Dynamic inconsistency
Encyclopedia
In economics
, dynamic inconsistency, or time inconsistency, describes a situation where a decision-maker's preferences change over time
in such a way that what is preferred at one point in time is inconsistent with what is preferred at another point in time. It is often easiest to think about preferences over time in this context by thinking of decision-makers as being made up of many different "selves", with each self representing the decision-maker at a different point in time. So, for example, there is my today self, my tomorrow self, my next Tuesday self, my year from now self, etc. The inconsistency will occur when somehow the preferences of some of the selves are not aligned with each other.
One type of inconsistency is more closely affiliated with game theory
, and "dynamic inconsistency" is the more commonly used terminology in this case. Another type of inconsistency is more closely affiliated with behavioral economics, and "time inconsistency" is the more commonly used terminology there.
. In this context, the inconsistency is primarily about commitment and credible threats
. This manifests itself through a violation of Bellman's principle of optimality by the leader or dominant player, as shown in Simaan and Cruz (1973a, 1973b).
For example, a firm
might want to commit itself to dramatically dropping the price
of a product it sells if a rival firm enters its market
. If this threat were credible, it would discourage the rival from entering. However, the firm might not be able to commit its future self to taking such an action because if the rival does in fact end up entering, the firm's future self might determine that, given the fact that the rival is now actually in the market and there is no point in trying to discourage entry, it is now not in its interest to dramatically drop the price. As such, the threat would not be credible. The present self of the firm has preferences that would have the future self be committed to the threat, but the future self has preferences that have it not carry out the threat. Hence, the dynamic inconsistency.
One common way in which selves may differ in their preferences is they may be modeled as all holding the view that now
has especially high value compared to any future time. This is sometimes called the immediacy effect or temporal discounting
. As a result the present self will care too much about herself and not enough about her future selves. The self control
literature relies heavily on this type of time inconsistency, and it relates to a variety of topics including procrastination
, addiction
, efforts at weight loss
, and saving for retirement
.
Time inconsistency basically means that there is disagreement between a decision-maker's different selves about what actions should be taken. Formally, consider an economic model with different mathematical weighting
s placed on the utilities
of each self. Consider the possibility that for any given self, the weightings that that self places on all the utilities could differ from the weightings that another given self places on all the utilities. The important consideration now is the relative weighting between two particular utilities. Will this relative weighting be the same for one given self as it is for a different given self? If it is, then we have a case of time consistency. If the relative weightings of all pairs of utilities are all the same for all given selves, then the decision-maker has time-consistent preferences. If there exists a case of one relative weighting of utilities where one self has a different relative weighting of those utilities than another self has, then we have a case of time inconsistency and the decision-maker will be said to have time-inconsistent preferences.
It is common in economic models that involve decision-making over time to assume that decision-makers are exponential discounters; this is generally what students are taught. Exponential discounting yields time-consistent preferences. Exponential discounting and, more generally, time-consistent preferences are often assumed in rational choice theory
, since they imply that all of a decision-maker's selves will agree with the choices made by each self. Any decision that the individual makes for himself in advance will remain valid (i.e. an optimal choice) as time advances, unless utilities themselves change.
However, empirical
research makes a strong case that time inconsistency is, in fact, standard in human
preferences. This would imply disagreement by people's different selves on decisions made and a rejection of the time consistency aspect of rational choice theory.
For example, consider having the choice between getting the day off work tomorrow or getting a day and a half off work one month from now. Suppose you would choose one day off tomorrow. Now suppose that you were asked to make that same choice ten years ago. That is, you were asked then whether you would prefer getting one day off in ten years or getting one and a half days off in ten years and one month. Suppose that then you would have taken the day and a half off. This would be a case of time inconsistency because your relative preferences for tomorrow versus one month from now would be different at two different points in time — namely now versus ten years ago. The decision made ten years ago may have been rational, but the decision made just before the fact is biased towards immediate pleasure due to an exaggerated value of "now".
More generally, humans have a systematic tendency to switch towards "vices" (products or activities which are pleasant in the short term) from "virtues" (products or activities which are seen as valuable in the long term) as the moment of consumption approaches, even if this involves changing decisions which were rationally made in advance.
One way that time-inconsistent preferences have been formally introduced into economic models is by first giving the decision-maker standard exponentially discounted preferences, and then adding an additional term that heavily discounts any time that is not now. Preferences of this sort have been called "present-biased preferences". The hyperbolic discounting
model is another commonly used model that allows to obtain more realistic results with regard to human decision-making.
A different form of dynamic inconsistency arises as a consequence of projection bias (not to be confused with a defense mechanism of the same name). Humans have a tendency to mispredict their future marginal utilities by assuming that they will remain at present levels. This leads to inconsistency as marginal utilities (for example, tastes) change over time in a way that the individual did not expect. For example, when individuals are asked to choose between a piece of fruit and an unhealthy snack (such as a candy bar) for a future meal, the choice is strongly affected by their current level of hunger. Individuals often become addicted to smoking or drugs because they underestimate future marginal utilities of these habits (such as craving for cigarettes) once they become addicted.
Economics
Economics is the social science that analyzes the production, distribution, and consumption of goods and services. The term economics comes from the Ancient Greek from + , hence "rules of the house"...
, dynamic inconsistency, or time inconsistency, describes a situation where a decision-maker's preferences change over time
Time
Time is a part of the measuring system used to sequence events, to compare the durations of events and the intervals between them, and to quantify rates of change such as the motions of objects....
in such a way that what is preferred at one point in time is inconsistent with what is preferred at another point in time. It is often easiest to think about preferences over time in this context by thinking of decision-makers as being made up of many different "selves", with each self representing the decision-maker at a different point in time. So, for example, there is my today self, my tomorrow self, my next Tuesday self, my year from now self, etc. The inconsistency will occur when somehow the preferences of some of the selves are not aligned with each other.
One type of inconsistency is more closely affiliated with game theory
Game theory
Game theory is a mathematical method for analyzing calculated circumstances, such as in games, where a person’s success is based upon the choices of others...
, and "dynamic inconsistency" is the more commonly used terminology in this case. Another type of inconsistency is more closely affiliated with behavioral economics, and "time inconsistency" is the more commonly used terminology there.
In game theory
In the context of game theory, dynamic inconsistency is a situation in a dynamic game where a player's best plan for some future period will not be optimal when that future period arrives. A dynamically inconsistent game is subgame imperfectSubgame perfect equilibrium
In game theory, a subgame perfect equilibrium is a refinement of a Nash equilibrium used in dynamic games. A strategy profile is a subgame perfect equilibrium if it represents a Nash equilibrium of every subgame of the original game...
. In this context, the inconsistency is primarily about commitment and credible threats
Non-credible threat
A non-credible threat is a term used in game theory and economics to describe a threat in a sequential game that a rational player would actually not carry out, because it would not be in his best interest to do so....
. This manifests itself through a violation of Bellman's principle of optimality by the leader or dominant player, as shown in Simaan and Cruz (1973a, 1973b).
For example, a firm
Business
A business is an organization engaged in the trade of goods, services, or both to consumers. Businesses are predominant in capitalist economies, where most of them are privately owned and administered to earn profit to increase the wealth of their owners. Businesses may also be not-for-profit...
might want to commit itself to dramatically dropping the price
Price
-Definition:In ordinary usage, price is the quantity of payment or compensation given by one party to another in return for goods or services.In modern economies, prices are generally expressed in units of some form of currency...
of a product it sells if a rival firm enters its market
Market
A market is one of many varieties of systems, institutions, procedures, social relations and infrastructures whereby parties engage in exchange. While parties may exchange goods and services by barter, most markets rely on sellers offering their goods or services in exchange for money from buyers...
. If this threat were credible, it would discourage the rival from entering. However, the firm might not be able to commit its future self to taking such an action because if the rival does in fact end up entering, the firm's future self might determine that, given the fact that the rival is now actually in the market and there is no point in trying to discourage entry, it is now not in its interest to dramatically drop the price. As such, the threat would not be credible. The present self of the firm has preferences that would have the future self be committed to the threat, but the future self has preferences that have it not carry out the threat. Hence, the dynamic inconsistency.
In behavioral economics
In the context of behavioral economics, time inconsistency is related to how each different self of a decision-maker may have different preferences over current and future choices.One common way in which selves may differ in their preferences is they may be modeled as all holding the view that now
Present (time)
The present is the time that is associated with the events perceived directly and in the first time, not as a recollection or a speculation . It is a period of time between the past and the future, and can vary in meaning from being an instant to a day or longer...
has especially high value compared to any future time. This is sometimes called the immediacy effect or temporal discounting
Temporal discounting
Temporal discounting refers to the tendency of people to discount rewards as they approach a temporal horizon in the future or the past . 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"...
. As a result the present self will care too much about herself and not enough about her future selves. The self control
Self control
Self control is the ability to control one's emotions, behavior and desires in order to obtain some reward later. In psychology it is sometimes called self-regulation...
literature relies heavily on this type of time inconsistency, and it relates to a variety of topics including procrastination
Procrastination
In psychology, procrastination refers to the act of replacing high-priority actions with tasks of low-priority, and thus putting off important tasks to a later time...
, addiction
Behavioral addiction
Behavioral addiction is a form of addiction which does not rely on drugs or alcohol. Increasingly referred to as process addiction or non-substance-related addiction ) behavioral addiction includes a compulsion to repeatedly engage in an action until said action causes serious negative consequences...
, efforts at weight loss
Weight loss
Weight loss, in the context of medicine, health or physical fitness, is a reduction of the total body mass, due to a mean loss of fluid, body fat or adipose tissue and/or lean mass, namely bone mineral deposits, muscle, tendon and other connective tissue...
, and saving for retirement
Retirement
Retirement is the point where a person stops employment completely. A person may also semi-retire by reducing work hours.Many people choose to retire when they are eligible for private or public pension benefits, although some are forced to retire when physical conditions don't allow the person to...
.
Time inconsistency basically means that there is disagreement between a decision-maker's different selves about what actions should be taken. Formally, consider an economic model with different mathematical weighting
Weighting
The process of weighting involves emphasizing the contribution of some aspects of a phenomenon to a final effect or result — giving them 'more weight' in the analysis. That is, rather than each variable in the data contributing equally to the final result, some data are adjusted to contribute...
s placed on the utilities
Utility
In economics, utility is a measure of customer satisfaction, referring to the total satisfaction received by a consumer from consuming a good or service....
of each self. Consider the possibility that for any given self, the weightings that that self places on all the utilities could differ from the weightings that another given self places on all the utilities. The important consideration now is the relative weighting between two particular utilities. Will this relative weighting be the same for one given self as it is for a different given self? If it is, then we have a case of time consistency. If the relative weightings of all pairs of utilities are all the same for all given selves, then the decision-maker has time-consistent preferences. If there exists a case of one relative weighting of utilities where one self has a different relative weighting of those utilities than another self has, then we have a case of time inconsistency and the decision-maker will be said to have time-inconsistent preferences.
It is common in economic models that involve decision-making over time to assume that decision-makers are exponential discounters; this is generally what students are taught. Exponential discounting yields time-consistent preferences. Exponential discounting and, more generally, time-consistent preferences are often assumed in rational choice theory
Rational choice theory
Rational choice theory, also known as choice theory or rational action theory, is a framework for understanding and often formally modeling social and economic behavior. It is the main theoretical paradigm in the currently-dominant school of microeconomics...
, since they imply that all of a decision-maker's selves will agree with the choices made by each self. Any decision that the individual makes for himself in advance will remain valid (i.e. an optimal choice) as time advances, unless utilities themselves change.
However, empirical
Empirical
The word empirical denotes information gained by means of observation or experimentation. Empirical data are data produced by an experiment or observation....
research makes a strong case that time inconsistency is, in fact, standard in human
Human
Humans are the only living species in the Homo genus...
preferences. This would imply disagreement by people's different selves on decisions made and a rejection of the time consistency aspect of rational choice theory.
For example, consider having the choice between getting the day off work tomorrow or getting a day and a half off work one month from now. Suppose you would choose one day off tomorrow. Now suppose that you were asked to make that same choice ten years ago. That is, you were asked then whether you would prefer getting one day off in ten years or getting one and a half days off in ten years and one month. Suppose that then you would have taken the day and a half off. This would be a case of time inconsistency because your relative preferences for tomorrow versus one month from now would be different at two different points in time — namely now versus ten years ago. The decision made ten years ago may have been rational, but the decision made just before the fact is biased towards immediate pleasure due to an exaggerated value of "now".
More generally, humans have a systematic tendency to switch towards "vices" (products or activities which are pleasant in the short term) from "virtues" (products or activities which are seen as valuable in the long term) as the moment of consumption approaches, even if this involves changing decisions which were rationally made in advance.
One way that time-inconsistent preferences have been formally introduced into economic models is by first giving the decision-maker standard exponentially discounted preferences, and then adding an additional term that heavily discounts any time that is not now. Preferences of this sort have been called "present-biased preferences". The hyperbolic discounting
Hyperbolic discounting
In behavioral economics, hyperbolic discounting is a time-inconsistent model of discounting.Given two similar rewards, humans show a preference for one that arrives sooner rather than later. Humans are said to discount the value of the later reward, by a factor that increases with the length of the...
model is another commonly used model that allows to obtain more realistic results with regard to human decision-making.
A different form of dynamic inconsistency arises as a consequence of projection bias (not to be confused with a defense mechanism of the same name). Humans have a tendency to mispredict their future marginal utilities by assuming that they will remain at present levels. This leads to inconsistency as marginal utilities (for example, tastes) change over time in a way that the individual did not expect. For example, when individuals are asked to choose between a piece of fruit and an unhealthy snack (such as a candy bar) for a future meal, the choice is strongly affected by their current level of hunger. Individuals often become addicted to smoking or drugs because they underestimate future marginal utilities of these habits (such as craving for cigarettes) once they become addicted.
Stylized examples
- Students, the night before an exam, often wish that the exam could be put off for one more day. If asked on that night, such students might agree to commit to paying, say, $10 on the day of the exam for it to be held the next day. Months before the exam is held, however, students generally do not care much about having the exam put off for one day. And, in fact, if the students were made the same offer at the beginning of the termAcademic termAn academic term is a division of an academic year, the time during which a school, college or university holds classes. These divisions may be called terms...
, that is, they could have the exam put off for one day by committing during registration to pay $10 on the day of the exam, they probably would reject that offer. The choice is the same, although made at different points in time. Because the outcome would change depending on the point in time, the students would exhibit time inconsistency.
- Government policy makers also suffer from dynamic inconsistency, as they are best off promising that there will be lower inflationInflationIn economics, inflation is a rise in the general level of prices of goods and services in an economy over a period of time.When the general price level rises, each unit of currency buys fewer goods and services. Consequently, inflation also reflects an erosion in the purchasing power of money – a...
tomorrow. But once tomorrow comes lowering inflation may have negative effects, such as increasing unemploymentUnemploymentUnemployment , as defined by the International Labour Organization, occurs when people are without jobs and they have actively sought work within the past four weeks...
, so they do not make much effort to lower it. This is why independent central bankCentral bankA central bank, reserve bank, or monetary authority is a public institution that usually issues the currency, regulates the money supply, and controls the interest rates in a country. Central banks often also oversee the commercial banking system of their respective countries...
s are believed to be advantageous for a country: their independence frees them to only worry about making decisions for the greater good, not to keep government policy makers popular.
- One famous example in literature of a mechanism for dealing with dynamic inconsistency is that of Odysseus and the Sirens. Curious to hear the Sirens' songs but mindful of the danger, Odysseus orders his men to stop their ears with beeswax and ties himself to the mast of the ship. Most importantly, he orders his men not to heed his cries while they pass the Sirens; recognizing that in the future he may behave irrationally, Odysseus limits his future agency and binds himself to a commitment mechanism (i.e. the mast) to survive this perilous example of dynamic inconsistency. While Homer likely did not have this in mind as a metaphor for the economic problem, this example has been used by economists to explain the benefits of commitment mechanisms in mitigating dynamic inconsistency.
- A curious case of dynamic inconsistency in psychology is described by Read, Loewenstein and Kalyanaraman (1999). In the experiment, subjects of the study were offered free rentals of movies which were classified into two categories - "lowbrow" (e.g. The Breakfast ClubThe Breakfast ClubThe Breakfast Club is a 1985 American teen drama film written and directed by John Hughes. The storyline follows five teenagers as they spend a Saturday in detention together and come to realize that they are all deeper than their respective stereotypes.-Plot:The plot follows five students at...
) and "highbrow" (e.g. Schindler's ListSchindler's ListSchindler's List is a 1993 American film about Oskar Schindler, a German businessman who saved the lives of more than a thousand mostly Polish-Jewish refugees during the Holocaust by employing them in his factories. The film was directed by Steven Spielberg, and based on the novel Schindler's Ark...
) - and researchers analyzed patterns of choices made. In the absence of dynamic inconsistency, the choice would be expected to be the same regardless of the delay between the decision date and the consumption date. In practice, however, the outcome was different. When subjects had to choose a movie to watch immediately, the choice was consistently lowbrow for the majority of the subjects. But when they were asked to pick a movie to be watched at later date, highbrow movies were chosen far more often. Among movies picked four or more days in advance, over 70% were highbrow.