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Intertemporal Choice Prof. 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

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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

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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)

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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

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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?

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$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

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

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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)

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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)

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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.

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Figure 1: - from Frederick et al,

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Figure 2: - from Frederick et al,

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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

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

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

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Figure 3: - from Laibson,

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

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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

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Figure 4: - from Angeletos et al,

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Figure 5: - from Angeletos et al,

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Figure 6: - from Angeletos et al,

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Figure 7: - from Angeletos et al,

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Table 1: - from Angeletos et al,

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Table 2: - from Angeletos et al,

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Two time systems (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 ↓

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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?

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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

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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)

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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

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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

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