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Intertemporal Choice Prof. Camerer

This paper explores the history, anomalies, and perspectives of intertemporal choice, with a focus on discounted utility theory. It discusses examples of hyperbolic discounting, results of simulations, and the implications for decision-making. The paper also references influential papers and figures in the field.

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Intertemporal Choice Prof. Camerer

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  1. Intertemporal ChoiceProf. Camerer Some history of intertemporal choice Anomalies from discounted utility theory Two examples of hyperbolic discounting Results of simulations in Angeletos et al Conclusions and perspectives

  2. Papers • Frederick, Loewenstein & O’Donoghue: ”A review of intertemporal choice” (2002) • Angeletos, Laibson, Repetto, Tobacman & Weinberg: ”The hyperbolic consumption model” (2001) • McClure et al Science

  3. History of intertemporal choice • Adam Smith (1776) • John Rae (1834) • Eugen von Böhm-Bawerk (1889) • Irving Fisher (1930) • Paul Samuelson (1937) • Robert Strotz (1956) • Phelps and Pollak (1968) • David Laibson (1994, 1997)

  4. Discounted Utility Model • Discount factor compresses many forces • mortality, uncertainty, time compression... • Accepted as normative and descriptive ...but initially arbitrary (Samuelson 1937) • Utility and consumption independence • Exponential  time consistency

  5. Anomalies from DU • Empirically discount factor is not constant • Over time • Across type of intertemporal choices • Sign effect (gains vs. losses) • Magnitude effect (small vs. large amounts) • Sequence effect (sequence vs. single) • Speedup-delay asymmetry (temporal loss-aversion). Very strong?

  6. Magnitude and hyperbolic effects • $15 now is same as ___ in a month. ___ in a year. ___ in 10 years. • Thaler (1981) $20 in a month (demand 345% interest), $50 in a year (120%), $100 in 10 years (19% interest) • Show discount rates decrease over time… • Students asked: • $150 vs. $x in 1 month, 1 year, 10 years • $5000 vs $x ….

  7. Results of class survey $160 $197 $500 $6,000 $14,000 $5,100

  8. An example of real consequence: Front-loaded buyouts for soldiers • After the Gulf War in the early 1990s the military had to reduce its size by buying soldiers into retirement for up to $3.4 billion • Soldiers had to choose between a lump sum payment (on the order of $20K) and an annuity (worth around $40K in present value)

  9. An example of real consequences (AER 03?) • After the Gulf War in the early 1990s the military had to reduce its size by buying soldiers into retirement for up to $3.4 billion • Soldiers had to choose between a lump sum payment (on the order of $20K) and an annuity (worth around $40K in present value)

  10. More than 90% of the 55,000 enlisted men chose the lump sum of $20K, suggesting very high discount rates (17-20%). • Savings to U.S. Government: $1.7 billion • If the soldiers really wanted money now, they could have taken out a loan for even more (say $25,000) and then used the annuity income to pay it back.

  11. Figure 1: - from Frederick et al ,

  12. Figure 2: - from Frederick et al ,

  13. Example 1: • ”Golden eggs and hyperbolic discounting” • Hyperbolics are tempted • Illiquid assets provide commitment • Two-thirds of US wealth illiquid (real estate) • Not counting human capital • Access to credit reduces commitment • Explain decline in savings rate 1980s? • Key issue: sophisticated vs naive

  14. Sophisticates seek self-control (from periodic food stamp checks, Ohls 92; Shapiro, 03 JPubEc)

  15. 80% of respondents have negative discount rates! voluntary “forced saving”(Shapiro JPubEc 03; cf. Ashraf et al QJE in press)

  16. Figure 3: - from Laibson ,

  17. Example 2: • ”The hyperbolic consumption model” • Hyperbolic preferences induce dynamic inconsistency • Sophisticated consumers • Model with simulations (calibration)

  18. Example 2 (continued) • Model features • uncertain future labour income • liquidity constraint • allow to borrow on credit cards - limit • hyperbolic discounting – implications • labour income autocorrelated – shocks • hold liquid and illiquid assets • Results

  19. Figure 4: - from Angeletos et al ,

  20. Figure 5: - from Angeletos et al ,

  21. Figure 6: - from Angeletos et al ,

  22. Figure 7: - from Angeletos et al ,

  23. Table 1: - from Angeletos et al ,

  24. Table 2: - from Angeletos et al ,

  25. Two time systems (McClure et al Sci 04):u(x0,x1,…)/ β = (1/β)u(x0) + [δu(x1) + δ2u(x2) +…] Impulsive β↓ long-term planning δ↓

  26. Problem: Measured δ system is all stimulus activity…use difficulty to separate δ (bottom left), δ more active in late decisions with immediacy…but is it δ or complexity?

  27. Other aspects of time in economics • Other models (instantaneous utility function) • Habit formation (common in macro) • Visceral influence (emotion-cognition) • Temptation preferences (Gul-Pesendorfer) • w {w,t} t • Projection bias • Overestimate duration of state-dependence (cf ”emotional immune system”) • Anxiety/savoring as a source of consumption (Caplin-Leahy) • Multiple selves/dual process models

  28. Types of anticipation preferences • Reference-dependent preferences (K-Rabin 04) • Belief about choice changes reference point • Endowment effects/”auction fever” • Explains experience effects (experienced traders expect to lose objects, doesn’t enter endowment/ f1) • Emotions and self-regulation • E.g. depression. Focusses attention on bad outcomes, causes further depression • Intimidating decisions • f1 may increase stress about future choices • health care, marriage, job market, etc. • Better to pretend future choice=status quo • Q: When are these effects economically large?’ • Avoid the doctor late cancer diagnosis • Supply side determination of endowment effects (marketing)

  29. Three interesting patterns • Self-fulfilling beliefs • u2(δz,z)>u2(δz,z’) u2(δz’,z’)> u2(δz’,z) • prefer z if you expect(ed) z, z’ if you expect(ed) z’ • Cognitive dissonance, encoding bias • “If I could change the way/I live my life today/I wouldn’t change/a single thing”– Lisa Stansfield • Undermines learning from mistakes • Time inconsistency • Self 2 prefers z’ given beliefs u2(f1,z’)>u2(f1,z) • but self 1 preferred to believe and pick z u1(x,δz,z)>u1(x,δz’,z’) • Problem: Beliefs occur after self 1 picks • Informational preferences • Resolution-loving: Likes to know actual period 2 choice ahead of time • Information-neutral: Doesn’t care about knowing choice ahead of time (“go with the flow”) • Information-loving: Prefers more information to less (convex utility in f1) • Disappointment-averse (prefers correct to incorrect guesses): • u1(x,δz,z)+u1(x,δz’,z’)> u1(x,δz’,z)+u1(x,δ • Surprising fact: If none of above hold, then personal equilibrium iff u* max’s E(u1(z1,z2) I.e. only way beliefs can matter is through these three

  30. Koszegi, “Utility from anticipation and personal equilibrium” • Framework: Two selves, 1 and 2 • Choices z1,z2 , belief about z2 is f1 • u1(z1,f1,z2) • anticipation function Φ(z1,d2)=f1 (d2 is period 2 decision problem) • personal equilibrium: • each self optimizes • Φ(z1,d2)=s2(z1,Φ(z1,d2),d2) anticipate s2(.) choice • Beliefs are both a source of utility and constraint • Timeline: • Choose from z1 X d2. • Choose f1 from Φ. • Choose z2

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