Intertemporal Choice Ec 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 $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 …. Magnitude and hyperbolic effects

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

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 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 –College –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 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

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(x 0,x 1,…)/ β = (1/β)u(x 0 ) + [δu(x 1 ) + δ 2 u(x 2 ) +…] 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)=max x  S [u(x)+v(x)] –max y  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/ f 1 ) Emotions and self-regulation –E.g. depression. Focusses attention on bad outcomes, causes further depression Intimidating decisions –f 1 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 –u 2 (δ z,z)>u 2 (δ z,z’) u 2 (δ z’,z’)> u 2 (δ z’,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 u 2 (f 1,z’)>u 2 (f 1,z) –but self 1 preferred to believe and pick z u 1 (x,δ z,z)>u 1 (x,δ z’,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 f 1 ) –Disappointment-averse (prefers correct to incorrect guesses): u 1 (x,δ z,z)+u 1 (x,δ z’,z’)> u 1 (x,δ z’,z)+u 1 (x,δ Surprising fact: If none of above hold, then personal equilibrium iff u* max’s E(u 1 (z 1,z 2 ) 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 z 1,z 2, belief about z 2 is f 1 –u 1 (z 1,f 1,z 2 ) –anticipation function Φ(z 1,d 2 )=f 1 (d 2 is period 2 decision problem) –personal equilibrium: each self optimizes Φ(z 1,d 2 )=s 2 (z 1,Φ(z 1,d 2 ),d 2 ) anticipate s 2 (.) choice –Beliefs are both a source of utility and constraint Timeline: –Choose from z 1 X d 2. –Choose f 1 from Φ. –Choose z 2