Page 1: ECON5350: LECTURE 11

Choices Over Time

Page 2: OBJECTIVES

Key Concepts to Explore

• Hyperbolic discounting: Understanding how individuals value rewards over time, particularly their tendency to favor immediate gratification over delayed rewards.

• Quasi-hyperbolic discounting: A model that incorporates both immediate preferences and the tendency to delay larger rewards, contrasting with traditional exponential discounting models.

• Time inconsistency: The phenomenon where an individual’s preferences change over time, leading to different choices and decisions than originally planned.

• Commitment and temptation: Examining how individuals can create commitments to resist short-term temptations for long-term benefits.

Page 3: DISCOUNT FACTOR UNDERSTANDING

Discount Factor Table

• Delayed Payments Examples:

  • 1 year: $40

  • 2 years: $200

  • 4 years: $1,000

  • 5 years: $5,000

• Key Insight: Individuals may display short-term impatience while being patient for long-term rewards.

Page 4: THALER (1981) STUDY

Indifference Amounts Required

• $15 Now vs. Delayed Rewards:

  • Indifferent amount in 1 month: $22

  • Indifferent amount in 1 year: $50

  • Indifferent amount in 10 years: $100

• Implied Discount Factors:

  • 1 month: 0.22

  • 1 year: 0.45

  • 10 years: 0.84

Page 5: HYPERBOLIC DISCOUNTING

Key Characteristics

• Decreasing Impatience: The recognition of different impatience levels over time.

• Discount Factor Approach: The increasing discount factor over time rather than a constant, modeled via hyperbolic equations.

• Intertemporal Utility Function: Represented as follows:

  • U = Σ(t=1 to n) [u(t)] where utility decreases over time in a non-linear manner.

Page 6: ANNUAL DISCOUNT FACTOR EXPLORATION

Annual Discount Factor Table

• Amounts Discounted using both exponential and hyperbolic methods illustrate differences in future value perception.

Page 7: QUASI-HYPERBOLIC DISCOUNTING

Choice Scenarios

• Immediate vs. Delayed Rewards:

  • Choose $100 today or $110 tomorrow?

  • Choose $100 in 30 days vs. $110 in 31 days?

• Time-based Changes: Consider whether answers would change after 30 days to highlight inconsistency in preference over time.

Page 8: CONSISTENCY REQUIREMENTS

Inconsistency in Choices

• Hyperbolic Model Consistency: Requires stable preferences over time.

• If a person chooses $110 in 31 days over $100 in 30 days, the same decision pattern should apply after the 30 days have elapsed.

Page 9: PRESENT BIASED PREFERENCES

Example Preference Analysis

• Dates: 1 May, 2 May, 30 May, 31 May

• Time Consistent Preferences versus Present Biased Preferences: Illustrated with discount factors over the given dates to demonstrate biases.

Page 10: PREFERENCES MODELING

Quasi-Hyperbolic Discounting Explained

• Mathematical representation: Summation of weighted preferences for the current time rather than later periods.

• Beta (β): A measure of present bias where a lower β reflects greater bias towards current consumption over future benefits.

Page 11: HOMEWORK EXAMPLE WITH QUASI-HYPERBOLIC PREFERENCES

Comparison of Plans Across Days

• Values Assigned to Tasks by Day:

  • Friday: Various preferences rated.

  • Contrast across Saturday and Sunday denotes varying desires for future consumption based on β values.

Page 12: TIME INCONSISTENCY

Dynamic Inconsistency Implications

• Behavioral Shifts: Plans often become altered based on shifting circumstances or desires.

• Policy Implications: Understanding time inconsistency is vital for crafting effective welfare policies.

Page 13: RESEARCH INSIGHTS FROM READ AND VAN LEEUWEN (1998)

Choosing Between Options Today and Next Week

• Decision example: Fruit versus Chocolate.

Page 14: PATIENT CHOICES FOR THE FUTURE

Preferences for Future Consumption

• Subjects typically choose fruit for future consumption (74%): A significant proportion favor healthier options when not in the moment.

Page 15: PRESENT CONSUMPTION CHOICES

Choices at the Moment of Eating

• Chocolate vs. Fruit for immediate choice illustrates preference for gratification.

Page 16: TIME INCONSISTENCY AS EVIDENCED

Chocolate Consumption Preference

• 70% select chocolate when choosing simultaneously, reflecting immediate temptation despite previous healthier choices.

Page 17: MOVIE CHOICES OVER TIME: READ ET AL. (1999)

Preference Trends Observed

• Low-brow vs. High-brow: Variability in selections based on time frame for viewing movies.

• Demonstrates time-inconsistent preferences.

Page 18: NAÏVE VS. SOPHISTICATED TIME INCONSISTENCY

Understanding Types of Participants

• A naïve individual may not recognize their time inconsistency, while a sophisticated individual does.

• This awareness can either mitigate procrastination or lead to preproperation tendencies.

Page 19: TIME INCONSISTENCY IN HOMEWORK CONTEXT

Repeat Homework Example

• Similar detailed analytical preferences across time periods contrasting β values and preferences noted.

Page 20: MOVIE EXAMPLE: SCHEDULING PLANS

Payoff Options for Movie Watching by Day

• Strategic planning shows differences in preference for timing movie viewings based on expected payoffs.

Page 21: PREPROPERATION IN MOVIE DECISION

Analysis of Movie Decision Timing

• Various payoff structures demonstrating changes in choice expectations based on enhanced precommitment strategies.

Page 22: DELAYED BENEFITS VS. COSTS

Comparing Choices for Long-term Rewards

• Analyzes scenarios in the homework example versus movie example illustrating the contrasts in decision modeling.

Page 23: COMMITMENT AND TEMPTATION

Understanding Sophisticated Commitments

• Strategies for constraining future choices that align with long-term benefits, intentional planning, and commitments help avoid short-term temptations.

Page 24: COMMITMENT DEVICES: ODYSSEUS BOUND TO THE MAST

Mythological Example Illustration

• Odysseus used commitment tactics to avoid temptation, showcasing the importance of pre-commitment strategies.

Page 25: EXAMPLES OF COMMITMENT DEVICES

Practical Commitment Strategies

• Cut bank cards, delete apps, limit screen time, buy memberships – these methods help maintain commitment to long-term decisions.

Page 26: SUMMARY

Key Topics Recap

• Hyperbolic discounting

• Quasi-hyperbolic discounting

• Time inconsistency

• Commitment and temptation