Time preference

Overview

In behavioral economics, time preference (or time discounting, delay discounting, temporal discounting, long-term orientation) is the current relative valuation placed on receiving a good at an earlier date compared with receiving it at a later date. Applications for these preferences include finance, health, and climate change. Time preferences are captured mathematically in the discount function. The main models of discounting include exponential, hyperbolic, and quasi hyperbolic. The higher the time preference, the higher the discount placed on returns receivable or costs payable in the future. Several factors correlate with an individual's time preference, including age, income, race, risk, and temptation. On a larger level, ideas such as sign effects, sub-additivity, and the elicitation method can influence how people display time preference. Time preference can also inform wider preferences about real world behavior and attitudes, such as pro-social behavior. Cultural differences can explain differences in discounting as they both have similar underlying psychological influences. The discount rate is also useful in many fields, such as finance and climate change.

Example

An individual's time preference can be found in choices between smaller-sooner and larger-later rewards. A person offered $100 today or $110 in one month reveals their discount rate. Choosing the immediate $100, suggests an annual discount rate of at least 10%, whereas indifference of preference for the delayed amount indicates a lower rate. Psychologists and economists use series of similar questions (money earlier or later or MEL methods) to estimate preferences. In everyday terms, time preferences appear in decisions like whether or not to contribute to a retirement account. Choosing to not contribute a portion of one's paycheck to a retirement account is a high time preference decision, whereas contributing to said account is a low time preference decision.

History and development

Work on time preference began with John Rae's "The Sociological Theory of Capital" in an attempt to answer why wealth differed across nations. He theorized that it was due to differences in saving and investment from the population, ultimately driven by tolerance for uncertainty and ability to delay gratification. Later, views expanded to examine why individuals may have differences in how they trade off benefits between the present and the future. Some theories include risk, preferences for immediate gratification, and ability to estimate future wants. This means that people may view the future as uncertain, and therefore, they should consume now instead of saving for later. They may also have a compulsion to consume now and are unable to delay the pleasure. Lastly, they may be unable to comprehend their future needs and wants. Irving Fisher was the first person to model these choices economically as a tradeoff between your current and future self. Such ideas were later formalized by Paul Samuelson in "A Note on Measurement of Utility." In this paper, he described a model wherein people want to maximize their utility over all future periods, with future utility being devalued exponentially from the present value.

Neoclassical views

In the neoclassical theory of interest due to Irving Fisher, the rate of time preference is usually taken as a parameter in an individual's utility function which captures the trade off between consumption today and consumption in the future, and is thus exogenous and subjective. It is also the underlying determinant of the real rate of interest. The rate of return on investment is generally seen as return on capital, with the real rate of interest equal to the marginal product of capital at any point in time. Arbitrage, in turn, implies that the return on capital is equalized with the interest rate on financial assets (adjusting for factors such as inflation and risk). Consumers, who are facing a choice between consumption and saving, respond to the difference between the market interest rate and their own subjective rate of time preference ("impatience") and increase or decrease their current consumption according to this difference. This changes the amount of funds available for investment and capital accumulation, as in for example the Ramsey growth model. In the long run steady state, consumption's share in a person's income is constant which pins down the rate of interest as equal to the rate of time preference, with the marginal product of capital adjusting to ensure this equality holds. In this view, it is not that people discount the future because they can receive positive interest rates on their savings. Rather, the causality goes in the opposite direction; interest rates must be positive in order to induce impatient individuals to forgo current consumption in favor of future. Time preference is a key component of the Austrian school of economics; it is used to understand the relationship between saving, investment and interest rates.

Historical understanding in relation to interest rates

The Catholic scholastic philosophers firstly brought up sophisticated explanations and justifications of return on capital, including risk and the opportunity cost of profit forgone, associated with the discount factor. However, they failed to interpret the interest on a riskless loan and hence denounced the time preference discounter as sinful and usurious. Later, Conrad Summenhart, a theologian at the University of Tübingen, used time preference to explain the discount loans, where the lenders won't profit usuriously from the loans as the borrowers would accept the price the lenders ask. A half-century later, Martin de Azpilcueta Navarrus, a Dominican canon lawyer and monetary theorist at the University of Salamanca, held the view that present goods, such as money, will naturally be worth more on the market than future goods (money). At about the same time, Gian Francesco Lottini da Volterra, an Italian humanist and politician, discovered time preference and contemplated time preference as an overestimation of "a present" that can be grasped immediately by the senses. Two centuries later, Ferdinando Galiani, a Neapolitan abbot, used an analogy to point out that just similar to the exchange rate, the interest rate links and equates the present value to the future value, and under people's subjective mind, these two physically non-identical items should be equal. These scattered thoughts and progression of theories inspired Anne Robert Jacques Turgot, a French statesman, to generate a full-scale time preference theory: what must be compared in a loan transaction is not the value of money lent with the value repaid, but rather the 'value of the promise of a sum of money compared to the value of money available now; in addition, he analyzed the relation between money supply and interest rates: If money supply increases and people with insensitive time preference receive the money, then these people tend to hoard money for savings instead of going for consumptions, which will cause interest rates to fall while prices to rise.

Models of discounting

Temporal discounting (also known as delay discounting, time discounting) is the tendency of people to discount rewards as they approach a temporal horizon in the future or the past (i.e., become so distant in time that they cease to be valuable or to have addictive effects). To put it another way, it is a tendency to give greater value to rewards as they move away from their temporal horizons and towards the "now". For instance, a nicotine deprived smoker may highly value a cigarette available any time in the next 6 hours but assign little or no value to a cigarette available in 6 months. Regarding terminology, from Frederick et al. (2002):

We distinguish time discounting from time preference. We use the term time discounting broadly to encompass any reason for caring less about a future consequence, including factors that diminish the expected utility generated by a future consequence, such as uncertainty or changing tastes. We use the term time preference to refer, more specifically, to the preference for immediate utility over delayed utility. This term is used in intertemporal economics, intertemporal choice, neurobiology of reward and decision making, microeconomics and recently neuroeconomics. Traditional models of economics assumed that the discounting function is exponential in time leading to a monotonic decrease in preference with increased time delay; however, more recent neuroeconomic models suggest a hyperbolic discount function which can address the phenomenon of preference reversal. Temporal discounting is also a theory particularly relevant to the political decisions of individuals, as people often put their short term political interests before the longer term policies. This can be applied to the way individuals vote in elections but can also apply to how they contribute to societal issues like climate change, that is primarily a long term threat and therefore not prioritized. There have been many mathematical models of time preference that attempt to explain intertemporal preferences.

Exponential discounted utility

Exponential discounted utility was first described in the discounted utility model. The equation is as follows:

U

t

(

c

t

, … ,

c

T

) =

∑

k = 0

T − t

D ( k ) u (

c

t + k

)

{\displaystyle U^{t}(c_{t},\dots ,c_{T})=\sum _{k=0}^{T-t}D(k)u(c_{t+k})}

where

D ( k ) =

Hyperbolic discounting

Although the exponential equation provides a nice rationale for discounting in accordance with utility theory, the apparent rate, when measured in the lab, is not constant. It actually declines over time. This means that the difference between receiving $10 tomorrow and $11 in two days is different from receiving $10 in 100 days and $11 in 101 days. Although the difference between the values and the times is the same, people value the two options at a different discount rate. The $1 is more heavily discounted between tomorrow and two days than it is between 100 and 101 days, meaning that people prefer the $10 option more in the two day case than in the 100 day case. Such preferences fit a hyperbolic curve. The first hyperbolic delay function was of the form

D ( k ) =

{

1

if

k = 0

β

δ

k

if

k > 0

{\displaystyle D(k)={\begin{cases}1&{\text{if }}k=0\\\beta \delta ^{k}&{\text{if }}k>0\end{cases}}}

This function describes a difference between the discount rate today and the next period, and then constant discounting after. It is commonly called the

( β , δ )

{\displaystyle (\beta ,\delta )}

model. A simple hyperbolic delay discounting equation is that of

v V

=

1

1 + k D

Quasi-hyperbolic discounting

The last major model is that of quasi-hyperbolic discounting. Researchers found that there is a first day effect, meaning that people greatly value immediate rewards over those in the future. Like the previous example, imagine now that you are offered $10 today or $11 tomorrow. You are also offered $10 tomorrow or $11 in two days. The preference for the $10 in the today case is typically greater than the preference for the $10 tomorrow case. This can be captured by a quasi-hyperbolic curve, wherein there is a fitted parameter for the magnitude of the first day effect. This is commonly called the beta-delta model, wherein there is a beta parameter that accounts for the present bias. The equation for utility over time looks like

U

t

(

u

t

,

u

t + 1

, … ,

u

T

) =

δ

t

u

t

+ β

∑

s = t + 1

Asymmetries

Despite the equations meant to describe behavior, when measuring preferences over real world decisions, it was noted that there were some inconsistencies. People's preferences would change based on the framing of the question or the exact decision being made; one discount rate was hard to find. The main findings are as follows "(1) gains are discounted more than losses; (2) small amounts are discounted more than large amounts; (3) greater discounting is shown to avoid delay of a good than to expedite its receipt; (4) in choices over sequences of outcomes, improving sequences are often preferred to declining sequences though positive time preference dictates the opposite; and (5) in choices over sequences, violations of independence are pervasive, and people seem to prefer spreading consumption over time in a way that diminishing marginal utility alone cannot explain".

Sign and magnitude effects

Work by Richard Thaler found the first two main effects. To measure gains and losses, he asked about the same numerical earnings or debts framed as winnings from a bank lottery or a traffic ticket. He found that gains are discounted more than losses, meaning that, they valued earning money sooner than delaying debts. He also found the discount rate to be higher when asking about tradeoffs between large amounts of money versus small amounts of money, even though the rate of substitution was the same. Some current work explains the psychological underpinnings of these findings. One suggestion is the idea of contemplation emotion, or the feeling of waiting for an event to occur. The idea is that one wants a positive event to occur and does not want to wait for it; on the other hand, people may not mind to delay a negative outcome such as a monetary loss. This can help explain the sign effect.

Temptation

Classic economic theory says that more options does not decrease utility. If you are given a completely useless option, it does not hurt you, because you can simply decide not to take it, and your information only increases. However, dynamic inconsistencies can be explained by rational beliefs and temptation. Essentially, there is a psychological cost to resisting the temptation of an activity, so you restrict your future choice set to not include the tempting activity for your long term benefit. Such theories explain why people pay in advance for commitment devices. For example, a person has to choose what to do in the future: nap or go to the gym. They may choose to form some sort of commitment device to go to the gym. Economic theory would argue that the person would be better off leaving the option to nap open, if there is no cost. However, theories of temptation argue that removing the option to nap removed the cost of rejecting the temptation to nap.