Present-Biased Preferencesecon.ucsb.edu/~grossman/teaching/Econ594BT_Spring2009/PB-prefs.pdf
Transcript of Present-Biased Preferencesecon.ucsb.edu/~grossman/teaching/Econ594BT_Spring2009/PB-prefs.pdf
Intro DU model Beta-Delta Model Self-Awareness
Present-Biased Preferences
April 23, 2009
Intro DU model Beta-Delta Model Self-Awareness
Today
Intertemporal choice: background
Discounted utility “anomalies” & present bias
Quasi-hyperbolic discounting: β, δ model
Example
Self-awareness: Sophistication vs. Naivete
Intro DU model Beta-Delta Model Self-Awareness
Next time(s)
More examples
Welfare
Some applications
Intro DU model Beta-Delta Model Self-Awareness
Intertemporal Choice: Background
Early perspective:
Rae: wealth differences across nations can be traced to “theeffective desire of accumulation”, a psychological factor
Joint determinants of desire for wealth accumulation:
Bequest motive
promotes
Self-restraint
promotesUncertainty of human life
limits
excitement/passion of immediate consumption, discomfort ofdelayed gratification
limits
Time preference is an amalgamation of motives
DU model condenses all these into one parameter, discountrate, but resurrection distinct motives is crucial forunderstanding intertemporal choices.
Intro DU model Beta-Delta Model Self-Awareness
Intertemporal Choice: Background
Early perspective:
Rae: wealth differences across nations can be traced to “theeffective desire of accumulation”, a psychological factor
Joint determinants of desire for wealth accumulation:
Bequest motive promotesSelf-restraint promotes
Uncertainty of human life
limits
excitement/passion of immediate consumption, discomfort ofdelayed gratification
limits
Time preference is an amalgamation of motives
DU model condenses all these into one parameter, discountrate, but resurrection distinct motives is crucial forunderstanding intertemporal choices.
Intro DU model Beta-Delta Model Self-Awareness
Intertemporal Choice: Background
Early perspective:
Rae: wealth differences across nations can be traced to “theeffective desire of accumulation”, a psychological factor
Joint determinants of desire for wealth accumulation:
Bequest motive promotesSelf-restraint promotesUncertainty of human life
limits
excitement/passion of immediate consumption, discomfort ofdelayed gratification
limits
Time preference is an amalgamation of motives
DU model condenses all these into one parameter, discountrate, but resurrection distinct motives is crucial forunderstanding intertemporal choices.
Intro DU model Beta-Delta Model Self-Awareness
Intertemporal Choice: Background
Early perspective:
Rae: wealth differences across nations can be traced to “theeffective desire of accumulation”, a psychological factor
Joint determinants of desire for wealth accumulation:
Bequest motive promotesSelf-restraint promotesUncertainty of human life limitsexcitement/passion of immediate consumption, discomfort ofdelayed gratification limits
Time preference is an amalgamation of motives
DU model condenses all these into one parameter, discountrate, but resurrection distinct motives is crucial forunderstanding intertemporal choices.
Intro DU model Beta-Delta Model Self-Awareness
Intertemporal Choice: Background
Early perspective:
Rae: wealth differences across nations can be traced to “theeffective desire of accumulation”, a psychological factor
Joint determinants of desire for wealth accumulation:
Bequest motive promotesSelf-restraint promotesUncertainty of human life limitsexcitement/passion of immediate consumption, discomfort ofdelayed gratification limits
Time preference is an amalgamation of motives
DU model condenses all these into one parameter, discountrate, but resurrection distinct motives is crucial forunderstanding intertemporal choices.
Intro DU model Beta-Delta Model Self-Awareness
Intertemporal Choice: Background
Early perspective:
Rae: wealth differences across nations can be traced to “theeffective desire of accumulation”, a psychological factor
Joint determinants of desire for wealth accumulation:
Bequest motive promotesSelf-restraint promotesUncertainty of human life limitsexcitement/passion of immediate consumption, discomfort ofdelayed gratification limits
Time preference is an amalgamation of motives
DU model condenses all these into one parameter, discountrate, but resurrection distinct motives is crucial forunderstanding intertemporal choices.
Intro DU model Beta-Delta Model Self-Awareness
Semantics
Time discounting vs. time preference
Time discounting encompasses any reason for caring lessabout future consequence.
Includes uncertainty, possibility of changing tastes (hueristicdiscounting)
E.g. If each period, world will end w/ prob. p =⇒ discountfactor δ = 1− p makes sense
E.g. If inner-city 10-year-old has 1% chance of beingmurdered by age 25, ought to discount “life utility” more than10-year-old suburban child w/ 0% chance of being murdered.
Time preference refers to the preference for immediate utilityover delayed utility (hedonic discounting)
Aside/strong claim: once we account for the heuristiccomponent of intertemporal choice, the proper welfaremeasure should feature no time discounting.
Intro DU model Beta-Delta Model Self-Awareness
Semantics
Time discounting vs. time preference
Time discounting encompasses any reason for caring lessabout future consequence.
Includes uncertainty, possibility of changing tastes (hueristicdiscounting)
E.g. If each period, world will end w/ prob. p =⇒ discountfactor δ = 1− p makes sense
E.g. If inner-city 10-year-old has 1% chance of beingmurdered by age 25, ought to discount “life utility” more than10-year-old suburban child w/ 0% chance of being murdered.
Time preference refers to the preference for immediate utilityover delayed utility (hedonic discounting)
Aside/strong claim: once we account for the heuristiccomponent of intertemporal choice, the proper welfaremeasure should feature no time discounting.
Intro DU model Beta-Delta Model Self-Awareness
Semantics
Time discounting vs. time preference
Time discounting encompasses any reason for caring lessabout future consequence.
Includes uncertainty, possibility of changing tastes (hueristicdiscounting)
E.g. If each period, world will end w/ prob. p =⇒ discountfactor δ = 1− p makes sense
E.g. If inner-city 10-year-old has 1% chance of beingmurdered by age 25, ought to discount “life utility” more than10-year-old suburban child w/ 0% chance of being murdered.
Time preference refers to the preference for immediate utilityover delayed utility (hedonic discounting)
Aside/strong claim: once we account for the heuristiccomponent of intertemporal choice, the proper welfaremeasure should feature no time discounting.
Intro DU model Beta-Delta Model Self-Awareness
Semantics
Time discounting vs. time preference
Time discounting encompasses any reason for caring lessabout future consequence.
Includes uncertainty, possibility of changing tastes (hueristicdiscounting)
E.g. If each period, world will end w/ prob. p =⇒ discountfactor δ = 1− p makes sense
E.g. If inner-city 10-year-old has 1% chance of beingmurdered by age 25, ought to discount “life utility” more than10-year-old suburban child w/ 0% chance of being murdered.
Time preference refers to the preference for immediate utilityover delayed utility (hedonic discounting)
Aside/strong claim: once we account for the heuristiccomponent of intertemporal choice, the proper welfaremeasure should feature no time discounting.
Intro DU model Beta-Delta Model Self-Awareness
Semantics
Time discounting vs. time preference
Time discounting encompasses any reason for caring lessabout future consequence.
Includes uncertainty, possibility of changing tastes (hueristicdiscounting)
E.g. If each period, world will end w/ prob. p =⇒ discountfactor δ = 1− p makes sense
E.g. If inner-city 10-year-old has 1% chance of beingmurdered by age 25, ought to discount “life utility” more than10-year-old suburban child w/ 0% chance of being murdered.
Time preference refers to the preference for immediate utilityover delayed utility (hedonic discounting)
Aside/strong claim: once we account for the heuristiccomponent of intertemporal choice, the proper welfaremeasure should feature no time discounting.
Intro DU model Beta-Delta Model Self-Awareness
Intertemporal Choice: Background
(Exponential) Discounted Utility model (Samuelson, 1937):
Ut(ct , . . . , cT ) =T−t∑k=0
δku(ct+k),
where δ = ( 11+ρ).
Can be applied more generally than 2-period indifferencecurve analysis, make connection to investment decisions
Condenses psychological motives into one parameter
Not endorsed as normative, descriptive model
Rapidly gained popularity and perceived legitimacy
Features constant, stationary discounting
Intro DU model Beta-Delta Model Self-Awareness
Discounted Utility “Anomalies”
Best documented is hyperbolic discounting: a declining rate oftime preference over longer horizons
‘Hyperbolic’ because hyperbolic functional form, featuringdeclining discount rate, fits data better than exponential form,with constant discount rate.
Others: gains discounted more than losses; small outcomesdiscounted more than large ones; preference for improvingsequences, etc. (see FLO (2002))
Unlike other expected-utility anomalies, these “anomalies” donot necessarily violate any standard or principle. They aremerely incompatible with the DU model.
Intro DU model Beta-Delta Model Self-Awareness
Discounted Utility “Anomalies”
A calibration argument:
.99365×2 ≈ 11536
.9952×2 ≈ 12.8
.999365×2 ≈ 12.1
.999365×24×2 ≈ 140,987,013
.9999365×24×2 ≈ 15.7
What is your propensity to favor your well-being today overyour well-begin tomorrow?
What is your propensity to favor your well-being on a day 20years from now over a day 22 years from now?
Intro DU model Beta-Delta Model Self-Awareness
Discounted Utility “Anomalies”
A calibration argument:
.99365×2 ≈ 11536
.9952×2 ≈ 12.8
.999365×2 ≈ 12.1
.999365×24×2 ≈ 140,987,013
.9999365×24×2 ≈ 15.7
What is your propensity to favor your well-being today overyour well-begin tomorrow?
What is your propensity to favor your well-being on a day 20years from now over a day 22 years from now?
Intro DU model Beta-Delta Model Self-Awareness
A Simple Model of Present-Biased Preferences
From Laibson (1994,1997):
Ut(ct , . . . , cT ) = δtu(ct) + β
T−t∑k=1
δku(ct+k),
where β, δ ∈ [0, 1].
delta ≈ 1 is the standard discount factor
β = 1 implies standard, time-consistent (exponential)preferences
β < 1 implies time-inconsistent, present-biased preferences
Intro DU model Beta-Delta Model Self-Awareness
Example
Tenzin has to decide how to allocate lentils across time: one lentiltoday vs. two lentils tomorrowTenzin_Gyatzo_foto_1.jpg (JPEG Image, 308x400 pixels) http://upload.wikimedia.org/wikipedia/commons/8/85/Tenzin_Gyatzo_fo...
1 of 1 4/23/2009 2:42 PM
His consumption utility of eating lentils on each day is
u(1) = c
u(2) =3
2c
u(0) = 0
Intro DU model Beta-Delta Model Self-Awareness
Example
Tenzin has to decide how to allocate lentils across time: one lentiltoday vs. two lentils tomorrow
Time-consistent Lama: β = 1 implies that a lentil in period tis better than two lentils in period t + 1 ⇐⇒
δtc + 0 > 0 + δt+1(3
2)c,
or δ > 23 .
It doesn’t matter whether t is today, tomorrow, or any time inthe future
Intro DU model Beta-Delta Model Self-Awareness
Example
Tenzin has to decide how to allocate lentils across time: one lentiltoday vs. two lentils tomorrow
Time-inconsistent Lama: what if β = 12 and δ = 1?
When t = 1, he prefers one lentil on day 1 to two lentils onday 2:
c +1
2· 0 > 0 +
1
2(
3
2c)
He also prefers two lentils on day 3 to one lentil on day 2:
0 +1
2(0 +
3
2c) > 0 +
1
2(c + 0)
However, when t = 2, his preference reverses, and he prefersone lentil on day 2 to two lentils on day 3:
c +1
2· 0 > 0 +
1
2(
3
2c)
Time-inconsistency: Tenzin is willing to delay gratification in thefuture, but not today. So when the moment arrives, he changes hismind.
Intro DU model Beta-Delta Model Self-Awareness
Example
Tenzin has to decide how to allocate lentils across time: one lentiltoday vs. two lentils tomorrow
Time-inconsistent Lama: what if β = 12 and δ = 1?
When t = 1, he prefers one lentil on day 1 to two lentils onday 2:
c +1
2· 0 > 0 +
1
2(
3
2c)
He also prefers two lentils on day 3 to one lentil on day 2:
0 +1
2(0 +
3
2c) > 0 +
1
2(c + 0)
However, when t = 2, his preference reverses, and he prefersone lentil on day 2 to two lentils on day 3:
c +1
2· 0 > 0 +
1
2(
3
2c)
Time-inconsistency: Tenzin is willing to delay gratification in thefuture, but not today. So when the moment arrives, he changes hismind.
Intro DU model Beta-Delta Model Self-Awareness
Self-Awareness
A person with time-inconsistent preferences may or may notbe aware of her inconsistency
Let β̂ be the person’s beliefs about the true value of β
A person is sophisticated if β̂ = β
A person is naive if β < β̂ ≤ 1
Intro DU model Beta-Delta Model Self-Awareness
Self-Awareness: Example
Four-day trekkie convention film festival
Thursday (day 1): The Motion PictureFriday (day 2): The Wrath of KhanSaturday (day 2): The Search For SpockSunday (day 4): The Voyage Home
Pam and Paige must each miss one movie
Cannot commit in advance, must make decision day-by-day