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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

Intertemporal Choice

  • Traditional Approach
  • Anomalies
  • New Theories
  • Applications
  • Controversy
  • Extensions
dynamic choice theory
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
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
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
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
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
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
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
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
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
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
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
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 na ve vs sophistication
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
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
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
Application 1 – Life-cycle savings and consumption
  • Angeletos, Laibson, Repetto, Tobacman & Weinberg
application 2 steady state
Application 2 – Steady State
  • Gul & Pesendorfer (2002)
  • Changing consumption from &
  • Taking FOC of
  • For ,
  • We get
  • In steady state
application 3 depp or crap
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
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 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
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
controversies23
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.
controversies24
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
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
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
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
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
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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