YOLO - Netspar · SurvivalBeliefs SLEsandSavingsDecisions ImplicationsOverLife-Cycle Conclusion How do we think people die? NBCSanDiego(Aug. 31,2015),“BeachReopensAfter2

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.


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?










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?



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?



“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.”


Why do subjective survival beliefs matter?

Why do subjective survival beliefs matter?In practice...




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(·)]}



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, 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
















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


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


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)


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


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


Survey description



−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



even after we provide respondents w/ mortality statistics!−

20−

100

1020

subj

ectiv

e E

(sur

viva

l) −

pr(

surv

ival

), (

ppt)


Yesfitted pr(transition)95% CI

Nofitted pr(transition)95% CI

Did subjects receive info about survival probabilities?



Robust to:Gender link

Numerical literacy link

Survival confidence link

Question framing link


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



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



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


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


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


Pr(spend all of my income)

.38

.4.4

2.4

4.4

6.4

8


Pr(save ~10% of monthly income)

.1.1

5.2

.25



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


Pr(spend all of my income)

.48

.5.5

2.5

4.5

6−10 0 10

error in survival expectations (pp)


.1.1

5.2

.25

.3



Fraction monthly income saved? (old generation)



8.1

.12

.14

.16

.18


Pr(use savings any time now).2

5.3

.35

.4.4

5


Pr(use savings in 2 − 5 years)

.06

.08

.1.1

2.1

4.1

6



.2.3

.4.5

.6


Pr(use savings > 10 years from now)

When do you expect to use your savings? (young gen.)

.05

.1.1

5.2

.25


Pr(use savings any time now)

.2.2

2.2

4.2

6.2

8.3



.28

.3.3

2.3

4.3

6−10 0 10



.2.2

5.3

.35

.4


Pr(use savings > 10 years from now)

When do you expect to use your savings? (old gen.)



.25

.3.3

5


Pr(very inexperienced)

.2.2

2.2

4.2

6.2

8.3


Pr(somewhat inexperienced)

.06

.07

.08

.09

.1


Pr(experienced)

.25

.3.3

5.4

.45


Pr(somewhat experienced)

.03

.04

.05

.06

.07


Pr(very experienced)

Investing experience (young generation)

.28

.3.3

2.3

4.3

6.3

8


Pr(very inexperienced)

.15

.2.2

5.3

.35


Pr(somewhat inexperienced)

.15

.2.2

5.3

.35


Pr(somewhat experienced)

.05

.1.1

5.2


Pr(experienced)

0.0

5.1

.15

.2


Pr(very experienced)

Investing experience (old generation)


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


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


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


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)


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)


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



Age20 30 40 50 60 70 80 90 100

$

×105

0

1

2

3

4

5



Age20 30 40 50 60 70 80 90 100

$

×105

0

1

2

3

4

5

6

7





Robust to:Discount factors link

Risk-tolerance link

Bequests link

Education (income paths) link


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


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



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



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


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...


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



Gender differences back

−20

−10

010

20su

bjec

tive

E(s

urvi

val)

− p

r(su

rviv

al),

(pp

t)


Malefitted pr(transition)95% CI

Femalefitted pr(transition)95% CI

Gender differences in subjective survival probabilities?



Numerical literacy back

−20

−10

010

20su

bjec

tive

E(s

urvi

val)

− p

r(su

rviv

al),

(pp

t)




Can subjects correctly answer numeracy questions?



Confidence in responses back

−20

−10

010

20su

bjec

tive

E(s

urvi

val)

− p

r(su

rviv

al),

(pp

t)




Are subjects confident in their responses?



Consecutive survival horizons back

−20

−10

010

20su

bjec

tive

E(s

urvi

val)

− p

r(su

rviv

al),

(pp

t)




Are subjects asked about consecutive survival horizons?



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


Age20 30 40 50 60 70 80 90 100

$

×105

0

0.5

1

1.5

2

2.5

3Cash on hand


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





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


Age20 30 40 50 60 70 80 90 100

$

×105

0

1

2

3

4

5Cash on hand


Age20 30 40 50 60 70 80 90 100

Por

tfolio

wei

ght

0

0.2

0.4

0.6

0.8





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


Age20 30 40 50 60 70 80 90 100

$

×105

0

0.5

1

1.5

2

2.5

3Cash on hand


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





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


Edu =1Edu =2Edu =3



.15

.2.2

5


Pr(not willing to take any financial risks).3

5.4

.45

.5.5

5


Pr(take average fiancial risk)

.22

.24

.26

.28

.3.3

2


Pr(take above average financial risk)

.02

.04

.06

.08

.1


Pr(take substantial financial risk)

How much financial risk are you willing to take? (young gen.)

.25

.3.3

5.4


Pr(not willing to take any financial risks)

.4.4

5.5

.55


Pr(take average fiancial risk)

.08

.1.1

2.1

4.1

6.1

8−10 0 10


Pr(take above average financial risk)

0.0

5.1

.15

.2


Pr(take substantial financial risk)

How much financial risk are you willing to take? (old gen.)

Documents

YOLO - Netspar · SurvivalBeliefs SLEsandSavingsDecisions ImplicationsOverLife-Cycle Conclusion How do we think people die? NBCSanDiego(Aug. 31,2015),“BeachReopensAfter2