Intertemporal Choice
- SS200 Behavioural Economics
- 21 January 2004 by Martin Barner
Papers
 Frederick, Loewenstein & O’Donoghue:
”A review of intertemporal choice” (2002)
 Angeletos, Laibson, Repetto, Tobacman & Weinberg:
”The hyperbolic consumption model” (2001)
 Laibson:
”Golden eggs and hyperbolic discounting” (1997)
Agenda
 Motivation
 History of intertemporal choice
 Anomalies from discounted utility theory
 Two examples of hyperbolic discounting
 Results of simulations in Angeletos et al
 Conclusions and perspectives
Motivation
 What is analyzed
 Why care
 What to learn
 Citation
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 rate expresses motives
Accepted as normative and descriptive
Utility and consumption independence
Time consistency
Opposing forces
1.
2.
Diminishing marginal utility
Positive time preference
Definitions
 Time discounting
Reason for caring less about future
 Time preference
Immediate utility over delayed utility
Anomalies from DU
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Empirically discount rates 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. singly)
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Figure 1:
- from Frederick et al
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Figure 2:
- from Frederick et al
Hyperbolic discounting
 Declining rate of time preference
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Example 1:
 ”Golden eggs and hyperbolic discounting”
 Substancial benefit in long run…
 …But temptation in short run
 Illiquid assets provide commitment
 Two-thirds of American wealth illiquid
 Not counting human capital
 Access to credit reduce commitment
 Explain decline in savings rate 1980s
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Figure 3:
- from Laibson
Example 2:
 ”The hyperbolic consumption model”
 Long run intentions and short run actions
 Hyperbolic preferences induce dynamic inconsistency
 Sophisticated consumers
 Model with simulations
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
Conclusion
 Use insight from psychology
 Relinguish finding the right discount rate
 Intertemporal choice reflects considerations
 Descriptively adequate models are not easy
 Not general theory – degrees of freedom
Behavioural perspectives
 Other models (instantaneous utility function)
 Habit formation
 Reference point models
 Visceral influence
 Projection bias
 Multiple self