Lecture 12 - Economics of Time Inconsistency and Decision Making

Time Inconsistent Preferences: Refers to situations where an individual's preferences can shift over time, leading to a conflict between the initial plans and the actions ultimately taken. This can manifest in various contexts, such as personal goal-setting or financial decision-making, where immediate gratification may override long-term benefits.

Naïve Individual: This type of individual is typically unaware of their time inconsistency; they fail to recognize their tendency to procrastinate or alter their original plans. A naïve individual may set unrealistic goals or deadlines without foreseeing their potential struggles with self-control in the future.

Sophisticated Individual: In contrast, a sophisticated individual is aware of their inconsistency regarding preferences and proactively makes choices to counteract procrastination. They might employ tactics such as setting intermediate deadlines or using reminders to help guide their actions towards their long-term objectives and maintain self-discipline.

Consequences:

• Procrastination: This is the act of delaying action on a task, which often incurs a cost, whether in terms of missed opportunities, increased stress, or lower quality outcomes.

• Preproperation: Refers to the phenomenon where an individual completes a task earlier than anticipated due to present bias—a tendency to favor immediate rewards over future benefits. This can often lead to a feeling of relief or satisfaction that reinforces positive behavior.

EXAMPLE: MARIA'S HOMEWORK DECISION

Utility Plans: Breakdown of choices and utilities from deciding to do homework on different days based on the tradeoffs between immediate leisure time and the longer-term benefits of completing assignments ahead of schedule.

• Friday: Utilities of $-5$, $5$, $10$, and $4$ suggest that procrastination means Maria would face a negative utility from delaying her homework.

• Saturday: $0$, $-5$, $10$, and $10$ highlight the internal conflict of trying to balance homework and leisure activities, with negative consequences for procrastination.

• Sunday: A mix of $0$, $5$, $-5$, and $10$ showcases how the consequence of last-minute work impacts her overall well-being and satisfaction.

• Monday: The values of $0$, $5$, $10$, and $-5$ illustrate the potential penalties of neglecting earlier opportunities, leading to a last-minute rush.

QUASI-HYPERBOLIC PREFERENCES

Utility Function: The utility function is mathematically expressed as U(x1, x2, …, xT) = x1 + eta imes
ho^1 x2 + … + eta
ho^T^{T-1} xT where ( eta ) reflects present bias and (
ho ) denotes the degree of future discounting. Different values of ( eta ) and (
ho ) exemplify diverse choices made under various circumstances:

• Case A: With ( eta = 1 ) and (
  ho = 0.9 ), the intertemporal utility ends up being $10.5$, indicating a strong alignment between present and future preferences.

• Case B: When ( eta = 0.9 ) and (
  ho = 0.9 ), the intertemporal utility reduces to $9$, demonstrating a moderate inclination towards immediate rewards over future value.

• Case C: With ( eta = 0.8 ) and (
  ho = 0.9 ), the intertemporal utility further decreases to $7.4$, showcasing greater present bias leading to suboptimal long-term outcomes.

Time Inconsistency in Maria's Homework Example: Utilities calculated for her various preferences across the days illustrate the impact of procrastination on utilities, showing the importance of effective planning.

MOVIE EXAMPLE: DECISION TIMING

Assessment of payoffs for watching movies on different days provides insights into her decision-making structure:

• Go on Friday: Payoffs yield $5$, $0$, and $0$, indicating an immediate reward with no residual benefits.

• Go on Saturday: Payoffs of $0$, $6$, and $0$ suggest that delaying gratification results in a favorable outcome later.

• Go on Sunday: Payoffs at $0$, $0$, and $8$ demonstrate the highest potential reward, reinforcing present bias over weekend choices.

PREPROPERATION IN MOVIE EXAMPLE

Calculated intertemporal utilities based on movie decisions reveal differing utilities:

• For ( eta = 1 ) and (
  ho = 0.9 ): Utilities are calculated as: $5$, $5.4$, and $6.4$ showcasing the payoff for impulsive decisions versus well-thought-out planning.

• For ( eta = 0.8 ) and (
  ho = 0.9 ): With prevailing choices, utilities lead to values of $5$, $4.3$, and $5.8$, indicating that present bias is still a key factor affecting decision quality.

DELAYED BENEFITS VS. COSTS

Exploring delayed benefits from homework vis-à-vis costs associated with movie decisions sheds light on time-inconsistent behavior:

• A time-consistent choice allows for completion of homework on Saturday yielding a payoff of $10.9$ versus the decision to watch a movie on Sunday yielding a payoff of $6.5$.

• Choices vary significantly for naïve versus sophisticated planning and commitment.

COMMITMENT STRATEGIES

Commitment to Prevent Future Inconsistency: Various tools can be employed to constrain future choices, such as pre-purchasing movie tickets or scheduling specific homework time, ensuring that impulsive decisions do not override long-term goals.

• The quasi-hyperbolic model lacks full capacity to encapsulate the advantages of commitment.

• Purpose of pre-commitment is not limited to preventing time-inconsistent behavior but also serves to mitigate the costs associated with resisting temptation.

EGO DEPLETION STUDIES

Research conducted by Baumeister et al. (1998) investigates the impact of self-control on performance in tasks that rely on prior conditions (e.g., radish vs. cookies):

• Conclusion: Participants exposed to challenging prior conditions (like resisting cookies) demonstrated lower persistence in subsequent challenging tasks, reflecting the significant impact of ego depletion on decision quality.

BLOOD GLUCOSE AND TIME PREFERENCES

A study conducted by Wang and Dvorak (2010) examines the effects of sugar versus artificial sweeteners on choices involving delayed outcomes:

• Finding: Sugar consumption is linked with increased patience, leading to more favorable choice dynamics over time, demonstrating the physiological ties to decision-making.

MORE CHOICE OPTIONS FOR MARIA

Discussion on her decision-making process regarding Saturday activities highlights the tension between homework and sports:

• Committing on Friday can lead to more stable outcomes on Saturday, allowing for a structured approach towards balancing responsibilities and leisure.

REASONS FOR COMMITMENT WITH PRESENT BIAS

Maria's psychological costs of resisting temptation underscores the utility of commitment in her decisions:

• Acknowledging present bias directs efforts towards strategic decision-making to effectively manage preferences across time.

• Actions taken based on anticipated choices can reinforce self-control, reducing future regret through structured planning.