Intertemporal Choice
(1)Traditional Approach
(2)Anomalies
(3)New Theories
(4)Applications
(5)Controversy
(6)Extensions
Dynamic Choice Theory
• Kreps (1988, 1979)
• X = menu, A dishes
• Changing Tastes and Sophisticated choice,
Preference for Flexibility (states of
preferences)
• Binary relation > on X x A is strategically
rational iff
(x,a)>=(x,a`) => (x,a) ~ (x, aUa`)
Exponential Discounting
• Adam Smith (1776)>>>Rae (1834)>>>von BohmBawerk(1889)>>>Fisher (1930)>>> Samuelson (1937)
• Exponential discount function:
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u(cs, xs) is the felicity function
Monotonically falling, utility additive and independent across time
Constant Rate of Decline (
Recursive (
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Anomaly 1 – Time Inconsistency
• Ainslie (1975)
• Also Thaler (1981)
• Discount rates declined sharply with the length of
time to be waited (ie. not constant)
• Immediacy effect (Prelec & Loewenstein 1991)
Anomaly 2 – Magnitude Effect
• “most robust of the ‘classic’
anomalies” (Read 2003)
• Implicit discount rates declined
sharply with the size of amount
(Thaler 1981)
• People give smaller proportional
tips the larger the restaurant bill.
(Chapman 1996)
• People sensitive also to absolute
differences.
• Mental accounting (forgone
interest vs forgone consumption)
Anomaly 3 – Direction Effect
• Delay vs Speed-up
(expedite)
• Loewenstein (1988)
• Reference point effect
• Delay premium is at
least twice the mean
speed-up cost
• Loss aversion?
(Kahneman &
Tversky)
Anomaly 4 – Sign Effect
• Gains vs. losses
• Thaler (1981),
Antonides &
Wunderink (2001)
• Discount rates for
gains is much greater
than for losses.
• “debt aversion”
Anomaly 5 – Sequence Effect
• People care about the “gestalt”, or overall
pattern of sequence
• Violates independence
• Loewenstein & Prelec (1993), Loewenstein &
Sicherman (1991)
• People prefer an increasing wage profile to a
declining or flat one
• French & Greek restaurant experiment
• Savoring and Dread
• {100, 100, 100} > {90, 100, 110} > {110, 100, 90}
(Barsky, Juster, Kimball & Shapiro 1997)
New Theories
• Interval Effect, u(x1)=u(x3`), u(x1)=u(x2), u(x2)=u(x3), x3>x3`shorter
interval more discounting (Read, 2001)
• Visceral Influences on Behavior, intense visceral factors cause
departure from perceived self-interest (Loewinstein 1996)
• Comsumer sovereignty, multiple selves with conflicting preferences
(Ainslie 1975, Elster 1979, Schelling 1984, Thaler & Shefrin 1981)
• Value function approaches, steeper for losses than gains, more
elastic for losses than gains, more elastic the larger the absolute
value. Sign, magnitude and direction effects by proportional changes.
(Loewenstein & Prelec 1992)
• Emotion-based theories. Temporal and physical proximity of options
leads to a disproportionate but transient increase in attractiveness of
options. Arousal not caused by delay but by aggravating stimulus.
Similarity – Attribute-based
• Rubinstein (2003)
• Simiplifying choice
• (x,0) > (y,1) but (x,10) < (y,11) [10 & 11
similar]
• 3-stage procedure (x, t1) vs (y, t2)
– Looks for dominance (eg. x>y & t1<t2 )
– Looks for similarities (eg. between x & y)
– If not decisive, different criterion
Hyperbolic Discounting
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Loewenstein & Prelec (1992)
Discount rates are greater in the
short run than in the long run
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Instantaneous discount rate:
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As t goes to infinity, discount rate
goes to 0
Empirical Support both in animals
and humans (Ainslie 1975,
Benzion et al. 1989)
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Quasi-Hyperbolic Discounting
• Phelps & Pollack (1968)
• Laibson (1997). The Goose with Golden Eggs. Every morning, 1 golden
egg. Greedy, killed the goose and opened it up to find nothing.
• Analytical Tractability
• Most of the discounting takes place between the current period and the
immediate future
• People cares
more about ut+1 vs ut at t0<t but
more if
asked on day t
• There is little additional discounting between future periods
• We typically assume that beta = ½ and delta = 1
Self-Control and Temptation
• Gul & Pesendorfer (2001, 2002)
• 2 competing “utilities” (Long-term utility, u &
temptation, v). No dynamic inconsistency!!
• ct = actual consumption, mt = maximum possible
consumpion, u+v concave, v convex (+4 axioms)
• Choosing between
• Wait if:
Procrastination/Naïve vs
Sophistication
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O'Donoghue & Rabin (1999, 1999, 2001)
Cost of doing the project at are {1, 3/2, 5/2}
at dates 0, 1 and 2. Hyperbolic discounting.
With commitment technology, project will
be done in period 1
Naifs will choose under the false
assumption that the later selfs will dowhat
the earlier selfs want
Sophisticates make decisions based on
correct beliefs about choices of later selfs
The Naif equilibrium is to do it in period 2,
while the Sophisticate equilibrium is to do it
on period 0 (since he has an effective
choice between 0 &2)
Also, partial naivette believes:
Stationary Procrastination
• (Rabin) 120 minutes of “fixing” effort reduces 10 minutes each day
after.
• The Naif will never do the task
• The sophisticate will do it on day 1 or day 2
Cumulative Procrastination
• (Rabin) Task: Read 30 pages in 30 days
• Decision on Day 1:
• 15½ minutes on day 1, 0.5 pages read
• Decision on Day 2:
• 16 minutes on day 2, plans to read 64 every day afterwards
• So, day 3 – 17 min, day 10 – 22 min, day 24 – 72 min, day 30 –
23¾ hours!!!
• So total of 51 hours spent on task
Application 1 – Life-cycle savings
and consumption
• Angeletos, Laibson, Repetto, Tobacman &
Weinberg
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Application 2 – Steady State
• Gul & Pesendorfer (2002)
• Changing consumption from
• Taking FOC of
• For
• We get
• In steady state
&
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Application 3 – Depp or Crap?
• (Rabin)
• Week 1 – crap movie, 3 utils. Week 2 – good movie, 5 utils. Week 3 – great
movie, 8 utils. Week 4 – Johnny Depp movie, 13 utils.
• You must skip one movie to write your research paper for BEE
• What would a sophisticate do?
– Because 8+½0 > 0+½13, the sophisticate won’t skip Week 3.
– Because 0+½(8+13) > 5+½(8+0), the sophisticate will skip Week 2 (if didn’t for
Week 1).
– Because 3+½(0+8+13) > 0+½(5+8+13), the sophisticate won’t skip Week 1.
– Hence sophisticate will miss the 2nd movie.
• What would a naif do?
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Because 8+½0 > 0+½13, the naif won’t skip Week 3.
Because 5+½(0+13) > 0+½(8+13), the naif won’t skip Week 2.
Because 3+½(0+8+13) > 0+½(5+8+13), the sophisticate won’t skip Week 1.
Hence the naif will miss the Johnny Depp movie : (
Application 4 – Health Clubs
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DellaVigna & Malmendier (2002)
Future benefits, b, “lose weight, get fit, stay healthy, and develop new social
contracts.”
Current costs, e, “logistic cost….. (and psychic) cost of exercising.”
Additional benefits for additional visits for flat rate, x.
Sign-up fee, F, for flat rate membership.
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Flat rate contract will be chosen if:
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At time 0, He believe he will attend at time t iff c <
b -10. But will actually attend if
c<
b - 10. The result is that he will always attend less often than he believes.
Sophisticates may use flat rate as commitment device. (Also, cancellation)
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Other Applications
• Other forms of procrastination, drug addiction,
self-deception, retirement timing, undersaving,
marketing. (Akerlof 1991, Barro 1999, Benabou
& Tirole 2000, Carrillo & Marriotti 2000, Diamond
& Koszegi 1998, Laibson 1997, O’Donoghue &
Rabin 1999, 1999, 2000, Wertenbroch 2003).
• Job-search, Trying new means of commuting,
etc. (Rabin)
• Behavioral Contract theory (DellaVigna &
Malmendier 2004)
Controversies
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Rubinstein (2003, 2004), HD misses the core of psychological decision-making
process
Rejected by 3 experiments, eg.
Same $2. NOT willing to accept delay at t = 60 => NOT willing to accept delay
at t = 0 (hyperbolic discounting)
¼ of the subjects made a switch (Q5 & Q6)
Q5 In 60 days you are suppose to receive a new stereo system to replace
your current one. Upon receipt of the system, you will have to pay $960. Are
you willing to delay the transaction by 1 day for a discount of $2?
Q6 Tomorrow you are supposed to receive a new stereo system to replace
your current one. Upon receipt of the system, you will have to pay $1080. Are
you willing to pay the delay the delivery and the payment by 60 days for a
discount of $120
“(I)nfinite number of functional forms consistent with the psychological findings”.
Procedure based on similarity explains observations better and is more
intuitive
Controversies
• Outta Control! (Loewenstein 1996)
• Usefulness of multiple self approach limited by
imperfections in analogy between interpersonal
and intrapersonal conflict (inherent asymmetry,
can’t punish past, unidirectional self-control)
• Multiple self model metaphorical only, difficult to
draw connections between multiple self models
and research on brain neurochemistry or
physiology.
• Impulsive selfs never promote one another’s
behavior. Motivational impact of visceral factors.
Controversies
• Gintis (2000)
• “rational” nature of time consistency?
• “No plausible models within which time consistency has
optimal welfare-enhancing properties”
• Hurwicz, “piggy bank effect”
• Quick temper today => tomorrow’s cost, possible if time
inconsistent, might lead to enemy giving way.
Evolutionary fitness.
• Time consistency doesn’t imply additivity and constant
rate. Aging => P(death) increases, higher discount rate
for future.
Extensions
• Continuous-time hyperbolic models
• Instantaneous gratification (Laibson &
Harris, 2001)
• 1 shock only, Tt is a Poisson arrival time
• Asset Uncertainty
• Harris &Laibson (2001)
• Corrects for non-monotonic hyperbolic
consumption function induced by borrowing
constraints
• Disappears if noisy enough
Extensions (cont.)
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Getting Sophisticated
Chan (on-going research)
Game among selfs
Physiology of Intertemporal Choice
Manuck, Flory, Muldon & Ferrell (2003)
Neurology
Long Term decision-making – prefrontal lobe
Homo Sapien brain structure is structured for
present-biased
Recommended reading
• Harris & Laibson (2001), “Hyperbolic
Discounting and Consumption” in the
Eighth World Congress of the Econometric
Society.
• It will supplement the forgone
technicalities in my presentation
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References
Angeletos, George-Marios, David Laibson, Andrea Repetto, Jeremy Tobacman, and Stephen
Weinberg (2001). The Hyperbolic ConsumptionModel: Calibration, Simulation, and Empirical
Evaluation. Journal of Economic Perspectives, 15(3), Summer, 47-68.
Benabou and Pycia (2002) “Dynamic inconsistency and self-control: a planner-doer interpretation”
Economic Letters 77, 419-424.
Chapman G. B. “Temporal discounting and utility for health and money” Journal of Experimental
Psychology-Learning Memory and Cognition, 22(3) 771-791
DellaVigna, and Malmendier. Contract Design and Self-control: Theory and Evidence. May 2004,
Quarterly Journal of Economics 119, 2, 353-402.
DellaVign, and Malmendier. November 2003. Overestimating Self-Control: Evidence from the health
Club Industry. Stanford GSB Research Paper 1800
Gintis H. Game Theory Evolving. Princeton University Press.
F. Gul and W. Pesendorfer (2001), Temptation And Self-Control, Econometrica 69, 1403-35
Gul and Pesendorfer (2002), Self Control, Revealed Preference and Consumption Choice.
Kreps (1990) Notes on Choice Theory, Westview
Laibson (2004), Intertemporal Decision Making, Encyclopedia of Cognitive Science (forthcoming)
Laibson, David. Golden Eggs and Hyperbolic Discounting.?Quarterly Journal of Economics, 62, May
1997, 443?7.
Laibson, David, Andrea Repetto, and Jeremy Tobacman. Debt Puzzle.?NBER working paper 7879,
2000.
Loewenstein, G. (1988) Frames of Mind in Intertemporal Choice. Management Science, 34(2), 200214.
Loewenstein, George and Drazen Prelec. Preferences for Sequences of Outcomes.?In Choices,
Values and Frames, Ch. 32, pp. 565?77.
Loewenstein, George and Drazen Prelec. Anomalies in intertemporal: Evidence and an
interpretation.?Quarterly Journal of Economics, May 1992, 573?97.
Loewenstein, George and Drazen Prelec. (1993). Preferences over outcome sequences.
Psychological Review, 100(1), 91-108.
Mulligan, C. (1996) A Logical economist’s argument against hyperbolic discounting. Working Paper. U
of Chicago.
References 2
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O’Donoghue, Ted and Matthew Rabin. Choice and Procrastination. Quarterly Journal of
Economics, February 2001, 121-160.
O’Donoghue, Ted and Matthew Rabin. Doing it now or doing it later.American Economic
Review, 89(1), 103?24, March 1999.
O’Donoghue, Ted and Matthew Rabin. Incentives for Procrastinators.Quarterly Journal of
Economics, 114(3), 769?16, August 1999.
Rabin M. “Psychology and Economics" Journal of Economic Literature, Vol. XXXVI, 11-46,
March 1998.
Read D. “Intertemporal Choice” London School of economics and Political Science Working
paper
Rubinstein, A. "Economics and Psychology"? The Case of Hyperbolic
Discounting, International Economic Review 44 (2003), 1207-1216.
Rubinstein, A.(2004) Presidential Address. Econometric Society
Schelling, Thomas C. "Self-Command: A New Discipline.?In Choice Over Time, Ch. 7, pp.
167?76.
Shefrin, Hersh M. and Thaler, Richard. "Mental Accounting, Saving, and Self-Control.In
Choice Over Time, Ch. 12, pp. 287?30.
Simonson, Itamar. The Effect of Purchase Quantity and Timing on Variety-Seeking.In Choices,
Values and Frames, Ch. 41, pp. 735?57.
Thaler, Richard. "Some Empirical Evidence on Dynamic Inconsistency.” In Quasi Rational
Economics, CH. 6, pp. 127?36.
Thaler, Richard. Intemporal Choice.In The Winner's Curse, Ch. 8,
Thaler, Richard. Savings, Fungibility, and Mental Accounts.In The Winner's Curse, Ch. 9