Intertemporal Choice

Prof. Camerer

Some history of intertemporal choice Anomalies from discounted utility theory Two examples of hyperbolic discounting Results of simulations in Angeletos et al Conclusions and perspectives

Papers Frederick, Loewenstein & O’Donoghue:

”A review of intertemporal choice” (2002) Angeletos, Laibson, Repetto, Tobacman & Weinberg:

”The hyperbolic consumption model” (2001) McClure et al Science

History of intertemporal choice Adam Smith (1776)

John Rae (1834) Eugen von Böhm-Bawerk (1889) Irving Fisher (1930) Paul Samuelson (1937) Robert Strotz (1956) Phelps and Pollak (1968) David Laibson (1994, 1997)

Discounted Utility Model

Discount factor compresses many forces mortality, uncertainty, time

compression... Accepted as normative and descriptive

...but initially arbitrary (Samuelson 1937)

Utility and consumption independence Exponential time consistency

Anomalies from DU Empirically discount factor is not

constant 1. Over time2. Across type of intertemporal choices

Sign effect (gains vs. losses) Magnitude effect (small vs. large

amounts) Sequence effect (sequence vs. single) Speedup-delay asymmetry (temporal

loss-aversion). Very strong?

• $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

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

An example of real consequence: Front-loaded buyouts for soldiers

• After the Gulf War in the early 1990s the military had to reduce its size by buying soldiers into retirement for up to $3.4 billion

• Soldiers had to choose between a lump sum payment (on the order of $20K) and an annuity (worth around $40K in present value)

An example of real consequences (AER 03?)

• After the Gulf War in the early 1990s the military had to reduce its size by buying soldiers into retirement for up to $3.4 billion

• Soldiers had to choose between a lump sum payment (on the order of $20K) and an annuity (worth around $40K in present value)

• More than 90% of the 55,000 enlisted men chose the lump sum of $20K, suggesting very high discount rates (17-20%).

• Savings to U.S. Government: $1.7 billion

• If the soldiers really wanted money now, they could have taken out a loan for even more (say $25,000) and then used the annuity income to pay it back.

Figure 1: - from Frederick et al

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Figure 2: - from Frederick et al

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Example 1: ”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? Key issue: sophisticated vs naive

Sophisticates seek self-control (from periodic food stamp checks, Ohls 92;

Shapiro, 03 JPubEc)

80% of respondents have negative discount rates! voluntary “forced

saving” (Shapiro JPubEc 03; cf. Ashraf et al QJE in press)

Figure 3: - from Laibson

,

Example 2: ”The hyperbolic consumption model” Hyperbolic preferences induce dynamic inconsistency Sophisticated consumers Model with simulations (calibration)

Example 2 (continued) Model features

uncertain future labour income liquidity constraint allow to borrow on credit cards - limit hyperbolic discounting – implications labour income autocorrelated – shocks hold liquid and illiquid assets

Results

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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Two time systems (McClure et al Sci 04):u(x0,x1,…)/ β = (1/β)u(x0) + [δu(x1) + δ2u(x2) +…]

Impulsive β ↓ long-term planning

δ ↓

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?

Other aspects of time in economics

Other models (instantaneous utility function) Habit formation (common in macro) Visceral influence (emotion-cognition)Temptation preferences (Gul-Pesendorfer)

w {w,t} t Projection bias

Overestimate duration of state-dependence (cf ”emotional immune system”)

Anxiety/savoring as a source of consumption (Caplin-Leahy) Multiple selves/dual process models

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)

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

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