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Intertemporal Choice. Traditional Approach Anomalies New Theories Applications Controversy Extensions. Dynamic Choice Theory. Kreps (1988, 1979) X = menu, A dishes Changing Tastes and Sophisticated choice, Preference for Flexibility (states of preferences)

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Intertemporal choice l.jpg

Intertemporal Choice

  • Traditional Approach

  • Anomalies

  • New Theories

  • Applications

  • Controversy

  • Extensions


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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`)


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Exponential Discounting

  • Adam Smith (1776)>>>Rae (1834)>>>von Bohm-Bawerk(1889)>>>Fisher (1930)>>> Samuelson (1937)

  • Exponential discount function:

  • 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)


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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)


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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)


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Anomaly 4 – Sign Effect

  • Gains vs. losses

  • Thaler (1981), Antonides & Wunderink (2001)

  • Discount rates for gains is much greater than for losses.

  • “debt aversion”


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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)


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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.


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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


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Hyperbolic Discounting

  • Loewenstein & Prelec (1992)

  • Discount rates are greater in the short run than in the long run

  • Instantaneous discount rate:

  • 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


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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:


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Procrastination/Naïve vs Sophistication

  • 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:


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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


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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


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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?

    • 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 : (


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Application 4 – Health Clubs

  • 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.

  • Flat rate contract will be chosen if:

  • 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)


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Controversies

  • 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


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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.


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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.


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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


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Extensions (cont.)

  • 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


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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), 200-214.

  • 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.


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References 2

  • 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