Week 3: Inter-temporal Choices Flashcards
How can an individuals inter temporal utility function be represented
- Utility of person t, in periods t all the way to T =
- The sum of the utility from period t all the way to T multiplied by:
- A discount factor D(k), this is because its happening in the future and we need to find a way to discount it multiplied by
- The utility from period C t + k
What is the discount rate
- The discount factor is how much they care about this thing in the future. For example, the utility of consuming good x in period t is the utility from consuming the good multiplied by the discount factor.
3 Assumptions of the discounted utility model
- Time is discounted at a constant rate - delaying or accelerating two dated outcomes should not change the preferences between the outcomes. e.g discount rate is constant is I prefer £10 today rather than £11 tomorrow and £10 in 30 days rather than £11 in 31 days.
2, There is inter-temporal independence of consumptions - A person’s utility in period t+k is the same as in any other period. E.g consuming ice cream for the next 5 days the utility from consuming it is the same. Time periods do not affect utility
- The utility function is stationary - Utility from making a choice and consuming a good at time t gives u the same utility as consuming the good in any other time period.
Time is discounted at a constant rate violation example
- Empirically observed that discount rates are not constant over time
- discount rates vary across different types of inter temporal choices
- e.g gains are discounted more than loses and small amount as discounted more than large amount.
Hyperbolic discounting as an alternative model description:
Ted O’Donoghue and Matthew Rabin (1991)
Empirical Application 1: Field experiment on savings and commitments Ashraf, Karlan and Yin (2006)
Objective: Test the effect of a commitment savings device
Three treatments: Save, Earn, Enjoy deposits
The experiment made individuals commit to savings where you cannot access ur deposits and you gain no reward from savings
Main results: 28.4% of people asked took on the experiment, average savings balances increased by 81%, more ‘’hyperbolic’’ individuals seem more likely to take up SEED especially wommen
Marketing treatment had no effect
Empirical application 2: Field experiment on exercise and health: Royer, Stehr and Sydnor (2015):
Objective: Examine if self funded commitment contracts can improve the long run effects of an incentive program
Design: 1. Offer one month financial incentive to attend company’s existing facilities 2. Randomly select half of the sample offered to set up self funded commitment contracts. 3. Commitment contract: pledge to continue using the gym after the original incentive period.
Three treatments: Control (no incentive offered), Incentive group (10 USD per visit for up to 3 visits each week to the company onsite exercise facility). Incentive + commitment: half of the incentive group was randomly selected and offered participants to put money at stake for a pledge they would continue using the gym over the two months.
Effect of non-present consumption: Habit Formation Model
Effect of non-present consumption: Rational model of addiction
Effect of non-present consumption
Effect of non-present consumption: Gine, Karlan and Zinman (2009)
