Intertemporal Choice Ec 101 Prof. Camerer Time preference: Preferences for earlier vs later rewards Important choices involve time longer time horizon.

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)

Β- δ 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 1. Over time2. 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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• $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 ….

Magnitude and hyperbolic effects

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0%

10%

20%

30%

40%

50%

60%

70%

80%

90%

0 20 40 60 80 100 120 140

Months

Dis

co

un

t R

ate

150

5000

Results of class survey

$5,100

$160

$197$500

$6,000$14,000

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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 win…the 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 can’t wait any longer for better snack)

• Fun thoughts, covering snacks enhances patience…except 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 @ r=10%)

• 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 n=55,000 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)

• Θ=1 exponential =x*exp(-rt)

• Θ=2 hyperbolic =x/(1+rt)

• Graph for Θ=1,2,5 (r=.13)

• BBS est. Θ (2.62,4.14), r (6.37, 33.64)

• Vietnam villages: Θ=5.19, r=13, α=.88– ROSCA participants have higher α

(+.15), lower r (-.04)

• Can also add fixed cost (-b) and variable cost (α multiplier)

– Highly variable estimates

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0 1 5 10 15 20 25 30

5

2

1

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Projection bias (Loewenstein, Read, Rabin )

• Overestimate duration of state-dependence

is estimated utility in s’ from state s α=0 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, O’Donoghue, 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)

Structural estimates of α from .01-.64

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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”

$0

$500

$1,000

$1,500

$2,000

$2,500

$3,000

1970 1977 1983 1989 1992 1995 1998 2001

IQ 1

IQ 2

IQ 3

IQ 4

IQ 5

14.8%14.4% 14.5% 14.6% 14.4% 14.3% 14.3%

13.7%

12.8%12.3%

6.6% 6.4% 6.4%

5.3%5.7%

6.0%

5.0%4.6%

4.0% 4.3%

'95 '96 '97 '98 '99 '00 '01 '02 '03 '04

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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 econ:

Save 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,…)/ β = (1/β)u(x0) + [δu(x1) + δ2u(x2) +…]

Impulsive β ↓ long-term planning δ ↓

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Problem: Measured δ system is all stimulus activity…use difficulty to separate δ (bottom left), δ more active in late

decisions with immediacy…but is it δ 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)=maxxS[u(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, doesn’t 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 choice=status 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(δz,z)>u2(δz,z’) u2(δz’,z’)> u2(δz’,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 wouldn’t change/a single thing”– Lisa Stansfield

• Undermines learning from mistakes

• Time inconsistency– Self 2 prefers z’ given beliefs u2(f1,z’)>u2(f1,z)– but self 1 preferred to believe and pick z u1(x,δz,z)>u1(x,δz’,z’)– Problem: Beliefs occur after self 1 picks

• Informational preferences– Resolution-loving: Likes to know actual period 2 choice ahead of time– Information-neutral: Doesn’t 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,δz,z)+u1(x,δz’,z’)> u1(x,δz’,z)+u1(x,δ• Surprising fact: If none of above hold, then personal equilibrium iff u* max’s

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 Φ(z1,d2)=f1 (d2 is period 2 decision

problem)– personal equilibrium:

• each self optimizes• Φ(z1,d2)=s2(z1,Φ(z1,d2),d2) anticipate s2(.) choice

– Beliefs are both a source of utility and constraint

• Timeline: – Choose from z1 X d2. – Choose f1 from Φ. – Choose z2