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 Bohm- Bawerk(1889)>>>Fisher (1930)>>> Samuelson (1937) Exponential discount function: u(c s, x s ) is the felicity function Monotonically falling, utility additive and independent across time Constant Rate of Decline ( ) Recursive ( )

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(x 1 )=u(x 3 `), u(x 1 )=u(x 2 ), u(x 2 )=u(x 3 ), x 3 >x 3 `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, t 1 ) vs (y, t 2 ) – Looks for dominance (eg. x>y & t 1 <t 2 ) – Looks for similarities (eg. between x & y) – If not decisive, different criterion

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)

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 u t+1 vs u t at t 0 <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!! c t = actual consumption, m t = maximum possible consumpion, u+v concave, v convex (+4 axioms) Choosing between Wait if:

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:

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

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

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 : (

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 The result is that he will always attend less often than he believes. Sophisticates may use flat rate as commitment device. (Also, cancellation)

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 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) Q5In 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? Q6Tomorrow 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, T t 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.) 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

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, Benabou and Pycia (2002) “Dynamic inconsistency and self-control: a planner-doer interpretation” Economic Letters 77, Chapman G. B. “Temporal discounting and utility for health and money” Journal of Experimental Psychology-Learning Memory and Cognition, 22(3) DellaVigna, and Malmendier. Contract Design and Self-control: Theory and Evidence. May 2004, Quarterly Journal of Economics 119, 2, DellaVign, and Malmendier. November 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, 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, Loewenstein, G. (1988) Frames of Mind in Intertemporal Choice. Management Science, 34(2), 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), Mulligan, C. (1996) A Logical economist’s argument against hyperbolic discounting. Working Paper. U of Chicago.

References 2 O’Donoghue, Ted and Matthew Rabin. Choice and Procrastination. Quarterly Journal of Economics, February 2001, O’Donoghue, Ted and Matthew Rabin. Doing it now or doing it later.American Economic Review, 89(1), 103?24, March O’Donoghue, Ted and Matthew Rabin. Incentives for Procrastinators.Quarterly Journal of Economics, 114(3), 769?16, August Rabin M. “Psychology and Economics" Journal of Economic Literature, Vol. XXXVI, 11-46, March 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), 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