Intertemporal choice

What Is Intertemporal Choice?

Intertemporal choice refers to the process of making decisions that involve trade-offs between costs and benefits occurring at different points in time. This core concept within behavioral finance explores how individuals and entities allocate resources across time, balancing immediate gratification against future well-being. These choices often necessitate weighing present consumption against future rewards, or comparing short-term gains to long-term costs. Intertemporal choice is fundamental to understanding decisions related to savings, investment, and debt, where current actions directly impact future financial states.³⁸

History and Origin

The study of intertemporal choice has deep roots in economic thought. The concept was first introduced by Canadian economist John Rae in his 1834 work, "Sociological Theory of Capital."³⁶, ³⁷ Later, in the late 19th and early 20th centuries, economists like Eugen von Böhm-Bawerk and Irving Fisher further elaborated on the model. ³⁵Irving Fisher, a prominent American neoclassical economist, made significant contributions to the theory of capital, investment, and interest rates, pioneering the rigorous study of intertemporal choice in markets. His 1930 treatise, The Theory of Interest, synthesized extensive research on capital, credit markets, and factors influencing interest rates, emphasizing the role of impatience in economic decisions.
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A cornerstone of modern intertemporal choice theory is the Discounted Utility (DU) model, formalized by Paul Samuelson in his 1937 paper, "A Note on Measurement of Utility." ³¹, ³², ³³Samuelson's model generalized intertemporal choice to multiple time periods, proposing that individuals evaluate future utility by discounting it at a constant rate. ²⁹, ³⁰While influential, Samuelson himself acknowledged some of the model's underlying assumptions, such as the idea that satisfaction at any given moment depends only on consumption at that specific time, which has since been a subject of further research and critique.
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Key Takeaways

• Intertemporal choice involves decisions that weigh present costs and benefits against future outcomes.
• These decisions are central to financial planning, including saving for retirement and making investment decisions.
• Traditional economic models, such as the Discounted Utility model, often assume rational, consistent preferences over time.
• Behavioral economics highlights cognitive biases like present bias that can lead to inconsistent intertemporal choices.
• Understanding intertemporal choice helps individuals make more informed financial decisions and aids policymakers in designing effective interventions.

Formula and Calculation

In the context of the Discounted Utility (DU) model, the present value of a stream of future utility is often calculated. This model assumes that an individual's total utility from a sequence of consumption over time can be represented as the sum of instantaneous utilities, each discounted by a factor that depends on how far into the future it occurs.

The standard exponential discounting formula for a stream of utilities is:

Where:

• (U_0) = Total discounted utility at time 0
• (u(c_t)) = Instantaneous utility derived from consumption (c_t) at time (t)
• (\delta) = Discount rate (or discount factor), where (0 < \delta \leq 1). A smaller (\delta) indicates a stronger preference for immediate gratification.
• (t) = Time period
• (T) = Total number of time periods

This formula suggests a constant rate of preference for present consumption over future consumption. However, behavioral models often use alternative discount functions, such as hyperbolic discounting, to better reflect observed human behavior.
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Interpreting the Intertemporal Choice

Interpreting intertemporal choice involves understanding how individuals value outcomes across different time horizons. In a perfectly rationality framework, individuals would consistently discount future rewards at a constant rate, aiming to maximize their lifetime utility. However, real-world behavior frequently deviates from this ideal. For example, a strong preference for immediate rewards over larger, delayed rewards is a common manifestation of present bias. This often leads to individuals prioritizing short-term needs or desires even when it may compromise long-term financial planning.
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A high implied discount rate in intertemporal choices suggests a strong preference for the present, meaning an individual significantly devalues future outcomes. Conversely, a low discount rate indicates a greater willingness to defer gratification for larger future rewards. Understanding these underlying preferences is critical for both personal financial decision-making and broader economic analysis.
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Hypothetical Example

Consider a recent college graduate, Alex, who has just landed their first job. Alex faces an intertemporal choice regarding a bonus of $5,000.

Scenario A: Immediate Gratification
Alex could use the entire $5,000 bonus to take an immediate, expensive vacation. This offers instant enjoyment and a high level of present utility.

Scenario B: Future Investment
Alternatively, Alex could invest the $5,000 in a retirement account. Assuming a conservative average annual return, this money could grow significantly over 40 years, potentially becoming over $100,000 by retirement. This choice involves delaying gratification for a much larger future benefit.

Alex's intertemporal choice between these scenarios reflects their time preference. Choosing the vacation indicates a higher weighting of immediate pleasure, while choosing to invest signifies a greater valuation of future financial security. This decision highlights the opportunity cost of each option.

Practical Applications

Intertemporal choice is a pervasive concept with numerous applications in finance and economics:

• Retirement Planning: Individuals make critical intertemporal choices when deciding how much of their current income to save for retirement versus how much to spend today. Behavioral biases, such as inertia and present bias, often lead to under-saving, even when individuals understand the long-term benefits of early and consistent contributions. ²², ²³Financial institutions and policymakers often design retirement plans with automatic enrollment features to leverage behavioral insights and encourage greater long-term savings.
  ²¹* Government Policy: Governments frequently employ policies that influence intertemporal choices, such as tax incentives for saving (e.g., tax-advantaged retirement accounts) or penalties for early withdrawals. These policies aim to shift individuals' preferences towards more future-oriented financial behaviors.
• Corporate Finance: Businesses constantly engage in intertemporal choice when making investment decisions, such as whether to invest in research and development for future growth or distribute profits to shareholders today. These decisions involve evaluating the risk-reward tradeoff over different time horizons.
• Consumer Credit: The use of credit cards and loans reflects an intertemporal choice to consume now and pay later. The interest rate charged represents the cost of accelerating consumption from the future to the present.

Limitations and Criticisms

While traditional models of intertemporal choice, particularly the Discounted Utility (DU) model, provide a foundational framework, they face several criticisms for their assumptions about human rationality.
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One significant limitation is the assumption of a constant discount rate over time, which implies that preferences remain consistent regardless of how far in the future the outcomes occur. Empirical evidence, however, frequently reveals "time inconsistency" or "preference reversal," where an individual's preference between two options changes as the waiting period for those options decreases. ¹⁷, ¹⁸For example, someone might prefer $110 in 53 weeks over $100 in 52 weeks but then prefer $100 immediately over $110 in one week. This phenomenon is often explained by hyperbolic discounting, which suggests that people discount immediate future rewards much more steeply than distant future rewards.
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Another criticism stems from the model's inability to fully account for various cognitive biases and emotional factors that influence decision-making. For instance, the framing of a choice, the presence of temptation, or even objective counter-party risks can distort intertemporal preferences in ways not predicted by simple exponential discounting. ¹², ¹³, ¹⁴Research in behavioral economics continues to explore these "anomalies" to develop more descriptively accurate models of how people make choices across time.
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Intertemporal Choice vs. Time Preference

While closely related and often used interchangeably in casual discourse, "intertemporal choice" and "time preference" refer to distinct but interconnected concepts.

Intertemporal choice is the broader concept, encompassing any decision that involves trade-offs between different points in time. It is the act of choosing between options whose consequences are realized at varying times. This can involve tangible elements like money and goods, as well as intangible aspects like effort or well-being.
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Time preference, on the other hand, is a specific component within intertemporal choice. It refers to an individual's relative valuation of receiving a good or service at an earlier date compared to receiving it at a later date. It quantifies the degree to which an individual discounts future utility or rewards. A high time preference indicates a strong preference for immediate gratification, while a low time preference suggests patience and a willingness to wait for larger, delayed rewards. ⁶, ⁷In essence, intertemporal choice describes what decision is made, while time preference helps explain why that decision is made in terms of the individual's inherent weighting of time.

FAQs

Why is intertemporal choice important in personal finance?

Intertemporal choice is crucial in personal finance because it dictates how individuals manage their money across their lifetime. Decisions about saving for retirement, taking on debt for immediate consumption, or investing for future goals are all intertemporal choices. Understanding these choices can help individuals make more deliberate and beneficial financial decisions over the long term.
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What is the concept of "present bias" in intertemporal choice?

Present bias is a cognitive bias where individuals place disproportionately more weight on immediate rewards or costs compared to future rewards or costs. This often leads to procrastination on beneficial long-term activities (like saving) or impulsive engagement in short-term gratifications (like overspending), even if it goes against their long-term interests.
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How do interest rates influence intertemporal choice?

Interest rates significantly influence intertemporal choice by altering the relative attractiveness of current versus future consumption. Higher interest rates make saving more appealing because the future reward (return on savings) is greater, thereby encouraging people to defer consumption. Conversely, lower interest rates make borrowing cheaper and saving less rewarding, potentially encouraging more present consumption.¹, ²