Intertemporal Choice Ec 101 Prof. Camerer

1. Intertemporal ChoiceEc 101 Prof. Camerer Time preference: Preferences for earlier vs later rewards Important choices involve time longer time horizon  more irreversibility careers, children, retirement Likely to be difficult the brain is not evolved for long-term reward self-control: addiction, obesity, procrastination Institutions may help or hurt ”No money down!” vs expert advice & external self-control (Soc. Security)

2. 1 Some history of intertemporal choice • 2 Anomalies from discounted utility theory (LFR review) • Field tests • 3 Projection bias • 4 Life-cycle savings • Mental accounting puzzles • Calibration exercise (Angeletos et al) • Experimental data • 5 Research frontiers: • Practical lessons • Sophistication vs naivete

3. 1. Some history of intertemporal choice (see Loewenstein, ch 1 L-Elster Choice Over Time) • Adam Smith (1776) • ”impartial spectator” (cingulate, PFC?) • John Rae (1834) • Eugen von Böhm-Bawerk (1889) • Irving Fisher (1930) • Paul Samuelson (1937) • Robert Strotz (1956) • Phelps and Pollak (1968) • Β- δ used to explain discounting of self and children (“future selves”) • David Laibson (1994,97) adapted PP 68

4. E.g., Fisher • Personal determinants of time preference • Foresight • Risk of future • Self-control • Habit • Life-expectancy • Concern for lives of other persons • Fashion: “In whatever direction the leaders of fashion first chance to move, the crowd will follow in mad pursuit…” • Was critical of econ-psych divide: • The fact that there are two schools, the productivity school and the psychological school, constantly crossing swords on this subject is a scandal in economic science and a reflection on the inadequate methods employed by these would-be destroyers of each other

5. Discounted Utility Model • Discount factor compresses many Fisherian forces into one term • Now accepted as normative and descriptive • ”It is completely arbitrary to assume that the individual behaves so as to maximize an integral of the form evisaged in [DU]. (Samuelson 1937) • Utility and consumption independence • Exponential  time consistency

6. 2. Anomalies from DU (LFR) • Measured discount factors are not constant • Over time • Across type of intertemporal choices • Sign effect (gains vs. losses) • Neural substitution of ”loss” and ”delay”? • Magnitude effect (small vs. large amounts) • Sequence effect (preference for upward-sloping profiles) • Speedup-delay asymmetry (temporal loss-aversion).

7. 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 ….

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

9. Figure 1 (LFR): Increasing variation over time as more studies are done ,

10. Figure 2 (LFR): Increasing patience with longer horizons ,

11. Discounting is important in other domains • Education (Duckworth, Seligman 05 Psych Sci): Predicts 14-yr olds’ grades • “Not the will to win…the will to practice”

12. Role of attention & cognition: Exposure and ‘distractions’ very powerful (Walter Mischel et al) • Delay-of-gratification in children (ring bell when they can’t wait any longer for better snack) • Fun thoughts, covering snacks enhances patience…except if they are thinking about the snacks! (see Fig 6.1) • Thoughts about “arousing” features versus “cognitive re-appraisal” creates impatience

13. Field test: Front-loaded buyouts for soldiers (Warner-Pleeter AER 01) • After the Gulf War in the early 1990s the military enticed soldiers into retirement • Choose between a lump sum payment (on the order of $20K) and an annuity (worth around $40K in PV @ r=10%) • Officers: 50% took lump sum • Enlisted: 90% took lump sum

14. Officers enlisted

15. Can estimate discount rates from large n=55,000 sample (enlisted results) • Male +.01 • Black +.035 • College -.048 • Test scores: high (-.016), medium (-.01) • Size of lump sum (-.059/$10k) (largest fx)

16. Vietnam exp (w/ Tomomi Tanaka, Quang Nguyen)

17. General model estimation • Benhabib, Bisin, Schotter (04) • Θ=1 exponential =x*exp(-rt) • Θ=2 hyperbolic =x/(1+rt) • Graph for Θ=1,2,5 (r=.13) • BBS est. Θ (2.62,4.14), r (6.37, 33.64) • Vietnam villages: Θ=5.19, r=13, α=.88 • ROSCA participants have higher α (+.15), lower r (-.04) • Can also add fixed cost (-b) and variable cost (α multiplier) • Highly variable estimates

18. Projection bias (Loewenstein, Read, Rabin ) • Overestimate duration of state-dependence is estimated utility in s’ from state s α=0 rational • Examples: • Shopping while hungry • Childbirth: Lamaze versus epidural painkiller during labor • Cannibalism • Interpersonal: Difficult to imagine what people will do in different emotional states...(looting, lynchmobs, corporate scandals, crimes of passion, heroic acts...) • Wilson-Gilbert ”affective forecasting” mistakes (fail to appreciate ’emotional immune system’)

19. Empirics: Catalog sales for winter clothes items • Winter-item catalog sales (Conlin, O’Donoghue, Vogelsang AER in press) • 2.4 million observations 95-99. One 1 day to process, 3-7 days to ship • Theory predicts returns will depend + on temperature on return day R - on temperature on order day O intuition: lower temp(O)  ”surprised” at ”high” temp(R) and then return temp(O) temp (R) Structural estimates of α from .01-.64

20. 4. Lifecycle savings • ”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?

21. Borrowing: Boom in bankruptcies

22. Borrowing: Credit card facts • Average debt outstanding by income quintile (IQ) • Rates (APR, red) have fallen as interest rates fall (blue). Blue is “spread”

23. Mental accounting and MPC (Thaler-Shefrin 1988)

24. Angeletos et al calibration • Model features • Quasi-hyperbolic sophisticated preferences • uncertain future labor income • liquidity constraint • allow to borrow on credit cards - limit • hyperbolic discounting – implications • labor income autocorrelated – shocks • hold liquid and illiquid assets • Calibration strategy: • Fix some parameters, simulate behavior, compare properties with data

25. Figure 3: Shapes of discount functions ,

26. Figure 4: - from Angeletos et al ,

27. Figure 5: - from Angeletos et al ,

28. Figure 6: - from Angeletos et al ,

29. Figure 7: - from Angeletos et al ,

30. Table 1: - from Angeletos et al ,

31. Table 2: - from Angeletos et al ,

32. Habit formation Spending • “The hedonic treadmill”

33. Habit formation Spending • “The hedonic treadmill”

34. Optimal saving and investing: Do ‘sufficiently rational agents optimize?’

35. Economics Nobel laureates reflect (from LA Times)

36. Beverage delivery apparatus

37. 5. Research frontiers: Sophistication vs naivete • Are hyperbolics “sophisticated”? or “naïve”? • Sophisticated hyperbolics will prefer pre-commitment • IRS refunds • Deadlines (Blockbuster vs Netflix) • Ulysses and the sirens • “Arrest me” list on riverboat casinos • Wertenbroch: • Smaller package sizes of “vices” than “virtues” • Cigarettes by the pack, gym contracts (Malmendier-Della Vigna AER 06, $19/visit vs $10 visit fee) • Q: Will markets work? Or does government have special legal power to enforce these contracts? (e.g. Army AWOL)

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

39. Factoid…

40. 80% of respondents have negative discount rates! voluntary “forced saving”(Shapiro JPubEc 03; cf. Ashraf et al QJE in press)

41. Frontiers: Practical value of behavioral econ:Save More Tomorrow™(Benartzi-Thaler JPE 04) • Exploit power of inertia and desire to avoid a nominal decrease in pay • Commit 1/3 of future raise to 401(k)

42. Swedish privatization c 2000: (Cronqvist-Thaler AER 04) • Driven by desire for investor autonomy • 456 funds, could advertise & set fees • Information (fees, performance, risk) in book form • Big ad campaign: Investors encouraged to choose their own fund (57% of young did) • What happened?

43. Swedish privatization: (Cronqvist-Thaler AER 04) • Autonomous investors • “home biased” • high fees • Poor performance • 03: 92% of young choose default

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

45. 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?

46. Other aspects of time in econ • Other models and phenomena • Habit formation (common in macro) • Visceral influence (emotion-cognition) • Temptation preferences (Gul-Pesendorfer 01 Emetrica) w{w,t}t iff U(S)=maxxS[u(x)+v(x)] –maxy S v(y) • Anxiety/savoring/memory as consumption (Caplin-Leahy; e.g. wedding planning) • Multiple selves/dual process models

47. 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)

48. 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

49. 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