1、Jays quandaryAt midnight,Jay is deciding what route to take home.El Camino is faster but will take him past a fast food restaurant.The midnight version of Jay does not want to have fast food.The 12:15 version of Jay will want fast food.Which route should he take?Which route should we want him to tak
2、e?Chapter 24:Time inconsistency and healthTHE BETA-DELTA DISCOUNTING MODELBeta-delta discountingIndividuals derive utility not only from present joys but also from the anticipation of future happiness.People do not maximize simply their instantaneous utility levels but rather some function of presen
3、t and future utility.This is why we pay now for tickets to concerts months in advance and get flu vaccinations that will not pay off until flu season.To account for this fact,economists model overall utility as a weighted sum of instantaneous utility levels from the present period and all future per
4、iods:Uoverall =aUtoday+bUtomorrow+cUthe next day+The coefficients a,b and c are weights that represent the fact that individuals do not necessarily value utility in all periods equally.People value utility now more than utility later.Thus a b c Beta-delta discountingThe vector of weights a,b,c,.is c
5、alled a discounting function.Discounting function:a vector of weights that indicates how much an individual values utility in present and future periods.In theory,ones discounting function could take any shape,but in general,economists who study time inconsistency assume that discounting functions a
6、re monotonically decreasing and reasonably approximated with just two parameters.Beta-delta discountingWith beta-delta discounting,a discounting function can be specified by two parameters,and,where 0 1 and 0 1.Overall utility is the sum of instantaneous utility from period 0 and is given by the fol
7、lowing equation:Uoverall=U0+1U1+2U2+where:is the present bias parameter that discounts utility in all non-current periods,and is the discount rate parameter that discounts utility incrementally more in each subsequent period.The beta-delta discounting modelLike ,is assumed to range between 0 and 1.T
8、he term is absent from the first term in the equation but present in all other terms.This means that utility from any future period receives an extra devaluation.Alternatively,we could say that utility in the present is valued especially highly,even more highly than it would be based on the discount
9、 rate alone.This is what is meant by present bias.The closer it is to zero,the more future utility is discounted and the greater the bias toward the present.The beta-delta discounting modelChapter 24:Time inconsistency and healthTIME-CONSISTENT PREFERENCESTime-consistent preferencesThe traditional w
10、ay of modeling time preference assumes that people are time-consistent in their preferences.Time-consistent preferences:Preferences shared across all selves,so that future selves will not alter a plan that a previous self found optimal.Within the beta-delta model,preferences are time-consistent if,a
11、nd only if,=1.If =1,the resulting utility function is said to exhibit exponential discounting because utility from period t is worth t as much as utility in the current period.Time-consistent preferencesTime consistency might seem an unrealistic ideal if it means that plans must never change.Q:But w
12、hat if circumstances change or new information relative to the decision is uncovered?A:As long as past and present selves agree on the best course in a given circumstance,an individuals preferences are time-consistent.Nor is time consistency imperiled by preferences naturally changing over time.Exam
13、ple:Consider a formerly avid tennis player who is aging and is no longer agile enough to play a good game.In his old age he may prefer bocce ball to tennis,but that does not mean his preferences are time-inconsistent.Rational addictionAddictive goods,by their very nature,change the utility functions
14、 of addicts.Example:Each cigarette an individual smokes today increases his demand for cigarettes tomorrow.This could undermine even the optimal plans of time-consistent individuals.According to Becker and Murphy(1988),as long as we assume that addicts are fully aware of the addictive nature of thei
15、r favorite goods,addiction does not create time inconsistency.Chapter 24:Time inconsistency and healthTIME-INCONSISTENT PREFERENCES:MYOPIA AND HOT BRAINSTime-inconsistent preferencesA body of evidence from psychological,biological,and economic experiments suggests that in many domains humans and oth
16、er animals do not exhibit time-consistent preferences Instead,this evidence suggests that humans use something approximating hyperbolic discounting,which features steep discounting of utility in the near future and flatter discounting of utility in the far futureWithin the beta-delta model,a utility
17、 function is time-inconsistent if,and only if,1.The resulting utility function is said to exhibit hyperbolic discounting.Time-inconsistent preferencesSomeone with hyperbolically discounted preferences is time inconsistent:Time-inconsistent preferences:Preferences such that future selves will sometim
18、es alter a plan that a previous self found optimal.Because present bias features so prominently in this theory,these preferences are also called myopic preferences,after the medical term for nearsightedness.Time-inconsistent preferencesThe equations below display a hypothetical individuals utility f
19、unctions and demonstrates how hyperbolic discounting and present bias lead to time-inconsistency:This is the essence of time-inconsistent preferences:the different selves within a person do not see eye-to-eye about the relative valuation of utility in different periods.This is why myopic preferences
20、 can lead to behavior that appears pathological or self-destructive.Time-inconsistent preferencesThe notion that a single person does not really have a single utility function has troubling implications for welfare economics and its revealed-preference approach.Welfare economics presupposes that any
21、 voluntary action must improve an individuals utility,and that we can draw inferences about an individuals preferences from her actions.A hyperbolic discounter upends this logic,not necessarily because she takes actions that harm her utility,but because her utility function is no longer a well-defin
22、ed or coherent entity;instead,each of her selves has its own utility function.Evidence for time-inconsistent preferencesOne way that researchers determine whether discount functions are hyperbolic is by asking survey participants to compare different offers of money.They ask participants to rank pay
23、ments at different time points,like$1 now versus$2 tomorrow.From the survey responses,researchers can impute discount rates across various time horizons.This technique was pioneered by Thaler(1981),who found that discount rates varied wildly in the short term and long term.The hot brain/cold brain m
24、odelBernheim and Rangel(2004)propose an alternate model of time-inconsistent preferences that does not rely on hyperbolic discounting,but instead adopts the view that multiple selves a“hot brain”and a“cold brain”operate within a single person at the same time.In their model,the cold brain understand
25、s the individuals true utility function and always acts rationally to maximize it.The hot brain only appears momentarily in rare circumstances,injecting its own perverse goals and perhaps interfering with the cold brains plans.Even if the hot brain is only briefly in control,it can have a detrimenta
26、l impact on the individuals happiness.The cold brain has time-consistent preferences(=1),while the hot brain displays a present bias,0 1.Ucold=0Utoday+1Utomorrow+Uhot=0Utoday+1Utomorrow+If we assume a very small 0,then these two equations describe the plight of an individual with cold and hot brains
27、.The hot brain/cold brain modelThe rivalry between the hot brain and the cold brain is based on the neural relationship between the limbic system and the frontal cortex in the human brain.The hot brain/cold brain modelChapter 24:Time inconsistency and healthDEMAND FOR COMMITMENT MECHANISMSDemand for
28、 commitment mechanismsThe traditional,revealed-preference perspective assumes that constraints placed on a person will not improve that persons welfare.Therefore,the standard theory of demand implies that the demand for commitment mechanisms constraints that people put on themselves must be zero.But
29、 much empirical evidence suggests otherwise.Some examples of commitment mechanisms include:Restricted savings accounts that prohibit withdrawals until the holiday shopping season.GymPact:an iPhone application that pays customers for going to the gym and charges them when they do not.Demand for commi
30、tment mechanismsSome of these examples are difficult to understand from a revealed preference standpoint.Why would you want to constrain future selves if you always act optimally?One answer might be signaling:Sometimes even time-consistent actors may adopt commitment mechanisms as a strategic ploy.A
31、nother way to understand commitment devices is part of the battle between different selves within the same person.Authoritarian commitment mechanismsBy its very nature,a commitment mechanism purchased by the present self will prevent the future self from doing what it wants.We call such a commitment
32、 device authoritarian.Authoritarian commitment mechanism:A constraint demanded by a present self which benefits that present self but harms a future self.So,who would be willing to pay for a commitment mechanism?Sophisticates and naifsThe willingness to pay for self-commitment only arises if a perso
33、n is aware of his time-inconsistency.If a person with time-inconsistent preferences is aware of his time-inconsistency,he is a sophisticated hyperbolic discounter.By contrast,a person may assume(incorrectly)that his future self will be time-consistent.Such a person is a naive hyperbolic discounter(o
34、r naif).Saving for retirementOne example of time-inconsistent behavior is the failure of workers to save enough for retirement.Troubling implications for health economics,for example the Grossman model.People are probably less healthy than they planned to be when they reach old age.Chapter 24:Time i
35、nconsistency and healthBEHAVIORAL WELFARE ECONOMICSBehavioral welfare economicsThere is an ongoing debate among economists about how best to judge whether an intervention benefits or harms a person with time-inconsistent preferences.This debate centers on whose preferences a society should recognize
36、.Should governments design policies that benefit present selves or future selves?Should they be careful to make sure no selves,present or future,are harmed?Is the cold-brain self the“real”self,or does the hot-brain self have valid preferences too?Behavioral welfare economicsWhose preferences should
37、count?Various perspectives:Revealed preferenceLong-run preferencesDictatorship of the presentHot-brain invaliditySmoking:a call for paternalism?Some would argue a paternalistic approach to public health is warranted.Paternalism refers to any outside constraint imposed by a third party designed to im
38、prove someones wellbeing at the cost of restricting their personal freedom.Example:A government which taxes cigarettes harms smokers but does so in the hopes of helping them quit a deadly habit.Smoking:a call for paternalism?Conventional welfare economics assumes no role for paternalism on the part
39、of third parties,because everyone always seeks to maximize their own utility and does not need any help doing so.The long-run preference approach comes to a very different conclusion.If we assume that smokers are beta-delta discounters with present bias,then they are indeed smoking“too much”from the
40、 perspective of their long-run preferences(which exclude present bias effects).In this case,a tax on each pack of cigarettes is appropriate,even if the smokers do not want one.Smoking:a call for paternalism?Under the normative standard of the dictatorship of the present,optimal cigarette taxes are p
41、ositive as well.Using this paternalistic standard,Gruber and Koszegi(2001)estimate that the optimal cigarette tax in the U.S.is at least one dollar per pack higher than current rates.But recall that their designation of optimality relies on their choice of whose utility function to maximize.Smoking:
42、a call for paternalism?The hot-brain invalidity school of thought suggests a different approach for governments trying to limit smoking.Cigarette taxes might not be optimal if they fall mostly on the rational cold-brain smokers who are already smoking the right amount.Instead,interventions should fo
43、cus on reducing the cues that trigger hot-brain episodes for example,restrictions on public smoking and cigarette advertisements.Pareto self-improving commitment mechanisms Bhattacharya and Lakdawalla(2004)propose the use of commitment devices that are Pareto self-improving.Pareto self-improving com
44、mitment mechanism:a commitment mechanism that benefits some selves without doing harm to any other selves.Example A“smokers bond”:The bond would resemble a bank account offered by the government where a smoker trying to cut back on cigarettes could deposit money in period t.Then,in period t+1,the ne
45、w self is offered a choice:He can choose to accept a tax on each pack of cigarettes,in which case he receives the money from the bond;or he can choose to continue smoking without any taxes,but then he loses access to the bond and the government keeps the money.ConclusionTime inconsistency can explai
46、n many puzzles in health,such as why people buy gym memberships but fail to visit the gym,postpone plans to quit smoking,have so much trouble keeping to a healthy dietand many other phenomena that are difficult to explain with standard neoclassical economics.It further implies that governments and markets can use tools to improve the ability of time-inconsistent individuals to keep to their cold brains plans.
