Transcript Globalproduktplatform og Integrationsprojektets fase 2 og 3

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
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Papers
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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
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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
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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
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Empirically discount factor is not constant
1. Over time
2. 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?
Magnitude and hyperbolic effects
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$15 now is same as ___ in a month. ___ in
a year. ___ in 10 years.
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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…
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Students asked:
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$150 vs. $x in 1 month, 1 year, 10 years
• $5000 vs $x ….
Results of class survey
90%
$160
80%
Discount Rate
70%
60%
50%
150
$197
40%
5000
$500
30%
20%
$6,000
$14,000
10%
$5,100
0%
0
20
40
60
80
Months
100
120
140
An example of real consequence:
Front-loaded buyouts for soldiers
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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
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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?)
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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
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Soldiers had to choose between a lump
sum payment (on the order of $20K) and
an annuity (worth around $40K in present
value)
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More than 90% of the 55,000 enlisted men
chose the lump sum of $20K, suggesting
very high discount rates (17-20%).
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Savings to U.S. Government: $1.7 billion
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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.
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Figure 1:
- from Frederick et al
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Figure 2:
- from Frederick et al
Example 1:
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”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)
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Figure 3:
- from Laibson
Example 2:
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”The hyperbolic consumption model”
Hyperbolic preferences induce dynamic inconsistency
 Sophisticated consumers
 Model with simulations (calibration)
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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
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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
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
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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
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Reference-dependent preferences (K-Rabin 04)
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Emotions and self-regulation
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E.g. depression. Focusses attention on bad outcomes, causes
further depression
Intimidating decisions
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Belief
about choice
changes reference
point
Types
of anticipation
preferences
Endowment effects/”auction fever”
Explains experience effects (experienced traders expect to lose
objects, doesn’t enter endowment/ f1)
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?’
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Avoid the doctor late cancer diagnosis
Supply side determination of endowment effects (marketing)
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Self-fulfilling beliefs
u2(δz,z)>u2(δz,z’) u2(δz’,z’)> u2(δz’,z)
Three
• prefer
z if youinteresting
expect(ed) patterns
z, z’ if you expect(ed) z’
• Cognitive dissonance, encoding bias
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“If I could change the way/I live my life today/I wouldn’t change/a single
thing”– Lisa Stansfield
• Undermines learning from mistakes
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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
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Informational preferences
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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):
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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
• Framework:
Two selves, 1 and 2
equilibrium”
• 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:
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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:
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Choose from z1 X d2.
Choose f1 from Φ.
Choose z2