Intertemporal choice

Intertemporal choice is the process by which people make decisions about what and how much to do at various points in time, when choices at one time influence the possibilities available at other points in time. These choices are influenced by the relative value people assign to two or more payoffs at different points in time. Most choices require decision-makers to trade off costs and benefits at different points in time. These decisions may be about saving, work effort, education, nutrition, exercise, health care and so forth.

Since early in the twentieth century, economists have analyzed intertemporal decisions using the discounted utility model, which assumes that people evaluate the pleasures and pains resulting from a decision in much the same way that financial markets evaluate losses and gains, exponentially 'discounting' the value of outcomes according to how delayed they are in time. Discounted utility has been used to describe how people actually make intertemporal choices and it has been used as a tool for public policy. Policy decisions about how much to spend on research and development, health and education all depend on the discount rate used to analyze the decision.[1]

Portfolio allocation

Intertemporal portfolio choice is the allocation of funds to various assets repeatedly over time, with the amount of investable funds at any future time depending on the portfolio returns at any prior time. Thus the future decisions may depend on the results of current decisions. In general this dependence on prior decisions implies that current decisions must take into account their probabilistic effect on future portfolio constraints. There are some exceptions to this, however: with a logarithmic utility function, or with a HARA utility function and serial independence of returns, it is optimal to act with (rational) myopia, ignoring the effects of current decisions on the future decisions.


The Keynesian consumption function was based on two major hypotheses. Firstly, the marginal propensity to consume lies between 0 and 1. Secondly, the average propensity to consume falls as income rises. Early empirical studies were consistent with these hypotheses. However, after World War II it was observed that saving did not rise as income rose. The Keynesian model therefore failed to explain the consumption phenomenon, and thus the theory of intertemporal choice was developed. The analysis of intertemporal choice was introduced by John Rae in 1834 in the "Sociological Theory of Capital". Later, Eugen von Böhm-Bawerk in 1889 and Irving Fisher in 1930 elaborated on the model. A few other models based on intertemporal choice include the Life Cycle Income Hypothesis proposed by Franco Modigliani and the Permanent Income Hypothesis proposed by Milton Friedman. The concept of Walrasian equilibrium may also be extended to incorporate intertemporal choice. The Walrasian analysis of such an equilibrium introduces two "new" concepts of prices: futures prices and spot prices.

Fisher's model of intertemporal consumption

Budget constraint
Intertemporal budget constraint with consumption of period 1 and 2 on x-axis and y-axis respectively.
Intertemporal Choice
The figure depicts the intertemporal choice exercised by the consumer, given the utility preferences and the budget constraint.

Irving Fisher developed the theory of intertemporal choice in his book Theory of interest (1930). Contrary to Keynes, who related consumption to current income, Fisher's model showed how rational forward looking consumers choose consumption for the present and future to maximize their lifetime satisfaction.

According to Fisher, an individual's impatience depends on four characteristics of his income stream: the size, the time shape, the composition and risk. Besides this, foresight, self-control, habit, expectation of life, and bequest motive (or concern for lives of others) are the five personal factors that determine a person's impatience which in turn determines his time preference.[2]

In order to understand the choice exercised by a consumer across different periods of time we take consumption in one period as a composite commodity. Suppose there is one consumer, commodities, and two periods. Preferences are given by where . Income in period is . Savings in period 1 is , spending in period is , and is the interest rate. If the person is unable to borrow against future income in the first period, then he is subject to separate budget constraints in each period:


On the other hand, if such borrowing is possible then the person is subject to a single intertemporal budget constraint:


The left hand side shows the present value of expenditure and right hand side depicts the present value of income. Multiplying the equation by would give us the corresponding future values.

Now the consumer has to choose a and so as to

subject to
If the consumer is a net saver, an increase in interest rate will have an ambiguous effect on the current consumption.
If the consumer is a net borrower, an increase in interest rate will reduce his current consumption.

A consumer may be a net saver or a net borrower. If he's initially at a level of consumption where he's neither a net borrower nor a net saver, an increase in income may make him a net saver or a net borrower depending on his preferences. An increase in current income or future income will increase current and future consumption(consumption smoothing motives).

Now, consider a scenario where the interest rates are increased. If the consumer is a net saver, he will save more in the current period due to the substitution effect and consume more in the current period due to the income effect. The net effect thus becomes ambiguous. If the consumer is a net borrower, however, he will tend to consume less in the current period due to the substitution effect and income effect thereby reducing his overall current consumption.[3]

Modigliani's life cycle income hypothesis

The life cycle hypothesis is based on the following model:

subject to


U(Ct) is satisfaction received from consumption in time period t,
Ct is the level of consumption at time t,
Yt is income at time t,
δ is the rate of time preference ( a measure of individual preference between present and future activity),
W0 is the initial level of income producing assets.
Life Cycle Hypothesis
Life Cycle Hypothesis

Typically, a person's MPC (marginal propensity to consume) is relatively high during young adulthood, decreases during the middle-age years, and increases when the person is near or in retirement. The Life Cycle Hypothesis(LCH) model defines individual behavior as an attempt to smooth out consumption patterns over one's lifetime somewhat independent of current levels of income. This model states that early in one's life consumption expenditure may very well exceed income as the individual may be making major purchases related to buying a new home, starting a family, and beginning a career. At this stage in life the individual will borrow from the future to support these expenditure needs. In mid-life however, these expenditure patterns begin to level off and are supported or perhaps exceeded by increases in income. At this stage the individual repays any past borrowings and begins to save for her or his retirement. Upon retirement, consumption expenditure may begin to decline however income usually declines dramatically. In this stage of life, the individual dis-saves or lives off past savings until death.[4][5]

Friedman's permanent income hypothesis

After the Second World War, it was noticed that a model in which current consumption was just a function of current income clearly was too simplistic. It could not explain the fact that the long-run average propensity to consume seemed to be roughly constant despite the marginal propensity to consume being much lower. Thus Milton Friedman's permanent income hypothesis is one of the models which seeks to explain this apparent contradiction.

According to the permanent income hypothesis, permanent consumption, CP, is proportional to permanent income, YP. Permanent income is a subjective notion of likely average future income. Permanent consumption is a similar notion of consumption.

Actual consumption, C, and actual income, Y, consist of these permanent components plus unanticipated transitory components, CT and YT, respectively:[6]

Ct = CPt + CTt
Yt = YPt + YTt

Labor supply

The choice of an individual as to how much labor to currently supply involves a trade-off between current labor and leisure. The amount of labor currently supplied influences not only current consumption opportunities but also future ones, and in particular influences the future choice of when to retire and supply no more labor. Thus the current labor supply choice is an intertemporal choice.

When the laborers face an increase in wage, three things happen: substitution effect, ordinary income effect, and endowment effect. Keep in mind that wage is the price of leisure, since wage is the foregone opportunity cost of consuming leisure. Substitution Effect: As wage goes up, leisure becomes expensive. Therefore, a laborer would consume less leisure and supply more labor. Income Effect: As wage goes up, leisure becomes expensive. Therefore, the purchasing power of each dollar would decrease. Since leisure is a normal good, the laborer would buy less leisure. Endowment Effect:As wage goes up, the value of the endowment (= wage times leisure + consumption) goes up. Therefore, income would increase holding labor fixed. Since leisure is a normal good, the laborer would buy more leisure.

Fixed investment

Fixed investment is the purchasing by firms of newly produced machinery, factories, and the like. The reason for such purchases is to increase the amount of output that can potentially be produced at various times in the future, so this is an intertemporal choice.

Hyperbolic discounting

The article so far has considered cases where individuals make intertemporal choices by considering the present discounted value of their consumption and income. Every period in the future is exponentially discounted with the same interest rate. A different class of economists, however, argue that individuals are often affected by what is called the temporal myopia. The consumer's typical response to uncertainty in this case is to sharply reduce the importance of the future of their decision making. This effect is called hyperbolic discounting. In the common tongue it reflects the sentiment “Eat, drink and be merry, for tomorrow we may die.”[7]

Mathematically, it may be represented as follows:


f(D) is the discount factor,
D is the delay in the reward, and
k is a parameter governing the degree of discounting.[8]

When choosing between $100 or $110 a day later, individuals may impatiently choose the immediate $100 rather than wait for tomorrow for an extra $10. Yet, when choosing between $100 in a month or $110 in a month and a day, many of these people will reverse their preferences and now patiently choose to wait the additional day for the extra $10.[9]

See also


  1. ^ Berns, Gregory S.; Laibson, David; Loewenstein, George (2007). "Intertemporal choice – Toward an Integrative Framework" (PDF). Trends in Cognitive Sciences. 11 (11): 482. doi:10.1016/j.tics.2007.08.011. PMID 17980645. Archived from the original on 2016-05-30.CS1 maint: BOT: original-url status unknown (link)
  2. ^ Thaler, Richard H. (1997). "Irving Fisher: Modern Behavioral Economist" (PDF). The American Economic Review. 87 (2): 439–441. JSTOR 2950963. Archived from the original on 2016-03-04.CS1 maint: BOT: original-url status unknown (link)
  3. ^ Varian, Hal (2006). Intermediate Micro Economics.
  4. ^ Barro, Robert J. (1998). Macroeconomics (5th ed.). Cambridge, Mass.: MIT Press. ISBN 9780262024365.
  5. ^ Mankiw, N. Gregory (2008). Principles of Macroeconomics (5th ed.). Cengage Learning. ISBN 9780324589993.
  6. ^ "Adaptive expectations: Friedman's permanent income hypothesis".
  7. ^ Bellows, Alan. "Hyperbolic Discounting".
  8. ^ Hyperbolic discounting
  9. ^ P. Redden, Joseph. "Hyperbolic Discounting".
Behavioral economics

Behavioral economics studies the effects of psychological, cognitive, emotional, cultural and social factors on the economic decisions of individuals and institutions and how those decisions vary from those implied by classical theory.Behavioral economics is primarily concerned with the bounds of rationality of economic agents. Behavioral models typically integrate insights from psychology, neuroscience and microeconomic theory. The study of behavioral economics includes how market decisions are made and the mechanisms that drive public choice. The three prevalent themes in behavioral economics are:

Heuristics: Humans make 95% of their decisions using mental shortcuts or rules of thumb.

Framing: The collection of anecdotes and stereotypes that make up the mental filters individuals rely on to understand and respond to events.

Market inefficiencies: These include mis-pricing and non-rational decision making.In 2002, psychologist Daniel Kahneman was awarded the Nobel Memorial Prize in Economic Sciences "for having integrated insights from psychological research into economic science, especially concerning human judgment and decision-making under uncertainty". In 2013, economist Robert J. Shiller received the Nobel Memorial Prize in Economic Sciences "for his empirical analysis of asset prices." (within the field of behavioral finance) In 2017, economist Richard Thaler was awarded the Nobel Memorial Prize in Economic Sciences for "his contributions to behavioral economics and his pioneering work in establishing that people are predictably irrational in ways that defy economic theory."

David Laibson

David Isaac Laibson (born June 26, 1966) is a professor of economics at Harvard University, where he has taught since 1994. His research focuses on macroeconomics, intertemporal choice, behavioral economics and neuroeconomics. In 2016, he became chairman of the Harvard economics department.

Laibson is the son of Ruth and Peter Laibson, and grew up in Haverford, Pennsylvania. He received an A.B. (summa) from Harvard in 1988, studying under Benjamin M. Friedman, and went on to study at the London School of Economics (MSc. in Econometrics and Mathematical Economics) where he was a recipient of a Marshall Scholarship. He received his PhD from MIT in 1994 and joined the faculty at Harvard once he graduated. He has since gained tenure. He is married to the mathematician Nina Zipser, and they have a son, Max.

At Harvard, he teaches a popular undergraduate class on "Psychology and Economics." In addition he teaches graduate courses on macroeconomics, behavioral economics and dynamic programming. Starting Fall 2019, he teaches Ec 10, the year-long introductory economics class at Harvard, together with Jason Furman. His research has been published in prestigious journals such as the QJE, AER, JEP, Econometrica, and Science.

Laibson is perhaps best known within economics for his work on time inconsistency, especially his model of quasi-hyperbolic discounting. One of his most prominent early contributions has been the "Golden Eggs and Hyperbolic Discounting" paper in QJE, 1997 where he studied the intertemporal behavior of a time-inconsistent consumer. This work provides a tractable model for self-control problems, in which agents have difficulty sticking to their long-term goals. Agents in Professor Laibson's models generally value "commitment devices," such as 401(k) plans or housing equity, that let them accumulate assets without as much temptation to splurge. These models also explain the "debt puzzle," that American consumers demonstrate both short-run impatience and long-run patience in their lifecycle savings decisions. Laibson has since developed hyperbolic discounting research in many directions, from more advanced theoretical models to computational macroeconomics to conceptual applications.

His own applications of his models have focused primarily on retirement savings, with considerable empirical work on 401(k) plans. He has acquired access to a proprietary dataset of the 401(k) plan account information for several dozen companies, which has let him look empirically at the effects of various 401(k) plan designs and on the investment strategies of the plan participants. Perhaps the most important result to come from this research is that plan participants tend to follow the "path of least resistance," showing remarkable responsiveness to defaults and other context effects from plan design. For example, a company can dramatically increase participation in its 401(k) plan if it moves to a default of automatically enrolling employees in the 401(k) plan unless they take a minor step to opt out. However, the employees tend to stick at the default contribution rates and investment allocations.

Much of this theoretical and empirical work has been co-authored with Brigitte Madrian, James Choi, John Beshears, Andrea Repetto, and Jeremy Tobacman, among many others. Laibson's quasi-hyperbolic discounting models have also been extended and applied to addiction by Matthew Rabin, Ted O'Donoghue, and Jonathan Gruber, among others. Laibson also has written a Principles of Economics textbook with MIT Economist Daron Acemoglu and Chicago Economist John A. List.

Laibson's second most important line of research, after savings and self-control, is models of bounded rationality in markets, generally co-authoring papers with Xavier Gabaix, among others. He has also worked on neuroeconomics.

For his career achievements, he was elected to the National Academy of Sciences in 2019.

Decision theory

Decision theory (or the theory of choice not to be confused with choice theory) is the study of an agent's choices. Decision theory can be broken into two branches: normative decision theory, which analyzes the outcomes of decisions or determines the optimal decisions given constraints and assumptions, and descriptive decision theory, which analyzes how agents actually make the decisions they do.

Decision theory is closely related to the field of game theory and is an interdisciplinary topic, studied by economists,

statisticians, psychologists, biologists, political and other social scientists, philosophers, and computer scientists.

Empirical applications of this rich theory are usually done with the help of statistical and econometric methods.

Economic cost

Economic cost is the combination losses of any goods that have a value attached to them by any one individual. Economic cost is used mainly by economists as means to compare the prudence of one course of action with that of another. The factors to be taken into consideration are money, time, and other resources.The comparison includes the gains and losses precluded by taking a course of action as well as those of the course taken itself. Economic cost differs from accounting cost because it includes opportunity cost. (Some sources refer to accounting cost as explicit cost and opportunity cost as implicit cost.)

George Loewenstein

George Freud Loewenstein (born August 9, 1955) is an American educator and economist. He is the Herbert A. Simon Professor of Economics and Psychology in the Social and Decision Sciences Department at Carnegie Mellon University and director of the Center for Behavioral Decision Research. He is a leader in the fields of behavioral economics (which he is also credited with co-founding) and neuroeconomics. He is the great-grandson of Sigmund Freud.

Goods and services

Goods are items that are usually (but not always) tangible, such as pens, salt, apples, and hats. Services are activities provided by other people, who include doctors, lawn care workers, dentists, barbers, waiters, or online servers, a book, a digital videogame or a digital movie. Taken together, it is the production, distribution, and consumption of goods and services which underpins all economic activity and trade. According to economic theory, consumption of goods and services is assumed to provide utility (satisfaction) to the consumer or end-user, although businesses also consume goods and services in the course of producing other goods and services.


In psychology, impulsivity (or impulsiveness) is a tendency to act on a whim, displaying behavior characterized by little or no forethought, reflection, or consideration of the consequences. Impulsive actions are typically "poorly conceived, prematurely expressed, unduly risky, or inappropriate to the situation that often result in undesirable consequences," which imperil long-term goals and strategies for success. Impulsivity can be classified as a multifactorial construct. A functional variety of impulsivity has also been suggested, which involves action without much forethought in appropriate situations that can and does result in desirable consequences. "When such actions have positive outcomes, they tend not to be seen as signs of impulsivity, but as indicators of boldness, quickness, spontaneity, courageousness, or unconventionality" Thus, the construct of impulsivity includes at least two independent components: first, acting without an appropriate amount of deliberation, which may or may not be functional; and second, choosing short-term gains over long-term ones.Impulsivity is both a facet of personality and a major component of various disorders, including ADHD, substance use disorders, bipolar disorder, antisocial personality disorder, and borderline personality disorder. Abnormal patterns of impulsivity have also been noted instances of acquired brain injury and neurodegenerative diseases. Neurobiological findings suggest that there are specific brain regions involved in impulsive behavior, although different brain networks may contribute to different manifestations of impulsivity, and that genetics may play a role.Many actions contain both impulsive and compulsive features, but impulsivity and compulsivity are functionally distinct. Impulsivity and compulsivity are interrelated in that each exhibits a tendency to act prematurely or without considered thought and often include negative outcomes. Compulsivity may be on a continuum with compulsivity on one end and impulsivity on the other, but research has been contradictory on this point. Compulsivity occurs in response to a perceived risk or threat, impulsivity occurs in response to a perceived immediate gain or benefit, and, whereas compulsivity involves repetitive actions, impulsivity involves unplanned reactions.

Impulsivity is a common feature of the conditions of gambling and alcohol addiction. Research has shown that individuals with either of these addictions discount delayed money at higher rates than those without, and that the presence of gambling and alcohol abuse lead to additive effects on discounting.

Irving Fisher

Irving Fisher (February 27, 1867 – April 29, 1947) was an American economist, statistician, inventor, and Progressive social campaigner. He was one of the earliest American neoclassical economists, though his later work on debt deflation has been embraced by the Post-Keynesian school. Joseph Schumpeter described him as "the greatest economist the United States has ever produced", an assessment later repeated by James Tobin and Milton Friedman.Fisher made important contributions to utility theory and general equilibrium. He was also a pioneer in the rigorous study of intertemporal choice in markets, which led him to develop a theory of capital and interest rates. His research on the quantity theory of money inaugurated the school of macroeconomic thought known as "monetarism." Fisher was also a pioneer of econometrics, including the development of index numbers. Some concepts named after him include the Fisher equation, the Fisher hypothesis, the international Fisher effect, the Fisher separation theorem and Fisher market.

Fisher was perhaps the first celebrity economist, but his reputation during his lifetime was irreparably harmed by his public statements, just prior to the Wall Street Crash of 1929, claiming that the stock market had reached "a permanently high plateau". His subsequent theory of debt deflation as an explanation of the Great Depression, as well as his advocacy of full-reserve banking and alternative currencies, were largely ignored in favor of the work of John Maynard Keynes. Fisher's reputation has since recovered in neoclassical economics, particularly after his work was rediscovered in the late 1950s, and more widely due to an increased interest in debt deflation after the late-2000s recession.Having made numerous contributions to economic theory, he later became the foremost proponent of the full-reserve banking reform until his death. He was one of the authors of A Program for Monetary Reform where the general concepts of 100% reserve system is outlined.


In economics, the microfoundations are the microeconomic behavior of individual agents, such as households or firms, that underpins a macroeconomic theory.Most early macroeconomic models, including early Keynesian models, were based on hypotheses about relationships between aggregate quantities, such as aggregate output, employment, consumption, and investment. Critics and proponents of these models disagreed as to whether these aggregate relationships were consistent with the principles of microeconomics. Therefore, in recent decades macroeconomists have attempted to combine microeconomic models of household and firm behavior to derive the relationships between macroeconomic variables. Today, many macroeconomic models, representing different theoretical points of view, are derived by aggregating microeconomic models allowing economists to test them both with macroeconomic and microeconomic data.


Neuroeconomics is an interdisciplinary field that seeks to explain human decision making, the ability to process multiple alternatives and to follow a course of action. It studies how economic behavior can shape our understanding of the brain, and how neuroscientific discoveries can constrain and guide models of economics.It combines research from neuroscience, experimental and behavioral economics, and cognitive and social psychology. As research into decision-making behavior becomes increasingly computational, it has also incorporated new approaches from theoretical biology, computer science, and mathematics. Neuroeconomics studies decision making by using a combination of tools from these fields so as to avoid the shortcomings that arise from a single-perspective approach. In mainstream economics, expected utility (EU) and the concept of rational agents are still being used. Many economic behaviors are not fully explained by these models, such as heuristics and framing.Behavioral economics emerged to account for these anomalies by integrating social, cognitive, and emotional factors in understanding economic decisions. Neuroeconomics adds another layer by using neuroscientific methods in understanding the interplay between economic behavior and neural mechanisms. By using tools from various fields, some scholars claim that neuroeconomics offers a more integrative way of understanding decision making.

Price level

The general price level is a hypothetical daily measure of overall prices for some set of goods and services (the consumer basket), in an economy or monetary union during a given interval (generally one day), normalized relative to some base set. Typically, the general price level is approximated with a daily price index, normally the Daily CPI. The general price level can change more than once per day during hyperinflation.

Query theory

Query theory (QT) is a theory that proposes that preferences are constructed, rather than pre-stored and immediately retrievable, as assumed by many economic models) by individuals in accordance with the answers to one or more internally posed questions, or queries. Further, the order of such queries is dependent on the structure of the choice situation or task, and can influence retrieval of information, leading to different decisions. This is a descriptive model that attempts to explain why individuals make a decision, rather than propose an optimal decision.

Rate of profit

In economics and finance, the profit rate is the relative profitability of an investment project, a capitalist enterprise or a whole capitalist economy. It is similar to the concept of rate of return on investment.


Scarcity is the limited availability of a commodity, which may be in demand in the market or by the commons. Scarcity also includes an individual's lack of resources to buy commodities.

Sequential decision making

In artificial intelligence, sequential decision making refers to algorithms that take the dynamics of the world into consideration, thus delay parts of the problem until it must be solved. It can be described as a procedural approach to decision-making, or as a step by step decision theory. Sequential decision making has as a consequence the intertemporal choice problem, where earlier decisions influences the later available choices.

Shane Frederick

Shane Frederick (born 1968) is a tenured professor at the Yale School of Management. He earlier worked at Massachusetts Institute of Technology. He is the creator of the cognitive reflection test, which has been found to be "predictive of the types of choices that feature prominently in tests of decision-making theories, like expected utility theory and prospect theory." People who score high are less vulnerable to various biases in thinking including prospect theory and irrational intertemporal choices.His specialties are decision-making and intertemporal choice, time preferences and discount functions, and has authored papers with, among others, George Loewenstein of Carnegie Mellon University and Nobel laureate Daniel Kahneman, emeritus of Princeton University.

Frederick was born in Park Falls, Wisconsin, and graduated from the University of Wisconsin with a B.A. in Zoology, from Simon Fraser University with an M.S. in Resource Management, and from Carnegie Mellon University with a Ph.D. in Decision Sciences.

Supply shock

A supply shock is an event that suddenly increases or decreases the supply of a commodity or service, or of commodities and services in general. This sudden change affects the equilibrium price of the good or service or the economy's general price level.

In the short run, an economy-wide negative supply shock will shift the aggregate supply curve leftward, decreasing the output and increasing the price level. For example, the imposition of an embargo on trade in oil would cause an adverse supply shock, since oil is a key factor of production for a wide variety of goods. A supply shock can cause stagflation due to a combination of rising prices and falling output.

In the short run, an economy-wide positive supply shock will shift the aggregate supply curve rightward, increasing output and decreasing the price level. A positive supply shock could be an advance in technology (a technology shock) which makes production more efficient, thus increasing output.

Time preference

In 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.There is no absolute distinction that separates "high" and "low" time preference, only comparisons with others either individually or in aggregate. Someone with a high time preference is focused substantially on their well-being in the present and the immediate future relative to the average person, while someone with low time preference places more emphasis than average on their well-being in the further future.

Time preferences are captured mathematically in the discount function. The higher the time preference, the higher the discount placed on returns receivable or costs payable in the future.

One of the factors that may determine an individual's time preference is how long that individual has lived. An older individual may have a lower time preference (relative to what they had earlier in life) due to a higher income and to the fact that they have had more time to acquire durable commodities (such as a college education or a house).


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