2. Intertemporal Choices Flashcards
(33 cards)
What are the 3 assumptions of intertemporal choices?
- Time is discounted at a constant rate
- There is inter-temporal INDEPENDENCE of consumptions
- the utility function is stationary
What is an individual’s intertemporal utility function under the Discounted Utility Model?
Utility = Sum[ D(k) * U(C_t+k) ]
t=today
D(k) = discount factor
Discount factor formula
(1/ (1+ p) ) ^ k
What is the 1st assumption of intertemporal choice?
Time is discounted at a constant rate
What is the 2nd assumption of intertemporal choice?
inter-temporal INDEPENDENCE of consumptions (consumption in t+k is independent of consumption in any other period)
What is the 3rd assumption of intertemporal choice?
instantaneous utility function is constant across time, so that the utility generated by an activity is the same in different periods
Give an example that violates constant discounting
£100 today or £110 tomorrow; £100 30 days or £110 31 days
Hyperbolic discounting
D(k)=β δ^k
How do empirically observed discount rates vary?
Low discount rate (impatient) in the short run and high, stable discount rate in the long run
What behavioral feature does the parameter β capture (in hyperbolic discounting)?
Present bias
Summarize the design of Tanaka, Camerer & Nguyen’s (2010) field experiment.
75 choices per subject between:
Option A: get x dong today
Option B: get y dong in t days
What were the main findings of Tanaka, Camerer & Nguyen (2010) in terms of present bias?
- Higher household and village income → more patience (lower ρ).
- Estimated β≈0.644, indicating widespread present bias.
- Wealth doesn’t predict individual β (present bias is universal).
Name three alternative models addressing non-stationary utility.
- Multiple-Self Models: conflict between a myopic and a farsighted self.
- Temptation Utility (Gul & Pesendorfer, 2001): disutility from resisting the most enjoyable now-option.
- Projection Bias: tendency to project current tastes into the future.
What is the third assumption (“stationarity”)?
The instantaneous utility function u(c) is the same in every period—preferences don’t change over time.
What are the key features of the Rational Model of Addiction?
Utility at t depends on goods y, addictive good c, and stock S.
Tolerance: higher stock → lower total utility of c.
Reinforcement: higher stock → higher marginal utility of c.
Adjacent complementarity: consumption today and tomorrow reinforce each other.
How can habit formation help explain the Equity Premium Puzzle?
Habit-forming consumers dislike fluctuations in habit-adjusted consumption, amplifying the effect of small consumption changes and justifying high equity premia with moderate risk aversion.
How does the Habit Formation Model alter assumption two?
Instantaneous utility depends on past consumption
What is the second assumption (“intertemporal independence”)?
Inter-temporal consumption of INDEPENDENT
What is an inconsistent time preference?
individual’s preferences change over time in a way that leads to time-inconsistent decisions (e.g., procrastination, over-consumption)
What are the three types of decision-makers described by O’Donoghue & Rabin (1999)?
Time Consistent (TC): Makes consistent plans and follows through.
Naïfs: Time-inconsistent and unaware of it.
Sophisticates: Time-inconsistent but aware of future self-control problems.
How do Naïfs behave differently from Sophisticates?
Naïfs underestimate their future procrastination, while Sophisticates anticipate it and plan around it (often with commitment devices).
In the movie report example, which week does a TC individual skip the movie?
Week 1, to maximise utility from all remaining weeks
Which week do Naïfs end up skipping the movie?
Week 4, due to constant procastination
Which week do Sophisticates skip the movie?
Week 2, balancing foresight and maximum utility.
