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Intertemporal Choice

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

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  1. Intertemporal Choice • Traditional Approach • Anomalies • New Theories • Applications • Controversy • Extensions

  2. 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`)

  3. 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 ( )

  4. 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)

  5. 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)

  6. 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)

  7. Anomaly 4 – Sign Effect • Gains vs. losses • Thaler (1981), Antonides & Wunderink (2001) • Discount rates for gains is much greater than for losses. • “debt aversion”

  8. 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)

  9. 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.

  10. 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

  11. 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)

  12. 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

  13. 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:

  14. 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:

  15. 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

  16. 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

  17. Application 1 – Life-cycle savings and consumption • Angeletos, Laibson, Repetto, Tobacman & Weinberg

  18. Application 2 – Steady State • Gul & Pesendorfer (2002) • Changing consumption from & • Taking FOC of • For , • We get • In steady state

  19. 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 : (

  20. 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)

  21. 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)

  22. 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

  23. 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.

  24. 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.

  25. 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

  26. 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

  27. 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

  28. 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.

  29. 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

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