62
2.12
1.81
1.75
1.57
C
1.34
1.30
1.36
1.29
1.59
1.46
1.31
1.23
K /Y
3.13
2.74
3.13
2.54
3.13
2.36
3.13
2.71
Table: Comparison of Equilibria: Homogeneous Vs. Heterogeneous Preferences
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On-going and Future work
1
Time varying preference heterogeneity (Across generations, Life-cycle,
Business Cycles).
2
Marginal Propensity to Consume out of transitory shocks (Italian
survey data + US tax rebates).
3
Portfolio Allocation (equity premium puzzle).
4
Epstein-Zin preferences.
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Conclusions
1
Empirically grounded preference heterogeneity accounts for some key
features of the wealth distribution in the U.S matching the degree of
wealth inequality.
2
Top 1% still problematic (not surprisingly, and a virtue).
3
The …ndings are robust along several dimensions, in particular
self-selection into risky careers.
4
Macroeconomic aggregates are heavily a¤ected.
5
Models without heterogeneous risk preferences underestimate
precautionary savings.
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