Intertemporal Choice Ec 101 Prof' Camerer

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Intertemporal ChoiceEc 101 Prof. Camerer

• Time preference
• Preferences for earlier vs later rewards
• Important choices involve time
• longer time horizon ? more irreversibility
• careers, children, retirement
• Likely to be difficult
• the brain is not evolved for long-term reward
• self-control addiction, obesity,
  procrastination
• Institutions may help or hurt
• No money down! vs expert advice external
  self-control (Soc. Security)

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• 1 Some history of intertemporal choice
• 2 Anomalies from discounted utility theory (LFR
  review)
• Field tests
• 3 Projection bias
• 4 Life-cycle savings
• Mental accounting puzzles
• Calibration exercise (Angeletos et al)
• Experimental data
• 5 Research frontiers
• Practical lessons
• Sophistication vs naivete

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1. Some history of intertemporal choice (see
Loewenstein, ch 1 L-Elster Choice Over Time)

• Adam Smith (1776)
• impartial spectator (cingulate, PFC?)
• John Rae (1834)
• Eugen von Böhm-Bawerk (1889)
• Irving Fisher (1930)
• Paul Samuelson (1937)
• Robert Strotz (1956)
• Phelps and Pollak (1968)
• ?- d used to explain discounting of self and
  children (future selves)
• David Laibson (1994,97) adapted PP 68

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E.g., Fisher

• Personal determinants of time preference
• Foresight
• Risk of future
• Self-control
• Habit
• Life-expectancy
• Concern for lives of other persons
• Fashion In whatever direction the leaders of
  fashion first chance to move, the crowd will
  follow in mad pursuit
• Was critical of econ-psych divide
• The fact that there are two schools, the
  productivity school and the psychological school,
  constantly crossing swords on this subject is a
  scandal in economic science and a reflection on
  the inadequate methods employed by these would-be
  destroyers of each other

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Discounted Utility Model

• Discount factor compresses many Fisherian forces
  into one term
• Now accepted as normative and descriptive
• It is completely arbitrary to assume that the
  individual behaves so as to maximize an integral
  of the form evisaged in DU. (Samuelson 1937)
• Utility and consumption independence
• Exponential ? time consistency

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2. Anomalies from DU (LFR)

• Measured discount factors are not constant
• Over time
• Across type of intertemporal choices
• Sign effect (gains vs. losses)
• Neural substitution of loss and delay?
• Magnitude effect (small vs. large amounts)
• Sequence effect (preference for upward-sloping
  profiles)
• Speedup-delay asymmetry (temporal loss-aversion).
  

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Magnitude and hyperbolic effects

• 15 now is same as ___ in a month. ___ in a year.
  ___ in 10 years.
• Thaler (1981) 20 in a month (demand 345
  interest), 50 in a year (120), 100 in 10 years
  (19 interest)
• Show discount rates decrease over time
• Students asked
• 150 vs. x in 1 month, 1 year, 10 years
• 5000 vs x .

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Results of class survey
160
197
500
6,000
14,000
5,100
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Figure 1 (LFR) Increasing variation over time as
more studies are done
,
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Figure 2 (LFR) Increasing patience with longer
horizons
,
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Discounting is important in other domains

• Education (Duckworth, Seligman 05 Psych Sci)
  Predicts 14-yr olds grades
• Not the will to winthe will to practice

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Role of attention cognition Exposure and
distractions very powerful (Walter Mischel et
al)

• Delay-of-gratification in children (ring bell
  when they cant wait any longer for better snack)
• Fun thoughts, covering snacks enhances
  patienceexcept if they are thinking about the
  snacks! (see Fig 6.1)
• Thoughts about arousing features versus
  cognitive re-appraisal creates impatience

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Field test Front-loaded buyouts for soldiers
(Warner-Pleeter AER 01)

• After the Gulf War in the early 1990s the
  military enticed soldiers into retirement
• Choose between a lump sum payment (on the order
  of 20K) and an annuity (worth around 40K in PV
  _at_ r10)
• Officers 50 took lump sum
• Enlisted 90 took lump sum

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• Officers
• enlisted

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• Can estimate discount rates from large n55,000
  sample (enlisted results)
• Male .01
• Black .035
• College -.048
• Test scores high (-.016), medium (-.01)
• Size of lump sum (-.059/10k) (largest fx)

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Vietnam exp (w/ Tomomi Tanaka, Quang Nguyen)
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General model estimation

• Benhabib, Bisin, Schotter (04)
• T1 exponential xexp(-rt)
• T2 hyperbolic x/(1rt)
• Graph for T1,2,5 (r.13)
• BBS est. T (2.62,4.14), r (6.37, 33.64)
• Vietnam villages T5.19, r13, a.88
• ROSCA participants have higher a (.15), lower r
  (-.04)
• Can also add fixed cost (-b) and variable cost (a
  multiplier)
• Highly variable estimates

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Projection bias (Loewenstein, Read, Rabin )

• Overestimate duration of state-dependence
• is estimated utility in s from
  state s
• a0 rational
• Examples
• Shopping while hungry
• Childbirth Lamaze versus epidural painkiller
  during labor
• Cannibalism
• Interpersonal Difficult to imagine what people
  will do in different emotional states...(looting,
  lynchmobs, corporate scandals, crimes of passion,
  heroic acts...)
• Wilson-Gilbert affective forecasting mistakes
  (fail to appreciate emotional immune system)

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Empirics Catalog sales for winter clothes items

• Winter-item catalog sales (Conlin, ODonoghue,
  Vogelsang AER in press)
• 2.4 million observations 95-99. One 1 day to
  process, 3-7 days to ship
• Theory predicts returns will depend on
  temperature on return day R
• 
  - on temperature on order day O
• intuition lower temp(O) ? surprised at high
  temp(R) and then return
• temp(O)
• temp (R)

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4. Lifecycle savings

• Golden eggs and hyperbolic discounting
• Hyperbolics are tempted
• Illiquid assets provide commitment
• Two-thirds of US wealth illiquid (real estate)
• Not counting human capital
• Access to credit reduces commitment
• Explain decline in savings rate 1980s?

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Borrowing Boom in bankruptcies
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Borrowing Credit card facts

• Average debt outstanding by income quintile (IQ)
• Rates (APR, red) have
• fallen as interest rates fall (blue). Blue is
  spread

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Mental accounting and MPC (Thaler-Shefrin 1988)
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Angeletos et al calibration

• Model features
• Quasi-hyperbolic sophisticated preferences
• uncertain future labor income
• liquidity constraint
• allow to borrow on credit cards - limit
• hyperbolic discounting implications
• labor income autocorrelated shocks
• hold liquid and illiquid assets
• Calibration strategy
• Fix some parameters, simulate behavior, compare
  properties with data

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Figure 3 Shapes of discount functions
,
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Figure 4 - from Angeletos et al
,
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Figure 5 - from Angeletos et al
,
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Figure 6 - from Angeletos et al
,
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Figure 7 - from Angeletos et al
,
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Table 1 - from Angeletos et al
,
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Table 2 - from Angeletos et al
,
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Habit formation Spending

• The hedonic treadmill

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Habit formation Spending

• The hedonic treadmill

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Optimal saving and investing Do sufficiently
rational agents optimize?
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Economics Nobel laureates reflect (from LA Times)
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Beverage delivery apparatus
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5. Research frontiers Sophistication vs naivete

• Are hyperbolics sophisticated? or naïve?
• Sophisticated hyperbolics will prefer
  pre-commitment
• IRS refunds
• Deadlines (Blockbuster vs Netflix)
• Ulysses and the sirens
• Arrest me list on riverboat casinos
• Wertenbroch
• Smaller package sizes of vices than virtues
• Cigarettes by the pack, gym contracts
  (Malmendier-Della Vigna AER 06, 19/visit vs 10
  visit fee)
• Q Will markets work? Or does government have
  special legal power to enforce these contracts?
  (e.g. Army AWOL)

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Sophisticates seek self-control (from periodic
food stamp checks, Ohls 92 Shapiro, 03 JPubEc)
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Factoid
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80 of respondents have negative discount rates!
voluntary forced saving (Shapiro JPubEc 03
cf. Ashraf et al QJE in press)
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Frontiers Practical value of behavioral
econSave More Tomorrow (Benartzi-Thaler JPE 04)

• Exploit power of inertia and desire to avoid a
  nominal decrease in pay
• Commit 1/3 of future raise to 401(k)

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Swedish privatization c 2000 (Cronqvist-Thaler
AER 04)

• Driven by desire for investor autonomy
• 456 funds, could advertise set fees
• Information (fees, performance, risk) in book
  form
• Big ad campaign Investors encouraged to choose
  their own fund (57 of young did)
• What happened?

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Swedish privatization (Cronqvist-Thaler AER 04)

• Autonomous investors
• home biased
• high fees
• Poor performance
• 03 92 of young choose default

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Neural evidence (McClure et al Sci
04)u(x0,x1,)/ ß (1/ß)u(x0) du(x1)
d2u(x2) Impulsive ß ?
long-term planning d ?
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Problem Measured d system is all stimulus
activityuse difficulty to separate d (bottom
left), d more active in late decisions with
immediacybut is it d or complexity?
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Other aspects of time in econ

• Other models and phenomena
• Habit formation (common in macro)
• Visceral influence (emotion-cognition)
• Temptation preferences (Gul-Pesendorfer 01
  Emetrica)
• w?w,t?t iff U(S)maxx?Su(x)v(x) maxy ? S
  v(y)
• Anxiety/savoring/memory as consumption
  (Caplin-Leahy e.g. wedding planning)
• Multiple selves/dual process models

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Types of anticipation preferences

• Reference-dependent preferences (K-Rabin 04)
• Belief about choice changes reference point
• Endowment effects/auction fever
• Explains experience effects (experienced traders
  expect to lose objects, doesnt enter endowment/
  f1)
• Emotions and self-regulation
• E.g. depression. Focusses attention on bad
  outcomes, causes further depression
• Intimidating decisions
• f1 may increase stress about future choices
• health care, marriage, job market, etc.
• Better to pretend future choicestatus quo
• Q When are these effects economically large?
• Avoid the doctor? late cancer diagnosis
• Supply side determination of endowment effects
  (marketing)

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Three interesting patterns

• Self-fulfilling beliefs
• u2(dz,z)gtu2(dz,z) u2(dz,z)gt u2(dz,z)
• prefer z if you expect(ed) z, z if you
  expect(ed) z
• Cognitive dissonance, encoding bias
• If I could change the way/I live my life today/I
  wouldnt change/a single thing Lisa Stansfield
• Undermines learning from mistakes
• Time inconsistency
• Self 2 prefers z given beliefs
  u2(f1,z)gtu2(f1,z)
• but self 1 preferred to believe and pick z
  u1(x,dz,z)gtu1(x,dz,z)
• Problem Beliefs occur after self 1 picks
• Informational preferences
• Resolution-loving Likes to know actual period 2
  choice ahead of time
• Information-neutral Doesnt care about knowing
  choice ahead of time (go with the flow)
• Information-loving Prefers more information to
  less (convex utility in f1)
• Disappointment-averse (prefers correct to
  incorrect guesses)
• u1(x,dz,z)u1(x,dz,z)gt u1(x,dz,z)u1(x,d
• Surprising fact If none of above hold, then
  personal equilibrium iff u maxs E(u1(z1,z2)
  I.e. only way beliefs can matter is through these
  three

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Koszegi, Utility from anticipation and personal
equilibrium

• Framework Two selves, 1 and 2
• Choices z1,z2 , belief about z2 is f1
• u1(z1,f1,z2)
• anticipation function F(z1,d2)f1 (d2 is period
  2 decision problem)
• personal equilibrium
• each self optimizes
• F(z1,d2)s2(z1,F(z1,d2),d2) anticipate s2(.)
  choice
• Beliefs are both a source of utility and
  constraint
• Timeline
• Choose from z1 X d2.
• Choose f1 from F.
• Choose z2