Utilit Utility and d Happiness pp Miles Kimball and Bob Willis - - PowerPoint PPT Presentation

“Utilit d “Utility and Happiness” pp

Miles Kimball and Bob Willis + Related Empirical Work With

1

Other Coauthors

Partial List of Coauthors on Related Empirical Papers Related Empirical Papers

• “What Do You Think Would Make You Happier? What Do You

Thi k Y W ld Ch ?” b D i l B j i Ki b ll O i Think You Would Choose?” by Daniel Benjamin, Kimball, Ori Heffetz and Alex Rees-Jones

• “Beyond Happiness and Satisfaction: Developing a National Well-

y pp p g Being Index Based on Stated Preference” by Benjamin, Kimball, Heffetz and Nichole Szembrot

• “Accounting for Adaptation in the Economics of Happiness” by
• Accounting for Adaptation in the Economics of Happiness by

Kimball, Ryan Nunn and Dan Silverman

• “Unhappiness After Hurricane Katrina” by Kimball, Helen Levy,

Fumio Ohtake and Yoshiro Tsutsui

• “Happiness and Elections” by Kimball, Ohtake, Collin Raymond and

Tsutsui Tsutsui

• “The Dynamics of Daily Happiness After Personal and National

News” by Kimball, Ohtake, Tsutsui and Yichuan Wang

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Motivations for Studying Happiness as an Economist

Neobenthamite Elation Theory/Price Theory

• f Happiness

V l k t d

• Value non-market goods

by their effect on the level

• f happiness
• Value non-market goods

by the effect of news about them on the short-

• f happiness
• Identify optimization

Mistakes about them on the short run dynamics of happiness Mistakes

• Determine the shape of

the utility function by

• Explain puzzles
• Study the determinants of

the utility function by looking at the shape of happiness y happiness as an important commodity

• Study hedonic loss

aversion

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Constructing National Well- Being Indices

• Use the level of 120 or so aspects of

subjective well-being, aggregated with j g, gg g weights based on revealed preference

• Need a comprehensive set of aspects
• Need a comprehensive set of aspects
• Need to adjust the weights for overlap in

the aspects

• Need to adjust for shifts in scale usage
• Need to adjust for shifts in scale usage

– Can be studied by looking at biometric data h f i l ti it di d f such as facial activity coding and measures of brain activity

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Key Elements of the Kimball-Willis Theory

• “Happiness” H in the narrow sense of

“feeling happy” is measurable. g ppy

• H is an important commodity.

A t f H d d t

• A component of H depends on recent

good or bad news.

• Good and bad news can be modeled as

rational-expectations innovations to rational-expectations innovations to lifetime utility.

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Integrating Happiness into Mainstream Economics

H i b i t t d i th t

• Happiness can be integrated in a way that

respects the canons of Economics.

– Consistency with revealed preference – Respecting the ordinal vs. cardinal distinction p g – Leaving standard economic methods undisturbed when happiness data are absent pp

• r discarded

– Adding key information when happiness data g y pp are used

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Measuring Happiness, in the Narrow Sense of Feeling Happy

• On a scale from one to

h i seven, where one is “extremely unhappy” and extremely unhappy and seven is “extremely happy ” seven is extremely happy, how do you feel right now? how do you feel right now?

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The Happiness Measure on HRS and the

• Univ. of Michigan Surveys of Consumers

“N thi k b t th t k d th f li h “Now think about the past week and the feelings you have

• experienced. Please tell me if each of the following was

true for you much of the time this past week: y p

• 1. Much of the time during the past week, you felt you

g p y y were happy. (Would you say yes or no)?

• 2. (Much of the time during the past week,) you felt sad.

(Would you say yes or no?) (Would you say yes or no?)

• 3. (Much of the time during the past week,) you enjoyed
• life. (Would you say yes or no?)
• life. (Would you say yes or no?)
• 4. (Much of the time during the past week,) you felt
• depressed. (Would you say yes or no?)”

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Measuring Utility: The Modern Tradition of Economics

• Look at an individual’s choices

(preferences). (p )

• What an individual chooses indicates what

she wants cares about and values she wants, cares about and values.

• This works well when the individual is

– Well informed – Thoughtful Thoughtful – Not at war with self

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Elements of the Theory In Words: Elements of the Theory In Words:

1 P f f H i M l l 1. Preference for Happiness: Many people value happiness, as evidenced by the fact that they will sacrifice other things for the sake of will sacrifice other things for the sake of happiness, but Happiness is not the only thing they care about they care about. (Price Theory of Happiness) 2 News and Happiness: Short run spikes and

• 2. News and Happiness: Short-run spikes and

dips in happiness signal what people consider good and bad – signal what people consider good and bad news, which in turn signals what they care about

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– which in turn signals what they care about. (Elation Theory of Happiness)

Preference for Happiness and D d f H i R t Dependence of Happiness on Recent Good and Bad News (Recent Innovations to Lifetime Utility)

T

vt  Et   tU(X ,H(X , , 1,...))

T



 t

1 t t t t

v E v 



 

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Price Theory of Happiness: Two Definitions of “Happiness”

• The Greatest Good

for an Individual for an Individual

• Feeling Happy
• Feeling Happy

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Price Theory of Happiness: Di i

i hi ili d h i

Distinguishing utility and happiness

as a matter of logic as a matter of logic.

• Utility = The extent to which people

y p p get what they want, where what they want is indicated by their choices want is indicated by their choices.

• Happiness = How positive people’s

Happiness How positive people s feelings are at a given time.

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Note on the word “Utility” Note on the word Utility

• Jeremy Bentham and the other Utilitarians used

the word “utility” for both “happiness” in our sense and for something closer to the modern meaning of “utility.”

• Jeremy Bentham probably believed that

happiness and utility were the same thing.

• Daniel Kahneman calls “utility” in our sense

“decision utility” and “happiness” in our sense decision utility and happiness in our sense “experienced utility.”

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Price Theory of Happiness: Distinguishing utility and h i i i ll happiness empirically

Evidence indicates that for t l h i most people happiness matters a lot but happiness matters a lot, but happiness is not the only thing they is not the only thing they care about. (U≠H) care about. (U≠H)

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Preference for Happiness and D d f H i R t Dependence of Happiness on Recent Good and Bad News (Recent Innovations to Lifetime Utility)

T

vt  Et   tU(X ,H(X , , 1,...))

T

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1 t t t t

v E v 

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 

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Choice and SWB in the Children vs. No Children Scenario: Women Only

SWB SWB Option 1 Option 2 Choice Option 1 89% 5% 94% Option 2 2% 3% 6% 92% 8%

Option 1: have kids Option 2: never have kids Liddell Exact Test p-value: 0 388 p value: 0.388 n=161

Choice and SWB over time in the Children vs. No Children Scenario: Women Only

SWB over time SWB over time Option 1 Option 2 Choice Option 1 87% 7% 94% Option 2 2% 4% 6% 89% 11%

Option 1: have kids Option 2: never have kids Liddell Exact Test p-value: 0 065 p value: 0.065 n=123

Choice and SWB in the Children vs. No Children Scenario: Men Only

SWB SWB Option 1 Option 2 Choice Option 1 86% 6% 92% Option 2 3% 5% 8% 89% 11%

Option 1: have kids Option 2: never have kids Liddell Exact Test dde act est p-value: 0.388 n=133

Choice and SWB over time in the Children vs. No Children Scenario: Men Only

SWB over time SWB over time Option 1 Option 2 Choice Option 1 85% 9% 94% Option 2 3% 3% 6% 88% 12%

Option 1: have kids Option 2: never have kids Liddell Exact Test p-value: 0.146 p n=98

The Easterlin Paradox The Easterlin Paradox

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Happiness by Income Quintile

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Even if True, the Easterlin Paradox is Not a Paradox: Paradox is Not a Paradox: Income and Price Effects Income and Price Effects

• The income effect on happiness is positive

The income effect on happiness is positive

• Because happiness is time-intensive,

i i th l i th i increases in the real wage raise the price

• f happiness
• Thus, theoretically, the the net effect of

secular increases in income + secular secular increases in income + secular increases in the real wage is ambiguous

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Raising Happiness in the Long-- Many Methods are Time-Intensive

1 P ( ti ) d T lk Th

• 1. Prozac (an exception) and Talk Therapy
• 2. Taking Care of Oneself

g

• Sleep
• Exercise
• Exercise
• Eating well
• 3. Enjoyable Activities
• Spending time with friends

Spending time with friends

• An engrossing hobby

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Choice and SWB over time in the Easterlin Scenario: Women Only

SWB over time SWB over time Option 1 Option 2 Choice Option 1 57% 36% 93% Option 2 0% 7% 7% 57% 43%

Option 1: born when you were Option 2: born 40 years earlier Liddell Exact Test p value: 0 000 p-value: 0.000 n=56

Choice and SWB over time in the Easterlin Scenario: Men Only

SWB over time SWB over time Option 1 Option 2 Choice Option 1 61% 31% 93% Option 2 0% 7% 7% 61% 39%

Option 1: born when you were Option 2: born 40 years earlier Liddell Exact Test p-value: 0 000 p value: 0.000 n=54

“The Paradox of Declining F l H i ” Female Happiness” Betsey Stevenson and Justin Betsey Stevenson and Justin Wolfers

Abstract: By most objective measures the lives of

y j women in the United States have improved over the past 35 years, yet we show that measures of subjective well- ’ being indicate that women’s happiness has declined both absolutely and relative to male happiness. The paradox of women’s declining relative well being is paradox of women s declining relative well-being is found examining multiple countries, datasets, and measures of subjective well-being, and is pervasive

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j g, p across demographic groups.

• Relative declines in female happiness
• Relative declines in female happiness

have eroded a gender gap in happiness in hi h i th 1970 t i ll which women in the 1970s typically reported higher subjective well-being than did men. These declines have continued and a new gender gap is emerging—one and a new gender gap is emerging

• ne

with higher subjective well-being for men. Our findings raise provocative questions Our findings raise provocative questions about the contribution of the women’s t t ’ lf d b t movement to women’s welfare and about the legitimacy of using subjective well-

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being to assess broad social changes.

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Choice and SWB over time in the Women’s Liberation Scenario: Women Only

SWB over time SWB over time Option 1 Option 2 Choice Option 1 84% 10% 94% Option 2 2% 3% 6% 87% 13%

Liddell Exact Test p-value: 0.007 Option 1: Women’s Liberation happened Option 2: Women’s Liberation never happened n=163 Option 2: Women s Liberation never happened

Choice and SWB over time in the Women’s Liberation Scenario: Men Only

SWB over time SWB over time Option 1 Option 2 Choice Option 1 61% 29% 90% Option 2 3% 7% 10% 64% 36%

Lidd ll E t T t Liddell Exact Test p-value: 0.000 n=110 Option 1: Women’s Liberation happened Option 2: Women’s Liberation never happened n 110 p pp

A Non-Judgmental View of the Effect of Materialism on Happiness

• Materialism lowers happiness (weak, but

interesting evidence in a Psychology g y gy paper “The Dark Side of the American Dream”) Dream ).

• Tradeoff between happiness and other

goods.

• Materialism means higher preferences for

Materialism means higher preferences for

• ther goods compared to happiness.

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Elicitations of Willingness to Pay for Happiness: Raw Distributions Raw Distributions

.2 .3 ensity

Depression Treatment

.2 .3 nsity

Time Spent On Meditation

.1 De

• t

f

• r

f r e e f r e e 1 % 2 % 5 % 1 % 2 % 3 3 % 5 % .1 Den m i n s 5 m i n s m i n s 5 m i n s m i n s m i n s 2 h

• u

r s 3 h

• u

r s 4 h

• u

r s 6 h

• u

r s 8 h

• u

r s n

• t

WTP as a Percentage of Income 1 5 3 4 5 6 9 2 h 3 h 4 h 6 h 8 h WTP as a Time Investment 3

Magnetic Stimulation

.1 .2 .3 Density n

• t

f

• r

f r e e f r e e 1 % 2 % 5 % 1 % 2 % 3 3 % 5 % WTP as a Percentage of Income g

Can Marginal Rates of Substitution Be Inferred From Substitution Be Inferred From Happiness Data? pp Evidence from Residency Ch i Choices

Daniel J Benjamin (Cornell) Daniel J. Benjamin (Cornell) Ori Heffetz (Cornell) Mil S Ki b ll (Mi hi ) Miles S. Kimball (Michigan) Alex Rees-Jones (Wharton)

Marginal Rate of Substitution (MRS) (MRS)

• The rate at which substitution of one good for

e a e a c subs u o

• o e good o

another would leave an individual indifferent.

• Estimation of MRSs:
• Estimation of MRSs:

– Traditionally: choice data. – Must seek alternatives when choice unobserved

• public goods, externalities, policy, mistakes, etc.

– One alternative: subjective well-being (SWB) data

• This paper: to what extent do tradeoffs

p p estimated from SWB data reflect (preference- based) MRSs? based) MRSs?

Figure 3: Tradeoff estimates: choice vs. anticipated SWB

Figure 3: Tradeoff estimates: choice vs. anticipated SWB

Beyond Happiness and Satisfaction: Satisfaction: Toward Well-Being Indices Toward Well Being Indices Based on Stated Preference

Daniel J. Benjamin (Cornell) Ori Heffetz (Cornell) Ori Heffetz (Cornell) Miles S. Kimball (Michigan) Nichole Szembrot (Cornell)

USC CESR Seminar USC CESR Seminar November 8, 2013

Key assumption: Stated preference an unbiased measure of true preference.

• Surely false; known deviations; the “right” prefs?; our evidence.

Policy Choice (131 aspects)

• cy C o ce ( 3

aspects)

The bottom of the table: The bottom of the table:

Preference for Happiness and D d f H i R t Dependence of Happiness on Recent Good and Bad News (Recent Innovations to Lifetime Utility)

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T



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1 t t t t

v E v 



 

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Hedonic Adaptation: “This, too, shall pass.”

1 Aft ti h d thi th t l h d

• 1. After time has passed, things that surely had a

big effect on happiness right after the event have surprisingly little effect on happiness (Not just surprisingly little effect on happiness. (Not just money.)

• incarceration
• incarceration
• loss of the use of limbs

i b

• serious burns
• death of a spouse
• winning the lottery
• 2. The dynamics of national happiness after news

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Figure 1

00 s

Impulse Response of Happiness to Widowing With and Without Life Insurance

g

80 10 esponse 60 8 positive re 40 6 tage of p 20 4 percent 2 50 100 months since widowed

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With Life Insurance Without Life Insurance

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What does it mean to say that lifetime utility has fallen lifetime utility has fallen permanently? p y

• Revealed Preference is the measure of

lifetime utility.

• If there were a lever to magically undo the

If there were a lever to magically undo the damage of Katrina, we would pull it.

True for the harm to others – True for the harm to others. – True for the harm to self, narrowly construed. T if th t t b h d b t – True even if the past cannot be changed but

• nly the harm from now on reversed.

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Electoral Outcomes and Happiness Electoral Outcomes and Happiness

F ll d i t l 2 000 i di id l i

• Followed approximately 2,000 individuals in

RAND ALP

– Two presidential elections: 2008, 2012 – Surveyed them immediately before election, soon ft l ti after election

• Before election asked about:

– Well-being – Political preferences – Beliefs about election outcomes

• After election asked about:

– Well-being

Electoral Outcomes and Happiness

Fi d t id i f f Ki b ll Willi

• Find strong evidence in favor of Kimball-Willis

Model

– Democrats have gain in happiness Democrats have gain in happiness – Republicans have loss in happiness

• Changes in happiness from before to after election

g pp driven by interaction of

– Strength and direction of political preferences Amount of suprise – Amount of suprise

• Strong hedonic adaptation

– Half-life of emtional reaction approximation 0 65 days – Half-life of emtional reaction approximation 0.65 days

• Evidence of gain-loss asymmetry

– Stronger reduction in happiness for equivalent g pp q amount of surprise and partisanship if Republican than gain if Democrat

Dynamics of Daily Happiness

Miles Kimball Fumio Ohtake Miles Kimball, Fumio Ohtake, Yoshiro Tsutsui and Yichuan Wang Wang

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Data Description Data Description

75 O k U i it U d d t 1 5

• 75 Osaka University Undergraduates, ~1.5 years,

~30,000 daily observations M diff t f h i

• Many different measures of happiness
• Also ask about sleep

D l h b t d d

• Demean, rescale each person by standard

deviation D li h b d f k

• De-seasonalize each person by day of week

effects Form happiness factor (1st principal component of

• Form happiness factor (1st principal component of

standardized happiness measures)

Relatively High Response Rates Relatively High Response Rates

Introduction Introduction

• Time series properties of happiness

matter!

• Stylized facts:

Sl tt f h d i d t ti – Sleep matters for hedonic adaptation – More than one “happiness” shock

• Different shocks seem to decay at different rates
• Duration hypothesis

– Measurement Error can play a large role in typical happiness measurements yp pp – National news matters less than personal news

HAPPY NEWS

Normalized and Weekly Adjusted Log Autocovariances

• 1.5
• 2.0

Cov)

Variable std_factor td

• 2.5

log(C

std_nnews std_pnews std_sleepfac

• 3.0
• 3.5

5 10 15 20 5 10 15 20

l

Structural Estimation Structural Estimation

• Three structural shocks, infinite

exponential decay p y

H i N Shock 1 2 3

Stacked Impulse Responses of Each Structural Shock

Happiness News 0.6 0.4 0.2 0.0 0.0 2.5 5.0 7.5 10.0 0.0 2.5 5.0 7.5 10.0

Number of Days Number of Days

Lessons from Structural Estimation

M d l i b t fit ith 3 h k ith diff t d

• Model is best fit with 3 shocks with different decay

rates

– Fastest decaying happiness shock ~50%/day. Fastest decaying happiness shock 50%/day. Slowest around 3%/day

• Measurement error matters

– Big contemporaneous variance, but covariances much smaller – Accounts for ~40% of variance of daily happiness Accounts for 40% of variance of daily happiness, ~60% of variance of daily personal news, and ~30%

• f contemporaneous covariance

Hedonic adaptation is fast

• Hedonic adaptation is fast

– Nothing after 6 months

Next Steps Next Steps

• No standard errors yet – working things
• ut with bootstrap

Reduced form Estimation? Reduced form Estimation?

• Problem: news innovation
• Can estimate news “innovations” through

Can estimate news innovations through an auto-regression on its own lags R i l d f h i

• Regress various leads of happiness

against current news innovations

Overall Class Friend 0.3 0.0 0.1 0.2 Teacher Part Time Job Parents/Family

• 0.2
• 0.1

0 3

ness

0.1 0.2 0.3

rdized Happin

• 0.2
• 0.1

0.0

its of Standar

Health Job Seeking Lover 0 1 0.2 0.3

Un

• 0.1

0.0 0.1

• 0.2

4 8 12 4 8 12 4 8 12

Days in the Future

National News National News

• Can adapt reduced form to see how

national news and personal news compare p p

• National news ~1/3 as important by

second day second day

News Type Personal National 0.15 0.10

est

0.05 0.00 4 8 12

lead

The Evolutionary Psychology of Elation and Dismay

• Functionally, elation and dismay may motivate

cognitive processing—much like curiosity.

– Elation: after good news, it pays to

• think what you did right, so you can do it again

f

• think how to take advantage of the new opportunities

– Dismay: after bad news, it pays to

think what you did wrong so you can avoid doing it again

• think what you did wrong, so you can avoid doing it again
• think how to mitigate the harm of the bad news

– Curiosity: after news that is neither clearly good nor Curiosity: after news that is neither clearly good nor bad, it pays to learn more for the sake of option value

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The News and Happiness Axioms The News and Happiness Axioms

1 H i t ti t i f ti f 1. Happiness at time t is a function of

• a. the other ultimate goods, represented by X,

b and the histor of reali ed lifetime tilit

• b. and the history of realized lifetime utility v

through time t. Holding X fixed, an individual is 2 happier if current expected lifetime utility is of

• 2. happier if current expected lifetime utility is of

a preferred future.

• 3. less happy if past expected lifetime utility was
• 3. less happy if past expected lifetime utility was
• f a preferred future.

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Lifetime Utility in the Additively Separable Case

T

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 t T

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1 t t t t

v E v 

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The Innovation ι in Lifetime Utility v

E t  vt  Et1vt

Note about the

vt1 U(X t1,Ht1)  Et1vt

lifetime utility innovation:

t 1 t 1 t 1 t 1 t

t  vt  

1[vt 1 U(X t 1,Ht 1)]

so

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t vt  [vt1 U(

t1, t1)]

N d H i A i News and Happiness Axioms + Additive Separability Imply + Additive Separability Imply

Ht  H(X t,t,t 1,...)

H 

t

(

t, t, t1, )

t t

H    

Axiom 2→

1 t t

H H       

Axiom 3→

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1 t j t j

  

  

 

Baseline Mood M and Elation e Baseline Mood M and Elation e

M H(X 0 0 ) M(X ) M t  H(X t,0,0,...)  M(X t)

e  H(X   ) H(X 0 0 ) et  H(X t,t,t1,...)  H(X t,0,0,...)  e(X , , , ) e(X t,t,t1,...)

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The Elation Theory of Happiness

Ht  M (X t)  e(X t,t,t1,...)

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The Elation Theory of Happiness (In Words)

Experienced happiness is the sum of two components: p

• elation: short-run happiness that depends
• n recent news about lifetime utility
• n recent news about lifetime utility
• baseline mood: long-run happiness that is

the output of a household production function (like health, entertainment, or function (like health, entertainment, or nutrition.)

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Key Implications of the Happiness and News Axioms

A th f h i b d ib d i t

• A theory of happiness can be described in terms
• f the objects that are well-defined by revealed

preference: preference:

– The fundamentals (state and control variables and

• utputs of household production functions) that
• utputs of household production functions) that

people care about and – The history of which indifference curves for lifetime plans one has been on.

Old b t th f t tt l f

• Old news about the future matters less for

happiness than recent news about the future.

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Why are Utility and Happiness Confused?

• Because they are dramatic, elation and dismay

may dominate people’s perception of happiness.

• Everyone wants good news. That is, everyone

wants what spikes in happiness signal. g

• Not everyone values the emotional spikes per

se, as distinct from what they signal. se, as distinct from what they signal.

• Not everyone will sacrifice other goods for the

long-run happiness that remains even when long-run happiness that remains even when there is no good or bad news.

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L A i f El ti Th Loss Aversion from Elation Theory:

Happiness Additively Separable with Elation pp y p Concave in Lifetime Utility Innovations U(X,H)=F(X)+M(X) +α min(ι ι /2) +α0min(ιt, ιt/2) + α1min(ιt-1, ιt-1/2) + …

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El ti I d d Elation-Independence:

Additively Separable Happiness with Elation y p pp Linear in Lifetime Utility Innovations U(X,H)=u(X)+M(X) +α0ιt + α1ιt-1 + …

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Factual Mistakes about Happiness Need Not Cause Decision Mistakes

• Given rational expectations, adding a linear

combination of lifetime utility innovations to the utility function has no effect on the preferences represented.

• In this case, mistakes about the rate of hedonic

adaptation cause no harm to utility maximization.

• However, mistakes about the controllable

determinants of baseline mood will cause determinants of baseline mood will cause material harm.

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Cumulative Elation Cumulative Elation

• Cumulative Elation=∆ Σe as the result of a

given news event g

• the extra area (or lost area) under the

curve of happiness against time (technically curve of happiness against time (technically

discounted by ρ), after correcting for any

change in baseline mood M.

• The Cumulative Elation Hypothesis: the

The Cumulative Elation Hypothesis: the size of an innovation in lifetime utility is monotonically related to the resulting monotonically related to the resulting cumulative elation.

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The Duration Hypothesis The Duration Hypothesis

• 1. Weak Version: The rate of hedonic

adaptation is slower for larger innovations p g in lifetime utility. 2 Strong Version: Variation in the rate of

• 2. Strong Version: Variation in the rate of

hedonic adaptation accounts for most of the variance in cumulative elation when looking at different sizes of innovations to g lifetime utility.

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elation=b(win-lose)xαe-δt/x^β x=eγ poorcash

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Gain Loss Asymmetry Gain-Loss Asymmetry

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Follow Up Study Follow Up Study

The main goal of this study was to test the extent to which a The main goal of this study was to test the extent to which a person's happiness is influenced by winning and losing small amounts

• f money and the rate at which subjects’ happiness adapts.

Participants in our experiment were sent text messages six times a day for six weeks asking them to rate their happiness on a scale from 0 to 100 (excluding multiples of 5). They were asked to visit th l b f t i t d d i th i t th the lab for a separate experiment, and during the experiment, they flipped a coin and could either win or lose a small amount of money (they believed this to be unrelated to the texting experiment). Before the coin flip participants were randomly assigned the amount of money the coin flip, participants were randomly assigned the amount of money they could win from the coin flip: $125, $25, $5, or $1. Changes in happiness following the coin flip were tracked g pp g p through the subjects’ response to text messages.

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Aggregating Local Preferences t G id P li to Guide Policy

Daniel J. Benjamin (Cornell and USC) Gabriel Carroll (Stanford) Ori Heffetz (Cornell) Miles S Kimball (Michigan) Miles S. Kimball (Michigan) ASSA/ESA Meeting – Political Engineering ASSA/ESA Meeting Political Engineering 4 January 2015

Our Motivation

Axiomatics to Generalize the NGA Mechanism

• 1. Ordinality: Multiplying the reported

gradient by a constant has no affect on g y the outcome of the mechanism. 2 Responsiveness: With any other shift in

• 2. Responsiveness: With any other shift in

an individual’s reported gradient, the ’ f mechanism’s outcome shifts strictly in a direction preferred according to the new p g reported gradient. (Note: this makes it

• ptimal to report the true gradient, except
• ptimal to report the true gradient, except

in the neighborhood of one’s bliss point.)

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Axiomatics (continued) Axiomatics (continued)

• 3. Anonymity: permutational symmetry

across people p p

• 4. Smoothness: The outcome of the

mechanism is twice continuously mechanism is twice continuously differentiable.

118

5 Merging

• 5. Merging

119

Definition Definition

Autocratic Outcome = what the mechanism Autocratic Outcome what the mechanism does as a function of a set of preferences if everyone has those same preferences everyone has those same preferences

120

Axiomatics (continued) Axiomatics (continued)

• 6. Marginal Citizen Sovereignty: If the

preferences of a subset of individuals shift, p , then the change in the outcome of the mechanism is in the span of the autocratic mechanism is in the span of the autocratic

• utcomes of the “before” and “after”

preferences of the subset of individuals preferences of the subset of individuals whose preferences shift.

121

Axiomatics (continued) Axiomatics (continued)

122

Comments on Theorem 1 Comments on Theorem 1

• Additively separable
• As if each individual is choosing from set S

As if each individual is choosing from set S the contribution to the outcome that most advances that individual’s interests advances that individual s interests

• S is strictly convex and compact

123

124

Pareto Optimality as an Additional Axiom

125

What Pareto Optimality Requires for the Shape of S

Lemma 2: If a mechanism satisfies responsiveness, then the associated p , autocratic mechanism restricted to the unit sphere is invertible sphere is invertible. Lemma 3: Guaranteeing weak local Pareto f f

• ptimality for any set of individuals and any

preferences requires 0 int S. p q Lemma 5: S = -S

126

Definitions Definitions

• Mapping hyperplanes through the origin to

hyperplanes through the origin when going yp p g g g g from gradients to autocratic outcomes

• Mapping halfspaces to halfspaces when
• Mapping halfspaces to halfspaces when

going from gradients to autocratic

• utcomes

127

How Pareto Optimality Characterizes the Shape of S

128

Comments on the Characterization of S

• In 2 dimensions all this gives is symmetry:

In 2 dimensions, all this gives is symmetry: S = -S

• In 3 or more dimensions we don’t know yet

3 o

• e d

e s o s e do t

• yet

how restrictive this is. Certainly ellipsoids work work.

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Results for the Continuous-Time Iterated NGA Mechanism

• 1. Any stationary point is Pareto optimal.

2 A stationary point exists

• 2. A stationary point exists
• 3. At every moment, the differential equation

i di ti th t h iti moves in a direction that has a positive dot product with any Pareto improvement (it will typically also move in “redistributive” directions orthogonal to redistributive directions orthogonal to that Pareto improvement)

132

Issues Issues

• Cycles

– but none found after many simulations y

• Multiple stationary points

l ti l b t th d – relatively rare but the do occur – probably tend to favor the status quo on average, which is not necessarily a bad property for acceptance of the mechanism

• Even among ellipsoids, which ellipsoid is

chosen matters chosen matters

– equivalent to the choice of coordinates

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The Power of Pareto Optimality The Power of Pareto Optimality

• Despite these issues, the fact that it is robustly

constrained Pareto optimal given any parameterization of the feasible policy space is promising.

• Incentive compatibility constraints (such as

those that matter for tax policy) can be built into the structure of the policy space.

• Even though the mechanism can be

Even though the mechanism can be redistributive, it is consistent with cost-benefit analysis as long as the appropriate financing analysis as long as the appropriate financing mechanisms are built into the policy space.

135

136