Notes on Temporal Discounting

Decisions Across Time & Distance: Temporal Discounting

1. Introduction to Temporal Discounting

  • Central Question: Why do individuals fail to save sufficiently for retirement despite knowing its importance and having the means?

2. Topics Covered Today

  • Temporal Discounting occurrence and implications:
      1. How discounting occurs
      2. Reasons behind discounting behavior
      3. Factors influencing discount rates
      4. Effects of domain on discounting
      5. Handling discounting in complex situations

3. Understanding Temporal Discounting

  • Comparative Choices on immediate versus delayed payments:
      - Scenario A: $100 now vs. $110 in three months.
      - Scenario B: $100 now vs. $120 in three months.
      - Scenario C: $100 now vs. $150 in three months.

4. How Do We Discount?

4.1 Normative Model: Exponential Discounting
  • Graphical Representation:
      - Present value is represented against different delays in years, showcasing a curve that illustrates diminishing value over time.
  • Mathematical Model:
      - V=Aimese−rDV = A imes e^{-rD}
        - Where:
          - VV = Present Value
          - AA = Absolute value of money (future offer)
          - DD = Delay (in years)
          - rr = Discount rate.

5. Another Discounting Problem

  • Preference Reversal:
      - A choice between $100 in one year vs. $110 in 15 months illustrates how immediately available options affect our valuations.
  • Implication:
      - The perception of time is not uniform; people are more willing to wait longer for greater rewards if they have no immediate options, indicating time is not fungible.

6. Descriptive Model: Hyperbolic Discounting

  • Graphical Comparison:
      - Exponential vs. Hyperbolic discounting graph showing different present values against delays.
  • Mathematical Model:
      - V = rac{A}{1+kD}
        - Where:
          - kk = discount rate.

7. Why Do We Discount?

7.1 Rational Justifications for Discounting
  • Reasons for discounted future value:
      1. Interest on Investment: Money today can be invested.
      2. Inflation: Future money holds less purchasing power.
      3. Uncertainty: Future outcomes are not guaranteed.
      4. Pressing Need: Immediate financial obligations (e.g., rent).
      5. Enduring Goods: Delayed receipt diminishes satisfaction over time.
      6. Resource Slack: Perception of future abundance adjusting current wants
7.2 Psychological Components
  • Self-Perception of Future Self: Individuals often view their future selves as different entities.
      - Influence of Closeness to Future Self: Closer perceived future selves reduce discounting behaviors.
      - Techniques to enhance closeness, such as self-reflection exercises, can decrease discounting.
7.3 Non-Rational Reasons to Discount
  • Impatience: A strong desire for immediate gratification.
      - Self-Control Issues: Difficulty in waiting, as demonstrated by the marshmallow test.
      - Children who demonstrate better self-control are likely to discount future values less in adulthood.

8. Influences on Discount Rates

  • Discernment of Discount Rates:
      - Discount rates indicate how much less a future reward is valued based on several factors:
      1. Sign Effect: Preference for delaying losses over gains.
      2. Magnitude Effect: Smaller gains are discounted more heavily than larger ones.
      3. Directional Frame: Default context impacts decision metrics.
      4. Immediate Options: Presence of an immediate choice can skew decisions.
8.1 Sign Effect
  • Preference for larger future losses over smaller immediate ones.
  • Discounting losses less aggressively than gains.
      - E.g., preferring receiving -$100 today vs. -$108 in one month.
8.2 Magnitude Effect
  • Demonstrated preference to delay larger sums than smaller ones, given equal percentage increases.
      - Scenario: $10,000 today vs. $11,000 in three months reflects this.
8.3 Direction Effect
  • The frame of the decision alters discounting preferences:
      - Standard delay perspectives display different discount rates compared to those focusing on accelerating future rewards.
8.4 Now vs. Not Now
  • Immediate options affect perceived value creating a bias towards choosing sooner options, showcasing variance in discount rates.

9. Reflection Effects

  • Systematic effects on discount rates manifest uniquely when comparing gains vs. losses; manipulating positively or negatively alters discounting substantially.

10. Domain Effects on Discounting

10.1 Intertemporal Choices in Various Domains
  • Examples:
      - Decision-making in financial, health, and environmental domains.
10.2 Health vs. Money
  • Health outcomes discounted similarly to financial but are often independent. Varies across individuals.
10.3 Environmental Discounting
  • Patterns of discounting for environmental outcomes align closely with monetary ones.

11. Discounting in Complex Situations

11.1 Outcome Streams
  • Preferences for distributions of outcomes over time (e.g., gifts or meals) can indicate higher value assigned to timing and sequence of benefits.
11.2 Anticipation of Outcomes
  • Positive anticipation may lead to a willingness to delay rewards, while negative anticipations can motivate speeding up payments.
      - Highlights a nuanced understanding of behavior surrounding discounting based on emotional engagement.

12. Conclusion on Temporal Discounting

  • The overall tendency is to favor immediate gains over larger future rewards, which reflects our impatience and psychological biases.
  • Negative discounting is prominent in scenarios that invoke anticipation either positively or negatively, demonstrating the complexity of decision-making across time.