Lecture 1: Instant Gratification

David LaibsonHarvard University and NBER

July 13, 2009Mannheim Summer School

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.

Self-regulationAriely and Wertenbroch (2002)

Three proofreading tasks: "Sexual identity is intrinsically impossible," says Foucault; however, according to de Selby[1], it is not so much sexual identity that is intrinsically impossible, but rather the dialectic, and some would say the satsis, of sexual identity. Thus, D'Erlette[2] holds that we have to choose between premodern dialectic theory and subcultural feminism imputing the role of the observer as poet.

• Evenly spaced deadlines. [$20 earnings]• Self-imposed deadlines -- subjects can adopt costly

deadlines ($1/day) and most did so. [$13 earnings] • End deadline. [$5 earnings]

Conceptual Outline

First lecture• People are not internally consistent decision-makers• Internal conflicts can be modeled and measured• Scalable, inexpensive policies can transform behavior

Second lecture: • Early understanding of neural foundations

Detailed Outline For Lecture 1

1. Motivating experimental evidence2. Theoretical framework 3. Field evidence4. Policy

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

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.

Beliefs about the future?

• Sophisticates: know that their plans to be patient tomorrow won’t pan out (Strotz, 1957).– “I won’t quit smoking next week, though I would like

to do so.”• Naifs: mistakenly believe that their plans to be patient

will be perfectly carried out (Strotz, 1957). Think that β=1 in the future.– “I will quit smoking next week, though I’ve failed to

do so every week for five years.”• Partial naifs: mistakenly believe that β=β* in the future

where β < β* < 1 (O’Donoghue and Rabin, 2001).

Example 1. A model of procrastinationCarroll et al (2009)

• Agent needs to do a task (once).

– For example, switch to a lower cost cell phone.

• Until task is done, agent losses θ units per period.

• Doing task costs c units of effort now.

– Think of c as opportunity cost of time

• Each period c is drawn from a uniform distribution on [0,1].

• Agent has quasi-hyperbolic discount function with β < 1 and δ = 1.

• So weighting function is: 1, β, β, β, …

• Agent has sophisticated (rational) forecast of her own future behavior. She knows that next period, she will again have the weighting function 1, β, β, β, …

Timing of game

1. Period begins (assume task not yet done)

2. Pay cost θ (since task not yet done)

3. Observe current value of opportunity cost c (drawn from uniform)

4. Do task this period or choose to delay again.

5. It task is done, game ends.

6. If task remains undone, next period starts.

Period t-1 Period t Period t+1

Pay cost θ Observe current value of c

Do task or delay again

Sophisticated procrastination

• There are many equilibria of this game.• Let’s study the equilibrium in which sophisticates act

whenever c < c*. We need to solve for c*. This is sometimes called the action threshold.

• Let V represent the expected undiscounted cost if the agent decides not to do the task at the end of the current period t:

*

21 **

cc cV V

Cost you’ll pay for certain in t+1, since job not yet done

Likelihood of doing it in t+1

Expected cost conditional on drawing a low enough c* so that you do it in t+1

Likelihood of not doing it in t+1

Expected cost starting in t+2 if project was not done in t+1

• In equilibrium, the sophisticate needs to be exactly indifferent between acting now and waiting.

• Solving for c*, we find:

• So expected delay is:

* [ ( *)( * /2) (1 *) ]c V c c c V

*1 1

2

c

2

2

delay 1 * 2 1 * * 3 1 * *

1 * 1 *1*

1 1 * 1 1 * 1 1 *

1 11 1 1 2

*1 1 * 1 1 * *

E c c c c c

c cc

c c c

cc c c

How does introducing β<1 change the expected delay time?

1 11 12

delay given 1 221

1 1delay given =1 1 11 21 2

E

E

If β=2/3, then the delay time is scaled up by a factor of 2

Example 2. A model of procrastination: naifs

• Same assumptions as before, but…• Agent has naive forecasts of her own future behavior.• She thinks that future selves will act as if β = 1.• So she (falsely) thinks that future selves will pick an

action threshold of

* 21 1

2

c

• In equilibrium, the naif needs to be exactly indifferent between acting now and waiting.

• To solve for V, recall that:

**

[ ( *)( * /2) (1 *) ]

2 2 / 2 1 2

2 1 2

c V

c c c V

V

V

2 1 2

2

1 ***

2c

c

V

VcV

• Substituting in for V:

• So the naif uses an action threshold (today) of

• But anticipates that in the future, she will use a higher threshold of

** 2 1 2 2

2

c

** 2c

* 2c

• So her (naïve) forecast of delay is:

• And her actual delay will be:

• Her actual delay time exceeds her predicted delay time by the factor of 1/β.

1 1delay

* 2Forecast

c

1 1 1delay

** 2 2E

c

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

33

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:

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

= 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

• Shapiro (????); monthly food stamp cycle

• Thornton (2005): HIV testing

• Trope & Fischbach (2000): commitment to medical adherence

• Wertenbroch (1998): individual packaging

Outline

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

4. 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)

52

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

55

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

56

$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

57

$255

$320

$385

$451

$516

$581Data from Harvard Staff

Control TreatmentFees salient

3% of Harvard staffin Control Treatment

put all $$$in low-cost fund

9% of Harvard staffin Fee Treatment

put all $$$in low-cost fund

$494$518

Fees from random allocation$431

Outline

1. Motivating experimental evidence2. Theoretical framework 3. Field evidence4. Policy applications

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