behavioral economics and aging david laibson harvard university and nber july 8, 2009 rand

Behavioral Economics and Aging

David LaibsonHarvard University and NBER

July 8, 2009RAND

1. Motivating Experiments

A Thought Experiment

Would you like to haveA) 15 minute massage now

orB) 20 minute massage in an hour

Would you like to haveC) 15 minute massage in a week

orD) 20 minute massage in a week and an hour

Read and van Leeuwen (1998)

TimeChoosing Today Eating Next Week

If you were deciding today,would you choosefruit or chocolatefor next week?

Patient choices for the future:

TimeChoosing Today Eating Next Week

Today, subjectstypically choosefruit for next week.

74%choosefruit

Impatient choices for today:

Time

Choosing and EatingSimultaneously

If you were deciding today,would you choosefruit or chocolatefor today?

Time Inconsistent Preferences:

Time

Choosing and EatingSimultaneously

70%choose chocolate

Read, Loewenstein & Kalyanaraman (1999)

Choose among 24 movie videos• Some are “low brow”: Four Weddings and a Funeral• Some are “high brow”: Schindler’s List

• Picking for tonight: 66% of subjects choose low brow.• Picking for next Wednesday: 37% choose low brow.• Picking for second Wednesday: 29% choose low brow.

Tonight I want to have fun… next week I want things that are good for me.

Extremely thirsty subjectsMcClure, Ericson, Laibson, Loewenstein and Cohen (2007)

• Choosing between, juice now or 2x juice in 5 minutes 60% of subjects choose first option.

• Choosing between juice in 20 minutes or 2x juice in 25 minutes 30% of subjects choose first option.

• We estimate that the 5-minute discount rate is 50% and the “long-run” discount rate is 0%.

• Ramsey (1930s), Strotz (1950s), & Herrnstein (1960s) were the first to understand that discount rates are higher in the short run than in the long run.

Outline

1. Motivating experimental evidence2. Theoretical framework 3. Field evidence4. Neuroscience foundations5. Neuroimaging evidence6. Policy discussion7. The age of reason

A copy of these slides will soon be available on my Harvard website.

2. Theoretical Framework

• Classical functional form: exponential functions.

D(t) = t

D(t) = 1, Ut = ut + ut+1 ut+2ut+3

• But exponential function does not show instant gratification effect.

• Discount function declines at a constant rate.• Discount function does not decline more quickly in

the short-run than in the long-run.

Exponential Discount Function

0

1

1 11 21 31 41 51

Week (time = t)

Dis

cou

nte

d v

alu

e o

f d

elay

ed r

ewar

d

Exponential Hyperbolic

Constant rate of decline

-D'(t)/D(t) = rate of decline of a discount function

Discount Functions

0

1

1 11 21 31 41 51

Week

Exponential Hyperbolic

Rapid rateof decline in short run

Slow rate of decline in long run

An exponential discounting paradox.

Suppose people discount at least 1% between today and tomorrow.

Suppose their discount functions were exponential.

Then 100 utils in t years are worth 100*e(-0.01)*365*t utils today.

• What is 100 today worth today? 100.00• What is 100 in a year worth today? 2.55• What is 100 in two years worth today? 0.07• What is 100 in three years worth today? 0.00

An Alternative Functional Form

Quasi-hyperbolic discounting

(Phelps and Pollak 1968, Laibson 1997)

D(t) = 1, Ut = ut + ut+1 ut+2ut+3

Ut = ut + ut+1 ut+2ut+3

uniformly discounts all future periods. exponentially discounts all future periods.

For continuous time: see Barro (2001), Luttmer and Marriotti (2003), and Harris and Laibson (2009)

Building intuition

• To build intuition, assume that = ½ and = 1.• Discounted utility function becomes

Ut = ut + ½ut+1 ut+2ut+3

• Discounted utility from the perspective of time t+1.

Ut+1 = ut+1 + ½ut+2 ut+3

• Discount function reflects dynamic inconsistency: preferences held at date t do not agree with preferences held at date t+1.

Application to massages = ½ and = 1

A 15 minutes nowB 20 minutes in 1 hour

C 15 minutes in 1 weekD 20 minutes in 1 week plus 1 hour

NPV in current minutes

15 minutes now10 minutes now

7.5 minutes now10 minutes now

Exercise

• Assume that = ½ and = 1.

• Suppose exercise (current effort 6) generates delayed benefits (health improvement 8).

• Will you exercise?

• Exercise Today: -6 + ½ [8] = -2

• Exercise Tomorrow: 0 + ½ [-6 + 8] = +1

• Agent would like to relax today and exercise tomorrow.

• Agent won’t follow through without commitment.

3. Field EvidenceDella Vigna and Malmendier (2004, 2006)

• Average cost of gym membership: $75 per month• Average number of visits: 4 • Average cost per vist: $19• Cost of “pay per visit”: $10

Choi, Laibson, Madrian, Metrick (2002)Self-reports about undersaving.

SurveyMailed to 590 employees (random sample)

Matched to administrative data on actual savings behavior

22

Typical breakdown among 100 employees

Out of every 100 surveyed employees

68 self-report saving too little 24 plan to

raise savings rate in next 2 months

3 actually follow through

Laibson, Repetto, and Tobacman (2007)

Use MSM to estimate discounting parameters:– Substantial illiquid retirement wealth: W/Y = 3.9.– Extensive credit card borrowing:

• 68% didn’t pay their credit card in full last month• Average credit card interest rate is 14%• Credit card debt averages 13% of annual income

– Consumption-income comovement: • Marginal Propensity to Consume = 0.23

(i.e. consumption tracks income)

LRT Simulation Model

• Stochastic Income• Lifecycle variation in labor supply (e.g. retirement)• Social Security system• Life-cycle variation in household dependents• Bequests• Illiquid asset• Liquid asset• Credit card debt

• Numerical solution (backwards induction) of 90 period lifecycle problem.

LRT Results:


= 0.70 (s.e. 0.11) = 0.96 (s.e. 0.01) Null hypothesis of = 1 rejected (t-stat of 3). Specification test accepted.

Moments: Empirical Simulated (Hyperbolic)%Visa: 68% 63%Visa/Y: 13% 17%MPC: 23% 31%f(W/Y): 2.6 2.7

Kaur, Kremer, and Mullainathan (2009):

Compare two piece-rate contracts: 1. Linear piece-rate contract (“Control contract”)

– Earn w per unit produced

2. Linear piece-rate contract with penalty if worker does not achieve production target T (“Commitment contract”)

– Earn w for each unit produced if production>=T, earn w/2 for each unit produced if production<T

T

Earnings

Production

Never earn more under commitment contract

May earn much less

Kaur, Kremer, and Mullainathan (2009):• Demand for Commitment (non-paydays)

– Commitment contract (Target>0) chosen 39% of the time– Workers are 11 percentage points more likely to choose

commitment contract the evening before

• Effect on Production (non-paydays)– Being offered contract choice increases average

production by 5 percentage points relative to control– Implies 13 percentage point productivity increase for those

that actually take up commitment contract– No effects on quality of output (accuracy)

• Payday Effects (behavior on paydays)– Workers 21 percentage points more likely to choose

commitment (Target>0) morning of payday– Production is 5 percentage points higher on paydays

Some other field evidence

• Ashraf and Karlan (2004): commitment savings• Della Vigna and Paserman (2005): job search• Duflo (2009): immunization• Duflo, Kremer, Robinson (2009): commitment fertilizer• Karlan and Zinman (2009): commitment to stop smoking• Milkman et al (2008): video rentals return sequencing• Oster and Scott-Morton (2005): magazine marketing/sales• Sapienza and Zingales (2008,2009): procrastination• Thornton (2005): HIV testing• Trope & Fischbach (2000): commitment to medical adherence• Wertenbroch (1998): individual packaging

4. Neuroscience Foundations• What is the underlying mechanism?• Why are our preferences inconsistent?• Is it adaptive?• How should it be modeled?• Does it arise from a single time preference

mechanism (e.g., Herrnstein’s reward per unit time)?• Or is it the resulting of multiple systems interacting

(Shefrin and Thaler 1981, Bernheim and Rangel 2004, O’Donoghue and Loewenstein 2004, Fudenberg and Levine 2004)?

Shiv and Fedorikhin (1999)

• Cognitive burden/load is manipulated by having subjects keep a 2-digit or 7-digit number in mind as they walk from one room to another

• On the way, subjects are given a choice between a piece of cake or a fruit-salad

Processing burden % choosing cake

Low (remember only 2 digits) 41%

High (remember 7 digits) 63%

Mesolimbic dopamine reward system

Frontalcortex

Parietalcortex

Affective vs. Analytic Cognition

mPFCmOFCvmPFC

• Hypothesize that the fronto-parietal system is patient• Hypothesize that mesolimbic system is impatient.• Then integrated preferences are quasi-hyperbolic

Relationship to quasi-hyperbolic model

now t+1 t+2 t+3

PFC 1 1 1 1 …

Mesolimbic 1 0 0 0 …

Total 2 1 1 1 …

Total normed 1 1/2 1/2 1/2 …

Relationship to quasi-hyperbolic model

• Hypothesize that the fronto-parietal system is patient• Hypothesize that mesolimbic system is impatient.• Then integrated preferences are quasi-hyperbolic


(1/)Ut = (1/)ut + ut+1 ut+2ut+3

(1/)Ut =(1/)ut + [ut + ut+1 ut+2ut+3

limbic fronto-parietal cortex

Hypothesis:

Limbic system discounts reward at a higher rate than does theprefrontal cortex.

time

disc

ount

val

ue prefrontal cortex

mesolimbic system

0.0

1.0

5. Neuroimaging EvidenceMcClure, Laibson, Loewenstein, and Cohen

Science (2004)

• Do agents think differently about immediate rewards and delayed rewards?

• Does immediacy have a special emotional drive/reward component?

• Does emotional (mesolimbic) brain discount delayed rewards more rapidly than the analytic (fronto-parietal cortex) brain?

Choices involving Amazon gift certificates:

delay d>0 d’

Reward R R’

Hypothesis: fronto-parietal cortex.

delay d=0 d’

Reward R R’

Hypothesis: fronto-parietal cortex and limbic.

Time

Time

Emotional system responds only to immediate rewards

y = 8mmx = -4mm z = -4mm0

7

T13

Earliest reward available todayEarliest reward available in 2 weeksEarliest reward available in 1 month

VStr MOFC MPFC PCC

Neu

ral

acti

vity

Seconds

McClure, Laibson, Loewenstein, and Cohen Science (2004)

0.4%

2s

x = 44mm

x = 0mm

0 15T13

VCtx

0.4%

2s

RPar

DLPFC VLPFC LOFC

Analytic brain responds equally to all rewardsPMA

Earliest reward available in 2 weeksEarliest reward available in 1 month

Earliest reward available today

0.0

-0.05

0.05

ChooseSmaller

ImmediateReward

ChooseLarger

DelayedReward

EmotionalSystem

Frontalsystem

Bra

in A

ctiv

ity

Brain Activity in the Frontal System and Emotional System Predict Behavior

(Data for choices with an immediate option.)

Conclusions of Amazon study

• Time discounting results from the combined influence of two neural systems:

• Mesolimbic dopamine system is impatient.

• Fronto-parietal system is patient.

• These two systems are separately implicated in ‘emotional’ and ‘analytic’ brain processes.

• When subjects select delayed rewards over immediately available alternatives, analytic cortical areas show enhanced changes in activity.

Open questions

New experiment on primary rewards: Juice McClure, Ericson, Laibson, Loewenstein, Cohen (Journal of Neuroscience, 2007)

1. What is now and what is later?• Our “immediate” option (Amazon gift certificate)

did not generate immediate “consumption.”• Also, we did not control the time of consumption.

2. How does the limbic signal decay as rewards are delayed?

3. Would our results replicate with a different reward domain?

4. Would our results replicate over a different time horizon?

Subjects water deprived for 3hr prior to experiment

(subject scheduled for 6:00)

Free (10s max.) 2s Free (1.5s Max)Variable Duration

15s

(i) Decision Period (ii) Choice Made (iii) Pause (iv) Reward Delivery

15s 10s 5s

iv. Juice/Water squirt (1s )

…Time

i ii iii

A

B

Figure 1

dd'-d (R,R')

{ This minute, 10 minutes, 20 minutes } { 1 minute, 5 minutes } {(1ml, 2ml), (1ml, 3ml), (2ml, 3ml)}

Experiment Design

d = This minuted'-d = 5 minutes(R,R') = (2ml, 3ml)

Figure 5

x = 0mm x = -48mm

x = 0mm y = 8mm

Juiceonly

Amazononly

Both

Patient areas (p<0.001)

Impatient areas (p<0.001)

x = 0mm x = -48mm

x = -4mm y = 12mm

Patient areas (p<0.01)

Impatient areas (p<0.01)

Comparison with Amazon experiment:

Measuring discount functions using neuroimaging data

• Impatient voxels are in the emotional (mesolimbic) reward system

• Patient voxels are in the analytic (prefrontal and parietal) cortex

• Average (exponential) discount rate in the impatient regions is 4% per minute.

• Average (exponential) discount rate in the patient regions is 1% per minute.

(D=0,D'=1)

(D=0,D'=5)

(D=10,D'=11)(D=10,D'=15)

(D=20,D'=21)(D=20,D'=25)

0.5

11.

52

Nor

med

Act

ivat

ion

0 5 10 15 20 25Time to later reward

Actual Predicted

Average Beta Area Activation, Actual and Predicted

(D=0,D'=1) (D=0,D'=5)(D=10,D'=11)

(D=10,D'=15)

(D=20,D'=21) (D=20,D'=25)

0.5

11.

52

Nor

med

Act

ivat

ion

0 5 10 15 20 25Time to later reward

Actual Predicted

Average Delta Area Activation, Actual and Predicted

Hare, Camerer, and Rangel (2009)

+

4sfood itempresentation

?-?s fixation

Rate Health

Rate Health

+

Rate Taste

Rate Taste

+

Decide

Decide

Health Session Taste Session Decision Session

Rating Details

• Taste and health ratings made on five point scale:-2,-1,0,1,2

• Decisions also reported on a five point scale: SN,N,0,Y,SY

“strong no” to “strong yes”

What is self-control?

• Rejecting a good tasting food that is not healthy• Accepting a bad tasting food that is healthy

More activity in DLPFC in trials with successful self control than in trials with

unsuccessful self-control

L

p < .001 p < .005

Summary of neuroimaging evidence

• One system associated with midbrain dopamine neurons (mesolimbic dopamine system) discounts at a high rate.

• Second system associated with lateral prefrontal and posterior parietal cortex responsible for self-regulation (and shows relatively little discounting)

• Combined function of these two systems accounts for decision making across choice domains, including non-exponential discounting regularities.

Outline

1. Experimental evidence for dynamic inconsistency.2. Theoretical framework: quasi-hyperbolic discounting.3. Field evidence: dynamic decisions.4. Neuroscience:

– Mesolimbic Dopamine System (emotional, impatient)– Fronto-Parietal Cortex (analytic, patient)

5. Neuroimaging evidence– Study 1: Amazon gift certificates– Study 2: juice squirts– Study 3: choice of snack foods

6. Policy

6. PolicyDefaults in the savings domain

• Welcome to the company• If you don’t do anything

– You are automatically enrolled in the 401(k) – You save 2% of your pay– Your contributions go into a default fund

• Call this phone number to opt out of enrollment or change your investment allocations

Madrian and Shea (2001)Choi, Laibson, Madrian, Metrick (2004)

401(k) participation by tenure at firm

0%

20%

40%

60%

80%

100%

0 6 12 18 24 30 36 42 48

Tenure at company (months)

Automaticenrollment

Standard enrollment

Survey given to workers who were subject to automatic enrollment:

“You are glad your company offers automatic enrollment.”

Agree? Disagree?

• Enrolled employees: 98% agree• Non-enrolled employees: 79% agree• All employees: 97% agree

Do people like a little paternalism?

Source: Harris Interactive Inc.

The power of deadlines: Active decisions Carroll, Choi, Laibson, Madrian, Metrick (2004)

Active decision mechanisms require employees to make an active choice about 401(k) participation.

• Welcome to the company• You are required to submit this form within 30 days of hire,

regardless of your 401(k) participation choice• If you don’t want to participate, indicate that decision • If you want to participate, indicate your contribution rate and

asset allocation• Being passive is not an option

401(k) participation by tenure

0%

20%

40%

60%

80%

100%

0 6 12 18 24 30 36 42 48 54

Tenure at company (months)

Frac

tion

of e

mpl

oyee

s ev

er

part

icip

ated

Active decision cohort Standard enrollment cohort

Active Decision Cohort

Standard enrollment cohort

0%

10%

20%

30%

40%

50%

0 3 6 9 12 15 18 21 24 27 30 33

Time since baseline (months)

Frac

tion

Ever

Par

ticip

atin

g in

Pl

an 2003

2004

2005

Simplified enrollment raises participationBeshears, Choi, Laibson, Madrian (2006)

Use automaticity and deadlines to nudge people to make better health decisions

One early example: Home delivery of chronic meds (e.g. maintenance drugs for diabetes and CVD)

• Pharmaceutical adherence is about 50%• One problem: need to pick up your meds • Idea: use active decision intervention to encourage

workers on chronic meds to consider home delivery• Early results: HD take up rises from 14% to 38%

Extensions to health domain

Cost saving at test company (preliminary estimates)

81

Annualized Savings

Plan $2,413,641

Members $1,872,263

Total Savings $4,285,904 0

50,000

100,000

150,000

200,000

250,000

300,000

350,000

Before SHD

After SHD

Rxs at Mail (annualized)

Now need to measure effects on health.

Policy Debates

• Pension Protection Act (2006)• Federal Thrift Savings Plan adopts autoenrollment (2009)• Auto-IRA mandate (2009?)• Consumer Financial Protection Agency (2009?)

– Default/privileged plain vanilla financial products– Disclosure– Simplicity– Transparency– Education

$100 bills on the sidewalkChoi, Laibson, Madrian (2004)

• Employer 401(k) match is an instantaneous, riskless return

• Particularly appealing if you are over 59½ years old– Can withdraw money from 401(k) without penalty

• On average, half of employees over 59½ years old are not fully exploiting their employer match

• Educational intervention has no effect

84

Education and DisclosureChoi, Laibson, Madrian (2007)

• Experimental study with 400 subjects

• Subjects are Harvard staff members

• Subjects read prospectuses of four S&P 500 index funds

• Subjects allocate $10,000 across the four index funds

• Subjects get to keep their gains net of fees

85

$255

$320

$385

$451

$516

$581Data from Harvard Staff

Control TreatmentFees salient

3% of Harvard staffin Control Treatment

put all $$$in low-cost fund

$494$518

Fees from random allocation$431

86

$255

$320

$385

$451

$516

$581Data from Harvard Staff

Control TreatmentFees salient

3% of Harvard staffin Control Treatment


9% of Harvard staffin Fee Treatment


$494$518

Fees from random allocation$431

7. The Age of ReasonAgarwal, Driscoll, Gabaix, Laibson (2008)

(1,2) Home Equity Loans and Home Equity Credit Lines

• Proprietary data from large financial institutions• 75,000 contracts for home equity loans and lines of

credit, from March-December 2002 (all prime borrowers)

• We observe:– Contract terms: APR and loan amount– Borrower demographic information: age, employment

status, years on the job, home tenure, home state location– Borrower financial information: income, debt-to-income ratio– Borrower risk characteristics: FICO (credit) score, loan-to-

value (LTV) ratio

Home Equity Regressions

• We regress APRs for home equity loans and credit lines on:– Risk controls: FICO score and Loan to Value (LTV)– Financial controls: Income and debt-to-income ratio– Demographic controls: state dummies, home tenure,

employment status– Age spline: piecewise linear function of borrower age with

knots at age 30, 40, 50, 60 and 70.

• Next slide plots fitted values on age splines

Home Equity Loan APR by Borrower Age

5.00

5.25

5.50

5.75

6.00

6.25

6.5020 23 26 29 32 35 38 41 44 47 50 53 56 59 62 65 68 71 74 77 80

Borrower Age (Years)

AP

R (

Pe

rce

nt)

Home Equity Credit Line APR by Borrower Age

4.00

4.25

4.50

4.75

5.00

5.25

5.5020 23 26 29 32 35 38 41 44 47 50 53 56 59 62 65 68 71 74 77 80


AP

R (

Pe

rce

nt)

(3) “Eureka”: Learning to Avoid Interest Charges on Balance Transfer

Offers• Balance transfer offers: borrowers pay lower APRs

on balances transferred from other cards for a six-to-nine-month period

• New purchases on card have higher APRs• Payments go towards balance transferred first, then

towards new purchases

• Optimal strategy: make no new purchases on card to which balance has been transferred

Eureka: Predictions

• Borrowers may not initially understand / be informed about card terms

• Borrowers may learn about terms by observing interest charges on purchases, or talking to friends– We should see “eureka” moments: new

purchases on balance-transfer cards should drop to zero (in the month after borrowers “figure out” the card terms)

• Study: 14,798 accounts which accepted such offers over the period January 2000 to December 2002

Propensity of Ever Experiencing a "Eureka" Moment by Borrower Age

40%

45%

50%

55%

60%

65%

70%

75%

80%

85%

90%

20

24

28

32

36

40

44

48

52

56

60

64

68

72

76

80


Pe

rce

nt

Fraction of Borrowers in Each Age Group Experiencing a Eureka Moment, by Month

0%

10%

20%

30%

40%

50%

60%

18 to 24 25 to 34 35 to 44 45 to 64 Over 65Borrower Age Category

Per

cen

t o

f B

orr

ow

ers

Month One Month TwoMonth Three Month FourMonth Five Month SixNo Eureka

Seven other examples

• Three kinds of credit card fees:– Late payment– Over limit– Cash advance

• Credit card APRs• Mortgage APRs• Auto loan APRs• Small business credit card APRs

Frequency of Fee Payment by Borrower Age

0.15

0.17

0.19

0.21

0.23

0.25

0.27

0.29

0.31

0.33

0.352

02

32

62

93

23

53

84

14

44

75

05

35

65

96

26

56

87

17

47

78

0


Fe

e F

req

ue

nc

y (

pe

r m

on

th)

Late Fee

Over Limit Fee

Cash Advance Fee

Auto Loan APR by Borrower Age

8.00

8.25

8.50

8.75

9.00

9.25

9.50


AP

R (

Pe

rce

nt)

Credit Card APR by Borrower Age

17.00

17.25

17.50

17.75

18.00

18.25

18.502

02

32

62

93

23

53

84

14

44

75

05

35

65

96

26

56

87

17

47

78

0


AP

R (

Pe

rce

nt)

Mortgage APR by Borrower Age

11.50

11.75

12.00

12.25

12.50

12.75

13.002

02

32

62

93

23

53

84

14

44

75

05

35

65

96

26

56

87

17

47

78

0


AP

R (

Pe

rce

nt)

Small Business Credit Card APR by Borrower Age

14.50

14.75

15.00

15.25

15.50

15.75

16.00

20

23

26

29

32

35

38

41

44

47

50

53

56

59

62

65

68

71

74

77

80


AP

R (

Pe

rce

nt)

U-shape for prices paid in 10 examples

– Home equity loans

– Home equity lines of credit

– Eureka moments for balance transfers

– Late payment fees

– Over credit limit fees

– Cash advance fees

– Auto loans

– Credit cards

– Small business credit cards

– Mortgages

Chronological Age

20 30 40 50 60 70 80 90

Z-S

core

-2.0

-1.5

-1.0

-0.5

0.0

0.5

1.0

1.5

Word Recall (N = 2,230)Matrix Reasoning (N = 2,440)Spatial Relations (N = 1,618)Pattern Comparison (N = 6,547)

84

69

50

31

16

7

Pe

rce

ntil

e

Salthouse Studies – Memory and Analytic Tasks

Source: Salthouse (forth.)

DementiaFerri et al 2005

Prevalence of dementia:

60-64: 0.8%

65-69: 1.7%

70-74: 3.3%

75-79: 6.5%

80-84: 12.8%

85+: 30.1%

Cognitive Impairment w/o Dementia(Plassman et al 2008)

Prevalence:

71–79: 16.0%

80–89: 29.2%

90+: 39.0%

Regulation?

• Regulator creates a very broad safe harbor for financial services (e.g., caps on mutual fund fees, plain vanilla credit cards, mortgages without prepayment penalties, etc…).

• An investor may conduct a financial transaction that is outside the safe harbor if the investor is advised by a fiduciary (with legal liability).

Outline

1. Motivating experimental evidence2. Theoretical framework 3. Field evidence4. Neuroscience foundations5. Neuroimaging evidence6. Policy applications7. The age of reason

A copy of these slides will soon be available on my Harvard website.

behavioral economics and aging david laibson harvard university and nber july 8, 2009 rand

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