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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)
- 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(cs, xs) 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(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

- 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 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

- 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 - 10. 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)

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.)

- 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, 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.

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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