What Is Hyperbolic Discounting?

An assumption on the rate of time preference that reflects a bias towards present rewards. Hyperbolic discounting contrasts with exponential discounting where the discount rate between any two periods is constant.

Historical Context

The concept of hyperbolic discounting emerged from observations that individuals tend to favor smaller, sooner rewards over larger, later ones. This deviates from the exponential discounting model, traditionally used in economics to describe rational decision-making over time. Richard Herrnstein and Drazen Prelec were among the pioneers in formulating the hyperbolic discounting theory.

Types and Categories

Exponential Discounting

• Constant Discount Rate: The discount rate between any two periods remains constant.
• Model: Future value = Present value / (1 + r)^t

Hyperbolic Discounting

• Decreasing Discount Rate: The discount rate declines as the time horizon increases.
• Model: Future value = Present value / (1 + k*t)

Quasi-Hyperbolic Discounting

• Beta-Delta Model: Incorporates an immediate bias for present rewards but uses exponential discounting for future periods.
• Model: U_t = u(c_t) + β ∑_(t=1)^T δ^t u(c_t)

Key Events

• 1961: Introduction of the concept by Richard Herrnstein.
• 1989: Formalization and empirical validation by Drazen Prelec.
• 2000s: Widespread adoption in behavioral economics and finance.

Detailed Explanations

Hyperbolic discounting captures the tendency to choose immediate rewards more heavily than future rewards, with the discount rate declining as delays increase.

Mathematical Formulation:

• Exponential Discounting:

  $$ PV = \frac{FV}{(1 + r)^t} $$

• Hyperbolic Discounting:

  $$ PV = \frac{FV}{(1 + k \cdot t)} $$

• Quasi-Hyperbolic Discounting:

  $$ U_t = u(c_t) + β ∑_{t=1}^T δ^t u(c_t) $$

Charts and Diagrams

    graph TD
	  A[Present Value] -->|Exponential| B[Future Value / (1 + r)^t]
	  A -->|Hyperbolic| C[Future Value / (1 + k*t)]
	  A -->|Quasi-Hyperbolic| D[Immediate Bias + Exponential for future periods]

Importance and Applicability

Hyperbolic discounting plays a crucial role in understanding procrastination, addiction, and savings behavior. Its implications are pivotal in designing policies and interventions in public health, retirement planning, and consumer finance.

Examples

1. Procrastination: Choosing immediate leisure over long-term benefits of work.
2. Savings: Preference for current consumption over future savings.
3. Addiction: Immediate gratification from substance use outweighing future health concerns.

Considerations

1. Behavioral Interventions: Nudges that promote future-oriented behaviors.
2. Policy Design: Crafting policies that consider time-inconsistent preferences.

Related Terms with Definitions

• Present Bias: Preference for immediate rewards over future ones.
• Temporal Myopia: Short-sightedness in evaluating future outcomes.

Comparisons

• Exponential vs Hyperbolic:
  • Constant vs declining discount rate.
  • Rational planning vs observed behavior.

Interesting Facts

• Hyperbolic discounting is used to explain the behavior of animals in laboratory experiments, highlighting its roots in evolutionary psychology.

Inspirational Stories

• Many successful retirement plans have incorporated hyperbolic discounting principles to encourage saving.

Famous Quotes

• “The future depends on what you do today.” - Mahatma Gandhi

Proverbs and Clichés

• “A bird in the hand is worth two in the bush.”

Expressions

• “Live for today, plan for tomorrow.”

Jargon and Slang

• Discount Function: A mathematical function representing time preferences.
• Beta-Delta Model: A specific form of quasi-hyperbolic discounting.

FAQs

1. What is hyperbolic discounting?

   • It’s the tendency to prefer smaller, sooner rewards over larger, later ones, with a declining discount rate over time.

2. How does it differ from exponential discounting?

   • Exponential discounting assumes a constant discount rate, whereas hyperbolic discounting assumes a declining discount rate.

References

1. Herrnstein, R.J. (1961). “Relative and absolute strength of response as a function of frequency of reinforcement”.
2. Prelec, D. (1989). “Decreasing impatience: A criterion for non-stationary time preference and hyperbolic discounting”.

Summary

Hyperbolic discounting reveals the nuanced ways humans evaluate time and rewards. Unlike exponential discounting, which maintains a consistent discount rate, hyperbolic discounting captures a more realistic portrayal of human behavior, emphasizing the declining value placed on delayed rewards. Understanding this concept is vital in fields ranging from economics and finance to psychology and public policy, providing insights that drive better decision-making processes and interventions.