Lecture 1: Instant Gratification

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Lecture 1 Instant Gratification
David Laibson Harvard University and NBER July
13, 2009 Mannheim Summer School
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1. Motivating Experiments A Thought Experiment

• Would you like to have
• 15 minute massage now
• or
• B) 20 minute massage in an hour
• Would you like to have
• C) 15 minute massage in a week
• or
• D) 20 minute massage in a week and an hour

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Read and van Leeuwen (1998)
Choosing Today
Eating Next Week
Time
If you were deciding today, would you
choose fruit or chocolate for next week?
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Patient choices for the future
Choosing Today
Eating Next Week
Time
Today, subjects typically choose fruit for next
week.
74 choose fruit
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Impatient choices for today
Choosing and Eating Simultaneously
Time
If you were deciding today, would you
choose fruit or chocolate for today?
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Time Inconsistent Preferences
Choosing and Eating Simultaneously
Time
70 choose chocolate
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Read, Loewenstein Kalyanaraman (1999)

• Choose among 24 movie videos
• Some are low brow Four Weddings and a Funeral
• Some are high brow Schindlers 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.

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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.

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Self-regulationAriely and Wertenbroch (2002)

• Three proofreading tasks "Sexual identity is
  intrinsically impossible," says Foucault
  however, according to de Selby1, 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'Erlette2 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

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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

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Detailed Outline For Lecture 1

• Motivating experimental evidence
• Theoretical framework
• Field evidence
• Policy
• A copy of these slides will soon be available on
  my Harvard website.

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2. Theoretical Framework

• Classical functional form exponential functions.
• D(t) dt
• D(t) 1, d, d2, d3, ...
• Ut ut d ut1 d2 ut2 d3 ut3 ...
• 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.

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Constant rate of decline
-D'(t)/D(t) rate of decline of a discount
function
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Slow rate of decline in long run
Rapid rate of decline in short run
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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
  100e(-0.01)365t 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

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An Alternative Functional Form

• Quasi-hyperbolic discounting
• (Phelps and Pollak 1968, Laibson 1997)
• D(t) 1, bd, bd2, bd3, ...
• Ut ut bdut1 bd2ut2 bd3ut3 ...
• Ut ut b dut1 d2ut2 d3ut3
  ...
• b 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)

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Building intuition

• To build intuition, assume that b ½ and d 1.
• Discounted utility function becomes
• Ut ut ½ ut1 ut2 ut3 ...
• Discounted utility from the perspective of time
  t1.
• Ut1 ut1 ½
  ut2 ut3 ...
• Discount function reflects dynamic inconsistency
  preferences held at date t do not agree with
  preferences held at date t1.

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Application to massagesb ½ and d 1
NPV in current minutes 15 minutes now 10
minutes now 7.5 minutes now 10 minutes now
A 15 minutes now B 20 minutes in 1 hour C
15 minutes in 1 week D 20 minutes in 1 week
plus 1 hour
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Application to massagesb ½ and d 1
NPV in current minutes 15 minutes now 10
minutes now 7.5 minutes now 10 minutes now
A 15 minutes now B 20 minutes in 1 hour C
15 minutes in 1 week D 20 minutes in 1 week
plus 1 hour
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Exercise

• Assume that b ½ and d 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 wont follow through without commitment.

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Beliefs about the future?

• Sophisticates know that their plans to be
  patient tomorrow wont pan out (Strotz, 1957).
• I wont 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 ß1 in the future.
• I will quit smoking next week, though Ive
  failed to do so every week for five years.
• Partial naifs mistakenly believe that ßß in
  the future where ß lt ß lt 1 (ODonoghue and
  Rabin, 2001).

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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 ? 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
  ß lt 1 and d 1.
• So weighting function is 1, ß, ß, ß,
• Agent has sophisticated (rational) forecast of
  her own future behavior. She knows that next
  period, she will again have the weighting
  function 1, ß, ß, ß,

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Timing of game

• Period begins (assume task not yet done)
• Pay cost ? (since task not yet done)
• Observe current value of opportunity cost c
  (drawn from uniform)
• Do task this period or choose to delay again.
• It task is done, game ends.
• If task remains undone, next period starts.

Pay cost ?
Observe current value of c
Do task or delay again
Period t-1
Period t
Period t1
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Sophisticated procrastination

• There are many equilibria of this game.
• Lets study the equilibrium in which
  sophisticates act whenever c lt 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

Likelihood of doing it in t1
Likelihood of not doing it in t1
Cost youll pay for certain in t1, since job not
yet done
Expected cost conditional on drawing a low enough
c so that you do it in t1
Expected cost starting in t2 if project was not
done in t1
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• In equilibrium, the sophisticate needs to be
  exactly indifferent between acting now and
  waiting.
• Solving for c, we find
• So expected delay is

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How does introducing ßlt1 change the expected
delay time?
If ß2/3, then the delay time is scaled up by a
factor of
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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 ß
  1.
• So she (falsely) thinks that future selves will
  pick an action threshold of

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• In equilibrium, the naif needs to be exactly
  indifferent between acting now and waiting.
• To solve for V, recall that

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• 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

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• 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/ß.

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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

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

• Survey
• Mailed to 590 employees (random sample)
• Matched to administrative data on actual savings
  behavior

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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
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Laibson, Repetto, and Tobacman (2007)

• Use MSM to estimate discounting parameters
• Substantial illiquid retirement wealth W/Y
  3.9.
• Extensive credit card borrowing
• 68 didnt 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)

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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.

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LRT Results

• Ut ut b dut1 d2ut2 d3ut3
  ...
• b 0.70 (s.e. 0.11)
• d 0.96 (s.e. 0.01)
• Null hypothesis of b 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
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Kaur, Kremer, and Mullainathan (2009)

• Compare two piece-rate contracts
• Linear piece-rate contract (Control contract)
• Earn w per unit produced
• Linear piece-rate contract with penalty if worker
  does not achieve production target T (Commitment
  contract)
• Earn w for each unit produced if productiongtT,
  earn w/2 for each unit produced if productionltT

Never earn more under commitment contract May
earn much less
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Kaur, Kremer, and Mullainathan (2009)

• Demand for Commitment (non-paydays)
• Commitment contract (Targetgt0) 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 (Targetgt0) morning of payday
• Production is 5 percentage points higher on
  paydays

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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

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Small immediate rewards Thornton (2005)
Dollar reward for picking up results
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Small immediate costs Thornton (2005)
Fraction picking up info on HIV status
Randomized distance (miles) to pick up info
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Outline

• Experimental evidence for dynamic inconsistency.
• Theoretical framework quasi-hyperbolic
  discounting.
• Field evidence dynamic decisions.
• Policy and interventions

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4. PolicyDefaults in the savings domain

• Welcome to the company
• If you dont 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

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Madrian and Shea (2001)Choi, Laibson, Madrian,
Metrick (2004)
Automatic enrollment
Standard enrollment
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Employees enrolled under automatic enrollment
cluster at default contribution rate.
Fraction of Participants at different
contribution rates
Default contribution rate under
automatic enrollment
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Participants stay at the automatic enrollment
defaults for a long time.
Fraction of Participants Hired Under Automatic
Enrollment who are still at both Default
Contribution Rate and Asset Allocation
Fraction of Participants
Tenure at Company (Months)
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Survey given to workers who were subject to
automatic enrollment You are glad your
company offers automatic enrollment. Agree?
Disagree?
Do people like a little paternalism?

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

Source Harris Interactive Inc.
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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 dont want to participate, indicate that
  decision
• If you want to participate, indicate your
  contribution rate and asset allocation
• Being passive is not an option

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Active Decision Cohort
Standard enrollment cohort
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Simplified enrollment raises participation Beshear
s, Choi, Laibson, Madrian (2006)
2005
2004
2003
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Extensions to health domain

• 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

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Cost saving at test company (preliminary
estimates)
Rxs at Mail (annualized)
Now need to measure effects on health.
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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

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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

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Education and DisclosureChoi, Laibson, Madrian
(2007)

• Experimental study with 400 subjects
• Subjects are Harvard staff members
• Subjects read prospectuses of four SP 500 index
  funds
• Subjects allocate 10,000 across the four index
  funds
• Subjects get to keep their gains net of fees

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Data from Harvard Staff
Control Treatment
Fees salient
518
494
Fees from random allocation 431
3 of Harvard staff in Control Treatment put all
in low-cost fund
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Data from Harvard Staff
Control Treatment
Fees salient
518
494
Fees from random allocation 431
3 of Harvard staff in Control Treatment put all
in low-cost fund
9 of Harvard staff in Fee Treatment put all
in low-cost fund
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Outline

• Motivating experimental evidence
• Theoretical framework
• Field evidence
• Policy applications
• A copy of these slides will soon be available on
  my Harvard website.