Present-Biased Preferencesecon.ucsb.edu/~grossman/teaching/Econ594BT_Spring2009/PB-prefs.pdf

25
Intro DU model Beta-Delta Model Self-Awareness Present-Biased Preferences April 23, 2009

Transcript of Present-Biased Preferencesecon.ucsb.edu/~grossman/teaching/Econ594BT_Spring2009/PB-prefs.pdf

Page 1: 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

Page 2: Present-Biased Preferencesecon.ucsb.edu/~grossman/teaching/Econ594BT_Spring2009/PB-prefs.pdf

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

Page 3: Present-Biased Preferencesecon.ucsb.edu/~grossman/teaching/Econ594BT_Spring2009/PB-prefs.pdf

Intro DU model Beta-Delta Model Self-Awareness

Next time(s)

More examples

Welfare

Some applications

Page 4: Present-Biased Preferencesecon.ucsb.edu/~grossman/teaching/Econ594BT_Spring2009/PB-prefs.pdf

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.

Page 5: Present-Biased Preferencesecon.ucsb.edu/~grossman/teaching/Econ594BT_Spring2009/PB-prefs.pdf

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.

Page 6: Present-Biased Preferencesecon.ucsb.edu/~grossman/teaching/Econ594BT_Spring2009/PB-prefs.pdf

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.

Page 7: Present-Biased Preferencesecon.ucsb.edu/~grossman/teaching/Econ594BT_Spring2009/PB-prefs.pdf

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.

Page 8: Present-Biased Preferencesecon.ucsb.edu/~grossman/teaching/Econ594BT_Spring2009/PB-prefs.pdf

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.

Page 9: Present-Biased Preferencesecon.ucsb.edu/~grossman/teaching/Econ594BT_Spring2009/PB-prefs.pdf

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.

Page 10: Present-Biased Preferencesecon.ucsb.edu/~grossman/teaching/Econ594BT_Spring2009/PB-prefs.pdf

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.

Page 11: Present-Biased Preferencesecon.ucsb.edu/~grossman/teaching/Econ594BT_Spring2009/PB-prefs.pdf

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.

Page 12: Present-Biased Preferencesecon.ucsb.edu/~grossman/teaching/Econ594BT_Spring2009/PB-prefs.pdf

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.

Page 13: Present-Biased Preferencesecon.ucsb.edu/~grossman/teaching/Econ594BT_Spring2009/PB-prefs.pdf

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.

Page 14: Present-Biased Preferencesecon.ucsb.edu/~grossman/teaching/Econ594BT_Spring2009/PB-prefs.pdf

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.

Page 15: Present-Biased Preferencesecon.ucsb.edu/~grossman/teaching/Econ594BT_Spring2009/PB-prefs.pdf

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

Page 16: Present-Biased Preferencesecon.ucsb.edu/~grossman/teaching/Econ594BT_Spring2009/PB-prefs.pdf

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.

Page 17: Present-Biased Preferencesecon.ucsb.edu/~grossman/teaching/Econ594BT_Spring2009/PB-prefs.pdf

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?

Page 18: Present-Biased Preferencesecon.ucsb.edu/~grossman/teaching/Econ594BT_Spring2009/PB-prefs.pdf

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?

Page 19: Present-Biased Preferencesecon.ucsb.edu/~grossman/teaching/Econ594BT_Spring2009/PB-prefs.pdf

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

Page 20: Present-Biased Preferencesecon.ucsb.edu/~grossman/teaching/Econ594BT_Spring2009/PB-prefs.pdf

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

Page 21: Present-Biased Preferencesecon.ucsb.edu/~grossman/teaching/Econ594BT_Spring2009/PB-prefs.pdf

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

Page 22: Present-Biased Preferencesecon.ucsb.edu/~grossman/teaching/Econ594BT_Spring2009/PB-prefs.pdf

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.

Page 23: Present-Biased Preferencesecon.ucsb.edu/~grossman/teaching/Econ594BT_Spring2009/PB-prefs.pdf

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.

Page 24: Present-Biased Preferencesecon.ucsb.edu/~grossman/teaching/Econ594BT_Spring2009/PB-prefs.pdf

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

Page 25: Present-Biased Preferencesecon.ucsb.edu/~grossman/teaching/Econ594BT_Spring2009/PB-prefs.pdf

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