YOLO - Netspar · SurvivalBeliefs SLEsandSavingsDecisions ImplicationsOverLife-Cycle Conclusion How...
Transcript of YOLO - Netspar · SurvivalBeliefs SLEsandSavingsDecisions ImplicationsOverLife-Cycle Conclusion How...
Survival Beliefs SLEs and Savings Decisions Implications Over Life-Cycle Conclusion
YOLO:Mortality Beliefs and Household Finance Puzzles
R. Heimer, K. Myrseth, and R. Schoenle
Federal Reserve Bank of Cleveland, St Andrews, Brandeis
Netspar, January 2016
The article’s views do not necessarily reflect those of the FRB-CLE or the BoG.
Survival Beliefs SLEs and Savings Decisions Implications Over Life-Cycle Conclusion
How do we think people die?
NBC San Diego (Aug. 31, 2015), “Beach Reopens After 2Shark Sightings in 2 Days”... but should we be more worried about cows?
Survival Beliefs SLEs and Savings Decisions Implications Over Life-Cycle Conclusion
How do we think people die?
NBC San Diego (Aug. 31, 2015), “Beach Reopens After 2Shark Sightings in 2 Days”... but should we be more worried about cows?
Survival Beliefs SLEs and Savings Decisions Implications Over Life-Cycle Conclusion
How do we think people die?
NBC San Diego (Aug. 31, 2015), “Beach Reopens After 2Shark Sightings in 2 Days”... but should we be more worried about cows?
Survival Beliefs SLEs and Savings Decisions Implications Over Life-Cycle Conclusion
How do we think people die?
Survival Beliefs SLEs and Savings Decisions Implications Over Life-Cycle Conclusion
How long do you expect to live?
Prudential: Austin, TX, survey of 400 people
What is the age of the oldest person they’ve known?living proof that we are living longer?
Survival Beliefs SLEs and Savings Decisions Implications Over Life-Cycle Conclusion
How long do you expect to live?
Prudential: Austin, TX, survey of 400 people
What is the age of the oldest person they’ve known?living proof that we are living longer?
Survival Beliefs SLEs and Savings Decisions Implications Over Life-Cycle Conclusion
How long do you expect to live?
“Oracle founder Larry Ellison has donated more than $430million to anti-aging research.”“The Palo Alto Longevity Prize is a $1 million life sciencecompetition dedicated to ending aging.”
Survival Beliefs SLEs and Savings Decisions Implications Over Life-Cycle Conclusion
Why do subjective survival beliefs matter?
Why do subjective survival beliefs matter?In practice...
Survival Beliefs SLEs and Savings Decisions Implications Over Life-Cycle Conclusion
Why do subjective survival beliefs matter?
Why do subjective survival beliefs matter?
Mortality beliefs, (st+1), affect inter-temporal trade-offbetween today’s consumption and discounted futureconsumption streams
Theory:V ∗t (·) = max
Ct{u(Ct)+βEt[st+1V ∗t+1(·)+(1− st+1)B∗t+1(·)]}
Survival Beliefs SLEs and Savings Decisions Implications Over Life-Cycle Conclusion
Why do subjective survival beliefs matter?
Our message...
Death plays a large cognitive role
Survival beliefs change (systematically) over life-cyle
How we think about death makes ...young more impatient than they should beold more patient than they should be
Survival Beliefs SLEs and Savings Decisions Implications Over Life-Cycle Conclusion
Survival beliefs, their origins and implications
New survey evidence on SLEs: distribution is heavy-tailedcompared to actuarial data
young overestimate likelihood of dying young, e.g. 28 year-oldsmake 1-year ahead forecast errors = 5 - 10 pptold overestimate likelihood of surviving to very old age, e.g. 68year-olds make a 10 ppt 10-year ahead forecast error
Theoretical mechanism for distorted beliefs: stereotypesabout cause-of-death across cohorts
young die in rare events, we overweight Pr(tail events)old die of bad health, old survivors are optimistic
Distorted beliefs correlate with financial behavior:save less and may rely on credit cardsless experience investing
Survival Beliefs SLEs and Savings Decisions Implications Over Life-Cycle Conclusion
Survival beliefs, their origins and implications
New survey evidence on SLEs: distribution is heavy-tailedcompared to actuarial data
young overestimate likelihood of dying young, e.g. 28 year-oldsmake 1-year ahead forecast errors = 5 - 10 pptold overestimate likelihood of surviving to very old age, e.g. 68year-olds make a 10 ppt 10-year ahead forecast error
Theoretical mechanism for distorted beliefs: stereotypesabout cause-of-death across cohorts
young die in rare events, we overweight Pr(tail events)old die of bad health, old survivors are optimistic
Distorted beliefs correlate with financial behavior:save less and may rely on credit cardsless experience investing
Survival Beliefs SLEs and Savings Decisions Implications Over Life-Cycle Conclusion
Survival beliefs, their origins and implications
New survey evidence on SLEs: distribution is heavy-tailedcompared to actuarial data
young overestimate likelihood of dying young, e.g. 28 year-oldsmake 1-year ahead forecast errors = 5 - 10 pptold overestimate likelihood of surviving to very old age, e.g. 68year-olds make a 10 ppt 10-year ahead forecast error
Theoretical mechanism for distorted beliefs: stereotypesabout cause-of-death across cohorts
young die in rare events, we overweight Pr(tail events)old die of bad health, old survivors are optimistic
Distorted beliefs correlate with financial behavior:save less and may rely on credit cardsless experience investing
Survival Beliefs SLEs and Savings Decisions Implications Over Life-Cycle Conclusion
Quantitative importance of biased survival beliefs
Mortality beliefs are quantitatively important: analyzetheir implications in a run-of-the mill life-cycle model
1 young people save too little, consume too muchSkinner (2007): not enough retirement savingsLaibson (1997): rely on credit cards month-to-month,hand-to-mouth consumption
2 retirees do not fully draw down their assetsPorteba et al. (2011): explanations for bequests incomplete
3 higher equity premium (EP) through lower return on bondsMehra and Prescott (1985): EP too high given reasonable ρ
Takeaway: SLEs contribute to seemingly unconnected puzzlesprevious explanations for puzzles are often contradictorybetter data ↑ life-cycle model’s explanatory power
Survival Beliefs SLEs and Savings Decisions Implications Over Life-Cycle Conclusion
Quantitative importance of biased survival beliefs
Mortality beliefs are quantitatively important: analyzetheir implications in a run-of-the mill life-cycle model
1 young people save too little, consume too muchSkinner (2007): not enough retirement savingsLaibson (1997): rely on credit cards month-to-month,hand-to-mouth consumption
2 retirees do not fully draw down their assetsPorteba et al. (2011): explanations for bequests incomplete
3 higher equity premium (EP) through lower return on bondsMehra and Prescott (1985): EP too high given reasonable ρ
Takeaway: SLEs contribute to seemingly unconnected puzzlesprevious explanations for puzzles are often contradictorybetter data ↑ life-cycle model’s explanatory power
Survival Beliefs SLEs and Savings Decisions Implications Over Life-Cycle Conclusion
Related literature
1 Surveyed beliefs... understand shortcomings of classical models (e.g. Greenwoodand Shleifer, 2015; Afrouzi, Coibion, Gorodnichenko, and Kumar,2015)
2 Probability weightingTversky and Kahneman (1992), Barberis and Huang (2008),Polkovnichenko (2005)many purchase too much insurance against unlikely events (Sydnor,2010, and Bhargava et al., 2015)
3 Household expectationsChristelis et al. (2015), Puri and Robinson (2007), Soo (2015)
4 Mortality expectationsHammermesh (1985), Inkmann, Lopes, and Michaelides (2011),Bisetti (2015), Grevenbrock, Groneck, Ludwig, and Zimper (2015),Wu, Stevens, and Thorp (2014)many over-weight unlikely deaths, linked to imaginability(Lichtenstein et al., 1979)
Survival Beliefs SLEs and Savings Decisions Implications Over Life-Cycle Conclusion
Biased survival beliefs
30 year olds’ beliefs about Pr(survival) beyond given age(Jarnebrant and Myrseth, 2013)
0 20 40 60 80 100 120 1400
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
prob
abili
ty d
eath
age
Survival Beliefs SLEs and Savings Decisions Implications Over Life-Cycle Conclusion
Survey description
Qualtrics Panels2000 U.S. respondents (wave 2, 5000+)uniformly distributed across ages 28, 38, 48, 58, 68
Survival likelihood for 1, 2, 5, 10 yearsComplementary questions (off-the-shelf):
expected longevity (SCF)confidence in answersfinancial preference (SCF)financial literacy (Lusardi and Mitchell, 2011)numeracy (Cokely et al., 2012)demographics e.g. income and education
Survival Beliefs SLEs and Savings Decisions Implications Over Life-Cycle Conclusion
Survey description
Survival Beliefs SLEs and Savings Decisions Implications Over Life-Cycle Conclusion
Biased survival beliefs
−20
−10
010
20su
bjec
tive
E(s
urvi
val)
− p
r(su
rviv
al),
(pp
t)
30 40 50 60 70 80survive at least to age
mean pr(transition)fitted pr(transition)95% CI
All respondents
Survival Beliefs SLEs and Savings Decisions Implications Over Life-Cycle Conclusion
Biased survival beliefs
even after we provide respondents w/ mortality statistics!−
20−
100
1020
subj
ectiv
e E
(sur
viva
l) −
pr(
surv
ival
), (
ppt)
30 40 50 60 70 80survive at least to age
Yesfitted pr(transition)95% CI
Nofitted pr(transition)95% CI
Did subjects receive info about survival probabilities?
Survival Beliefs SLEs and Savings Decisions Implications Over Life-Cycle Conclusion
Biased survival beliefs
Robust to:Gender link
Numerical literacy link
Survival confidence link
Question framing link
Survival Beliefs SLEs and Savings Decisions Implications Over Life-Cycle Conclusion
Where does the bias come from?
Rare events are vastly overweighted:
“When you assessed your survival likelihood, to what extent did you place weight on thefollowing risk factors?” (scale of 0 to 100)variable mean median std devThe natural course of life and aging (“normal risk”) 74.5 80 23.5Medical conditions (e.g., cancer and heart disease) 69.4 78 26.4Dietary habits (e.g., unhealthy foods) 62.3 69 28.2Traffic accidents (e.g., car crash) 45.3 50 29.8Physical violence (e.g., murder) 35.3 20 32.3Natural disasters (e.g., earth quakes) 34.7 23 31.5Animal attacks (e.g., shark attacks) 25.6 9 31.3Risky lifestyle (e.g., base jumping) 28.3 10 33.3“Freak events” (e.g., choking on your food) 32.7 23 30.8
N = 2357
Survival Beliefs SLEs and Savings Decisions Implications Over Life-Cycle Conclusion
Where does the bias come from?
Overweighting of rare events explains expectation errors:
(1) (2) (3) (4) (5) (6) (7) (8) (9)risk factor weight share natural aging medical diet traffic accident violence natur. disaster animal attack risky lifestyle freak eventsabsolute exp. error (Z) -2.776 0.362 -1.065 0.227 0.870 0.495 0.540 0.483 0.863
(0.74) (0.62) (0.28) (0.22) (0.19) (0.38) (0.27) (0.22) (0.37)age = 38 5.469 0.0634 0.818 -2.026 -1.502 -0.996 -0.725 -0.622 -0.478
(0.44) (0.18) (0.18) (0.068) (0.14) (0.075) (0.10) (0.13) (0.15)age = 48 3.237 0.760 2.055 -1.355 -0.542 -1.009 -1.051 -1.894 -0.201
(0.43) (0.32) (0.20) (0.13) (0.24) (0.086) (0.10) (0.21) (0.13)age = 58 3.327 3.344 2.704 -2.104 -1.495 -1.742 -1.617 -1.637 -0.781
(0.33) (0.40) (0.23) (0.12) (0.19) (0.064) (0.11) (0.20) (0.14)age = 68 3.053 1.021 3.956 -1.539 -0.721 -1.124 -1.493 -1.489 -1.664
(0.62) (0.28) (0.22) (0.13) (0.23) (0.14) (0.15) (0.25) (0.17)consecutive questions x x x x x x x x xeducation x x x x x x x x xnumeracy x x x x x x x x xN 2357 2357 2357 2357 2357 2357 2357 2357 2357R2 0.078 0.016 0.048 0.016 0.015 0.027 0.027 0.036 0.028
Standard errors in parentheses
Survival Beliefs SLEs and Savings Decisions Implications Over Life-Cycle Conclusion
Where does the bias come from?
Overweighting of rare events explains expectation errors:
(1) (2) (3) (4) (5) (6) (7) (8) (9)risk factor weight share natural aging medical diet traffic accident violence natur. disaster animal attack risky lifestyle freak eventsabsolute exp. error (Z) -2.776 0.362 -1.065 0.227 0.870 0.495 0.540 0.483 0.863
(0.74) (0.62) (0.28) (0.22) (0.19) (0.38) (0.27) (0.22) (0.37)age = 38 5.469 0.0634 0.818 -2.026 -1.502 -0.996 -0.725 -0.622 -0.478
(0.44) (0.18) (0.18) (0.068) (0.14) (0.075) (0.10) (0.13) (0.15)age = 48 3.237 0.760 2.055 -1.355 -0.542 -1.009 -1.051 -1.894 -0.201
(0.43) (0.32) (0.20) (0.13) (0.24) (0.086) (0.10) (0.21) (0.13)age = 58 3.327 3.344 2.704 -2.104 -1.495 -1.742 -1.617 -1.637 -0.781
(0.33) (0.40) (0.23) (0.12) (0.19) (0.064) (0.11) (0.20) (0.14)age = 68 3.053 1.021 3.956 -1.539 -0.721 -1.124 -1.493 -1.489 -1.664
(0.62) (0.28) (0.22) (0.13) (0.23) (0.14) (0.15) (0.25) (0.17)consecutive questions x x x x x x x x xeducation x x x x x x x x xnumeracy x x x x x x x x xN 2357 2357 2357 2357 2357 2357 2357 2357 2357R2 0.078 0.016 0.048 0.016 0.015 0.027 0.027 0.036 0.028
Standard errors in parentheses
Survival Beliefs SLEs and Savings Decisions Implications Over Life-Cycle Conclusion
Do SLEs matter for savings decisions?
Multinomial logit model for observation i and outcome k:
f (k, i) = β0k +β1k · exp.errori +βkXi
where Xi includesagegenderincomeeducationindicators for lnumeracy
Survival Beliefs SLEs and Savings Decisions Implications Over Life-Cycle Conclusion
Do SLEs matter for savings decisions?.0
3.0
4.0
5.0
6.0
7
−20 −10 0error in survival expectations (pp)
Pr(spend more than earn, rely on credit)
.2.2
2.2
4.2
6.2
8.3
−20 −10 0error in survival expectations (pp)
Pr(spend all of my income)
.38
.4.4
2.4
4.4
6.4
8
−20 −10 0error in survival expectations (pp)
Pr(save ~10% of monthly income)
.1.1
5.2
.25
−20 −10 0error in survival expectations (pp)
Pr(save ~25% of monthly income)
Fraction monthly income saved? (young generation)
.01
.02
.03
.04
.05
−10 0 10error in survival expectations (pp)
Pr(spend more than earn, rely on credit)
.15
.2.2
5.3
.35
−10 0 10error in survival expectations (pp)
Pr(spend all of my income)
.48
.5.5
2.5
4.5
6−10 0 10
error in survival expectations (pp)
Pr(save ~10% of monthly income)
.1.1
5.2
.25
.3
−10 0 10error in survival expectations (pp)
Pr(save ~25% of monthly income)
Fraction monthly income saved? (old generation)
Survival Beliefs SLEs and Savings Decisions Implications Over Life-Cycle Conclusion
Do SLEs matter for savings decisions?.0
8.1
.12
.14
.16
.18
−20 −10 0error in survival expectations (pp)
Pr(use savings any time now).2
5.3
.35
.4.4
5
−20 −10 0error in survival expectations (pp)
Pr(use savings in 2 − 5 years)
.06
.08
.1.1
2.1
4.1
6
−20 −10 0error in survival expectations (pp)
Pr(use savings in 6 − 10 years)
.2.3
.4.5
.6
−20 −10 0error in survival expectations (pp)
Pr(use savings > 10 years from now)
When do you expect to use your savings? (young gen.)
.05
.1.1
5.2
.25
−10 0 10error in survival expectations (pp)
Pr(use savings any time now)
.2.2
2.2
4.2
6.2
8.3
−10 0 10error in survival expectations (pp)
Pr(use savings in 2 − 5 years)
.28
.3.3
2.3
4.3
6−10 0 10
error in survival expectations (pp)
Pr(use savings in 6 − 10 years)
.2.2
5.3
.35
.4
−10 0 10error in survival expectations (pp)
Pr(use savings > 10 years from now)
When do you expect to use your savings? (old gen.)
Survival Beliefs SLEs and Savings Decisions Implications Over Life-Cycle Conclusion
Do SLEs matter for savings decisions?.2
.25
.3.3
5
−20 −10 0error in survival expectations (pp)
Pr(very inexperienced)
.2.2
2.2
4.2
6.2
8.3
−20 −10 0error in survival expectations (pp)
Pr(somewhat inexperienced)
.06
.07
.08
.09
.1
−20 −10 0error in survival expectations (pp)
Pr(experienced)
.25
.3.3
5.4
.45
−20 −10 0error in survival expectations (pp)
Pr(somewhat experienced)
.03
.04
.05
.06
.07
−20 −10 0error in survival expectations (pp)
Pr(very experienced)
Investing experience (young generation)
.28
.3.3
2.3
4.3
6.3
8
−10 0 10error in survival expectations (pp)
Pr(very inexperienced)
.15
.2.2
5.3
.35
−10 0 10error in survival expectations (pp)
Pr(somewhat inexperienced)
.15
.2.2
5.3
.35
−10 0 10error in survival expectations (pp)
Pr(somewhat experienced)
.05
.1.1
5.2
−10 0 10error in survival expectations (pp)
Pr(experienced)
0.0
5.1
.15
.2
−10 0 10error in survival expectations (pp)
Pr(very experienced)
Investing experience (old generation)
Survival Beliefs SLEs and Savings Decisions Implications Over Life-Cycle Conclusion
Life-cycle model w/ biased survival beliefs
Canonical dynamic life-cycle model w/ precautionary savingsCarroll (2011), Love (2013)
Key features of life-cycle model:Agents choose in discrete time t = 0, 1, 2, 3,...Tretire ,...,T
consumption and portfolio share φt
Recursive maximization problem:
V ∗t (Xt , Pt) = maxCt ,φt{u (Ct)+βstEt
[V ∗t+1 (Xt+1, Pt+1)
]+ ...
...+β (1− st)Et [Bt+1 (Rt+1 (Xt −Ct))]
where st is the period-transition probability, β rate of timepreference, B bequest motive.
Mortality beliefs enter through effective discount factor
Survival Beliefs SLEs and Savings Decisions Implications Over Life-Cycle Conclusion
Life-cycle calibration
Horse-race between two specifications:benchmark actuarial tables (SSA) vs. SLEssubjective probabilities st :
our survey-elicited beliefs vs. ...survival rates from Social Security Administration, 2007
Other parameters:rate of time preference β = 0.98R f = 2%, R r = 6%, and σ r = 18%risk aversion ρ = 51970 - 2007 PSID to calibrate income process for marriedcollege graduates without dependentsCorr (R r
t , Pt)> 0 during working life, 0 when retired
Survival Beliefs SLEs and Savings Decisions Implications Over Life-Cycle Conclusion
Life-cycle calibration
Horse-race between two specifications:benchmark actuarial tables (SSA) vs. SLEssubjective probabilities st :
our survey-elicited beliefs vs. ...survival rates from Social Security Administration, 2007
Other parameters:rate of time preference β = 0.98R f = 2%, R r = 6%, and σ r = 18%risk aversion ρ = 51970 - 2007 PSID to calibrate income process for marriedcollege graduates without dependentsCorr (R r
t , Pt)> 0 during working life, 0 when retired
Survival Beliefs SLEs and Savings Decisions Implications Over Life-Cycle Conclusion
Life-cycle model results
Age20 40 60 80 100
$
×104
1
2
3
4
5
6Consumption
SSASubj Pr(Surv)
Age20 40 60 80 100
$
×104
0
1
2
3
4
5
6Savings
SSASubj Pr(Surv)
Age20 40 60 80 100
$
×105
0
1
2
3
4
5Cash on hand
SSASubj Pr(Surv)
Age20 40 60 80 100
Por
tfolio
wei
ght
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1Share of risky assets
SSASubj Pr(Surv)
Survival Beliefs SLEs and Savings Decisions Implications Over Life-Cycle Conclusion
Results: SLEs and retirement
Age65 70 75 80 85 90 95
$
×104
3.2
3.4
3.6
3.8
4
4.2Consumption, Beq = 0
SSASubj Pr(Surv)
Age65 70 75 80 85 90 95
$
×104
1
1.5
2
2.5
3
3.5Savings, Beq = 0
SSASubj Pr(Surv)
Age65 70 75 80 85 90 95
$
×105
1
2
3
4
5
6Cash on hand, Beq = 0
SSASubj Pr(Surv)
Age65 70 75 80 85 90 95
$
×104
3.2
3.4
3.6
3.8
4
4.2Consumption, Beq = 1
SSASubj Pr(Surv)
Age65 70 75 80 85 90 95
$
×104
1
1.5
2
2.5
3
3.5Savings, Beq = 1
SSASubj Pr(Surv)
Age65 70 75 80 85 90 95
$
×105
1.5
2
2.5
3
3.5
4
4.5
5
5.5Cash on hand, Beq = 1
SSASubj Pr(Surv)
Survival Beliefs SLEs and Savings Decisions Implications Over Life-Cycle Conclusion
Results: SLEs and wealth accumulation
Age20 30 40 50 60 70 80 90 100
$
×105
0
0.5
1
1.5
2
2.5
3Cash on hand, CRRA =2
SSAePrem =0.01ePrem =0.02ePrem =0.04ePrem =0.08
Age20 30 40 50 60 70 80 90 100
$
×105
0
1
2
3
4
5Cash on hand, CRRA =5
SSAePrem =0.01ePrem =0.02ePrem =0.04ePrem =0.08
Age20 30 40 50 60 70 80 90 100
$
×105
0
1
2
3
4
5
6Cash on hand, CRRA =10
SSAePrem =0.01ePrem =0.02ePrem =0.04ePrem =0.08
Age20 30 40 50 60 70 80 90 100
$
×105
0
1
2
3
4
5
6
7
8Cash on hand, CRRA =20
SSAePrem =0.01ePrem =0.02ePrem =0.04ePrem =0.08
Survival Beliefs SLEs and Savings Decisions Implications Over Life-Cycle Conclusion
Life-cycle model results
Robust to:Discount factors link
Risk-tolerance link
Bequests link
Education (income paths) link
Survival Beliefs SLEs and Savings Decisions Implications Over Life-Cycle Conclusion
SLEs and asset returns
Inter-temporal rate of substitution affects rate of returns. Twoapproaches:
1 Estimate equity premium implied by model (partialequilibrium, GMM)
2 Comparative statics from an OLG model
Survival Beliefs SLEs and Savings Decisions Implications Over Life-Cycle Conclusion
SLEs and asset returns: OLG
Solve an over-lapping generations (OLG) model:Three periods: young (y), nearing retirement (r), and old (o)choose consumption (c), bond (b) and equity shares (e)
max(ct ,ct+1 ,ct+2 ,bt ,bt+1 ,et ,et+1)
U(cy
t)+β
y EU(cr
t+1)+β
yβ
r EU(co
t+2)
s.t.
cyt +qb
t byt +qe
t eyt = wy
t
crt+1+qb
t+1brt+1+qe
t+1ert+1 = w r
t+1+(
qbt+1+g
)by
t +(qe
t+1+dt+1)
eyt
cot+2 =
(qb
t+2+g)
brt+1+
(qe
t+2+dt+2)
ert+1
fixed supply of b and e, traded across generations
Survival Beliefs SLEs and Savings Decisions Implications Over Life-Cycle Conclusion
SLEs and asset returns: OLG
Solve an OLG model:Wage income and dividends come from outside modelKey ingredients (Constantinides, Donaldson, & Mehra, 2002):
correlations between wages and dividend incomeswage uncertainty resolved for middle generation
Causes: shift portfolio towards bonds near retirementOur insight: β r increases, β y falls relative to benchmark
r prices bonds, he’s more patient ⇒ ↓ return on bondsy would offset effects, but he just wants to consume today
Survival Beliefs SLEs and Savings Decisions Implications Over Life-Cycle Conclusion
SLEs and asset returns: OLG
0 0.1 0.2 0.3 0.4s
old - s
young
0
5
10
15eq
pre
mbeta = 0.88
0 0.1 0.2 0.3 0.4s
old - s
young
0
5
10
15
eq p
rem
beta = 0.9
0 0.1 0.2 0.3 0.4s
old - s
young
0
5
10
15
eq p
rem
beta = 0.92
0 0.1 0.2 0.3 0.4s
old - s
young
-15
-10
-5
0
5
eq p
rem
×1010 beta = 0.94
Survival Beliefs SLEs and Savings Decisions Implications Over Life-Cycle Conclusion
Conclusion
New survey evidence:SLEs have a robustly heavy-tailed distributionSLEs are very heterogeneousexpectation errors are correlated w/ financial decision-making
Using SLEs in a run-of-the-mill life-cycle model can helpexplain three seemingly disjoint puzzles:
the young’s under-savingretirees do not fully draw-down assetshigh required returns on risky asset, given reasonable riskaversion
Project is ongoing...
Survival Beliefs SLEs and Savings Decisions Implications Over Life-Cycle Conclusion
SLEs and asset returns: GMM from LC-model
What equity returns are required to compensate for mortalitybeliefs? Use GMM to back out equity premium:
1
0.98
Rate of Time Preference
0.96
0.94
0.92
0.90
Coefficient of Relative Risk Aversion
2
4
6
8
4%
12%
2%
16%
14%
6%
10%
8%
10
Equ
ity P
rem
ium
Sub
ject
ive
Bel
iefs
Survival Beliefs SLEs and Savings Decisions Implications Over Life-Cycle Conclusion
Biased survival beliefs
Gender differences back
−20
−10
010
20su
bjec
tive
E(s
urvi
val)
− p
r(su
rviv
al),
(pp
t)
30 40 50 60 70 80survive at least to age
Malefitted pr(transition)95% CI
Femalefitted pr(transition)95% CI
Gender differences in subjective survival probabilities?
Survival Beliefs SLEs and Savings Decisions Implications Over Life-Cycle Conclusion
Biased survival beliefs
Numerical literacy back
−20
−10
010
20su
bjec
tive
E(s
urvi
val)
− p
r(su
rviv
al),
(pp
t)
30 40 50 60 70 80survive at least to age
Yesfitted pr(transition)95% CI
Nofitted pr(transition)95% CI
Can subjects correctly answer numeracy questions?
Survival Beliefs SLEs and Savings Decisions Implications Over Life-Cycle Conclusion
Biased survival beliefs
Confidence in responses back
−20
−10
010
20su
bjec
tive
E(s
urvi
val)
− p
r(su
rviv
al),
(pp
t)
30 40 50 60 70 80survive at least to age
Yesfitted pr(transition)95% CI
Nofitted pr(transition)95% CI
Are subjects confident in their responses?
Survival Beliefs SLEs and Savings Decisions Implications Over Life-Cycle Conclusion
Biased survival beliefs
Consecutive survival horizons back
−20
−10
010
20su
bjec
tive
E(s
urvi
val)
− p
r(su
rviv
al),
(pp
t)
30 40 50 60 70 80survive at least to age
Yesfitted pr(transition)95% CI
Nofitted pr(transition)95% CI
Are subjects asked about consecutive survival horizons?
Survival Beliefs SLEs and Savings Decisions Implications Over Life-Cycle Conclusion
Life-cycle model results
Discount factors back
Age20 30 40 50 60 70 80 90 100
$
×104
1.5
2
2.5
3
3.5
4
4.5Consumption
Beta =1Beta =0.99Beta =0.98Beta =0.97Beta =0.9
Age20 30 40 50 60 70 80 90 100
$
×104
1
2
3
4
5
6Savings
Beta =1Beta =0.99Beta =0.98Beta =0.97Beta =0.9
Age20 30 40 50 60 70 80 90 100
$
×105
0
0.5
1
1.5
2
2.5
3Cash on hand
Beta =1Beta =0.99Beta =0.98Beta =0.97Beta =0.9
Age20 30 40 50 60 70 80 90 100
Por
tfolio
wei
ght
0.4
0.5
0.6
0.7
0.8
0.9
1Share of risky assets
Beta =1Beta =0.99Beta =0.98Beta =0.97Beta =0.9
Survival Beliefs SLEs and Savings Decisions Implications Over Life-Cycle Conclusion
Life-cycle model results
Risk-tolerance back
Age20 30 40 50 60 70 80 90 100
$
×104
1
2
3
4
5
6Consumption
CRRA =1CRRA =3CRRA =5CRRA =10
Age20 30 40 50 60 70 80 90 100
$
×104
-1
0
1
2
3
4
5
6Savings
CRRA =1CRRA =3CRRA =5CRRA =10
Age20 30 40 50 60 70 80 90 100
$
×105
0
1
2
3
4
5Cash on hand
CRRA =1CRRA =3CRRA =5CRRA =10
Age20 30 40 50 60 70 80 90 100
Por
tfolio
wei
ght
0
0.2
0.4
0.6
0.8
1Share of risky assets
CRRA =1CRRA =3CRRA =5CRRA =10
Survival Beliefs SLEs and Savings Decisions Implications Over Life-Cycle Conclusion
Life-cycle model results
Bequest motives back
Age20 30 40 50 60 70 80 90 100
$
×104
1
1.5
2
2.5
3
3.5
4
4.5Consumption
Bequest =0Bequest =1
Age20 30 40 50 60 70 80 90 100
$
×104
1
2
3
4
5
6Savings
Bequest =0Bequest =1
Age20 30 40 50 60 70 80 90 100
$
×105
0
0.5
1
1.5
2
2.5
3Cash on hand
Bequest =0Bequest =1
Age20 30 40 50 60 70 80 90 100
Por
tfolio
wei
ght
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1Share of risky assets
Bequest =0Bequest =1
Survival Beliefs SLEs and Savings Decisions Implications Over Life-Cycle Conclusion
Life-cycle model results
Education (income paths) back
Age20 30 40 50 60 70 80 90 100
$
×104
1.5
2
2.5
3
3.5
4
4.5Consumption
Edu =1Edu =2Edu =3
Age20 30 40 50 60 70 80 90 100
$
×104
-1
0
1
2
3
4
5
6Savings
Edu =1Edu =2Edu =3
Age20 30 40 50 60 70 80 90 100
$
×105
0
0.5
1
1.5
2
2.5
3Cash on hand
Edu =1Edu =2Edu =3
Age20 30 40 50 60 70 80 90 100
Por
tfolio
wei
ght
0.4
0.5
0.6
0.7
0.8
0.9
1Share of risky assets
Edu =1Edu =2Edu =3
Survival Beliefs SLEs and Savings Decisions Implications Over Life-Cycle Conclusion
Do SLEs matter for savings decisions?.1
.15
.2.2
5
−20 −10 0error in survival expectations (pp)
Pr(not willing to take any financial risks).3
5.4
.45
.5.5
5
−20 −10 0error in survival expectations (pp)
Pr(take average fiancial risk)
.22
.24
.26
.28
.3.3
2
−20 −10 0error in survival expectations (pp)
Pr(take above average financial risk)
.02
.04
.06
.08
.1
−20 −10 0error in survival expectations (pp)
Pr(take substantial financial risk)
How much financial risk are you willing to take? (young gen.)
.25
.3.3
5.4
−10 0 10error in survival expectations (pp)
Pr(not willing to take any financial risks)
.4.4
5.5
.55
−10 0 10error in survival expectations (pp)
Pr(take average fiancial risk)
.08
.1.1
2.1
4.1
6.1
8−10 0 10
error in survival expectations (pp)
Pr(take above average financial risk)
0.0
5.1
.15
.2
−10 0 10error in survival expectations (pp)
Pr(take substantial financial risk)
How much financial risk are you willing to take? (old gen.)