Public Finance and Public Policy: Responsibilities and Lim itations - - PowerPoint PPT Presentation

Hillman 2009 Social justice Chapter 7 1

Public Finance and Public Policy: Responsibilities and Lim itations of Governm ent

Arye L. Hillm an Cam bridge University Press, 2 0 0 9 Second edition

Presentation notes, chapter 7 SOCIAL JUSTICE

Hillman 2009 Social justice Chapter 7 2

Topics 7.1 Social justice and insurance 7.2 Moral hazard 7.3 Social justice without government

Hillman 2009 Social justice Chapter 7 3

What is the justification for involuntary income transfers? If the transfers are justified, we face the further normative question: How much income should be transferred from one person to another? We set aside principal-agent problems We shall see that once again efficiency and social justice cannot be separated

Hillman 2009 Social justice Chapter 7 4

7 .1 SOCI AL JUSTI CE AND I NSURANCE

Insurance

A

y y   

yA is known average income The distribution of the random component of income  can take various forms The distribution of  determines the pre-tax income distribution in a society

Hillman 2009 Social justice Chapter 7 5

A simple case:

H A H

y y    

.

0.

L A L

y y    

0.5

H L

probability probability    

H L

   

.

   

2 2

A A H L H L A

y y y y Ey y         

People know Ey=yA They do not know if they will have yH or yL

Hillman 2009 Social justice Chapter 7 6

Random income We shall consider two cases of uncertain income H and L are exogenous to personal actions, meaning that individuals’ ex-post incomes depend only on fate or luck H and L are endogenous to personal actions, meaning that individuals influence whether they experience a good

• r adverse outcome (moral hazard)
• μL

yH Ey=yA + μH Possible ex-post

• utcomes of low

and high income yL

Hillman 2009 Social justice Chapter 7 7

• A. Uncertain incom es and the dem and for insurance

We now view the source of all variability in income as luck A veil of ignorance The veil of ignorance is a metaphor for conditions under which people know nothing about their future selves. The metaphor of the veil of ignorance is counter-factual, because people in fact do know who they are and have information about their income prospects We view people behind a veil of ignorance as knowing the income distribution in the society into which they will be born

Hillman 2009 Social justice Chapter 7 8

Risk aversion and insurance People are usually risk-averse Risk-aversion through willingness to accept a fair gamble Risk-aversion through marginal utility of income For risk-averse people, the marginal utility of income is declining

Hillman 2009 Social justice Chapter 7 9

Expected utility and the fair gamble

Risk aversion and insurance

Certainty-equivalent income The income yC is the certainty-equivalent income for the fair gamble that gives expected income Ey and expected utility EU.

U(yH) Income O Utility U(Ey) EU U(yL) yL yC Ey=yA yH U(y) After paying ρ, the individual is indifferent between the fair gamble and receiving the income yC with certainty Declining MU of income indicates risk aversion in the common utility function of all people behind the veil of ignorance

Hillman 2009 Social justice Chapter 7 10

The amount that the individual is prepared to pay to avoid the fair gamble is maximally

c

Ey y    

The positive value of ρ confirms risk aversion The fair gamble is a gamble about ex-post inequality “How much are you prepared to pay to personally avoid ex-post inequality?” The answer is ρ

Hillman 2009 Social justice Chapter 7 11

Insurance markets Complete insurance completely compensates for adverse outcomes

• The insurance company receives a payment on

average of yA= Ey from each person

• The insurance company pays out yC per person
• The profit of the insurance company is ρ =(Ey – yC)

per person

• Profit is assured by the law of large numbers
• The profits of the insurance company depend on risk

aversion: ρ=0 gives no profits

Hillman 2009 Social justice Chapter 7 12

The gain from competitive insurance markets When competition in the insurance market eliminates above-competitive profits, ρ is the personal gain from insurance for insured individuals Mutual risk sharing contracts Agreement to share risk would duplicate the outcome of a competitive insurance market

Hillman 2009 Social justice Chapter 7 13

Efficiency and social justice through insurance

• The

voluntary pooling

• f

risk either through competitive insurance markets or mutual risk- sharing contracts is efficient

• Pareto-improvement takes place
• All people gain ρ from the risk sharing

With social justice defined as ex-post equality, competitive insurance markets efficiently solve the problem of ensuring social justice

Hillman 2009 Social justice Chapter 7 14

Social insurance

• There are no insurance markets behind the veil of

ignorance

• People seek insurance because of uncertainty or risk:

when people know who they are, they no longer want insurance

• Therefore we ask the government to provide social

insurance by acting as if the insurance market for income had existed behind a veil of ignorance

Hillman 2009 Social justice Chapter 7 15

Insurance through government is social insurance because everyone in society is included in the social insurance contract and participation is compulsory. Through the legal monopoly on coercion, governments can ensure that the people who experienced the good outcome H pay taxes to finance income transfers to people who experienced the unfortunate outcome L

Hillman 2009 Social justice Chapter 7 16

• B. Social w elfare functions and social insurance

contracts A social welfare function A social welfare function includes judgments about the distribution of benefits and costs among the people in a population With n people in a society

1 2 3

( , , ,....., )

n

W f U U U U 

Hillman 2009 Social justice Chapter 7 17

Pareto-improvement and social welfare Social welfare contours and anonymity

Pareto improvement increases social welfare

0, 1,..., .

i i

W i n U      

Social welfare can increase without Pareto improvement Anonymity

1 2 3 4 W W1 W2 U2 O U1 1 2 3 U2 O U1

45 450

Hillman 2009 Social justice Chapter 7 18

Interpersonal comparisons of utility We are making interpersonal comparisons of utility A common utility function provides a cardinal measure of utility

Hillman 2009 Social justice Chapter 7 19

Distribution of pre-determined income

1 2

Y y y  

.

1 1 1 2 2

( ), ( ) U U y U U y  

Distribution of pre- determined income Distribution with non- identical utilities

E

45o

S V U1 U2 O H

45

• S

V E F W0 W1 W2 W U1 U2 O

Hillman 2009 Social justice Chapter 7 20

Ex-post equality at E

• maximizes social welfare
• is also the outcome of private insurance markets

Private insurance is voluntary Redistribution through government (from F to E) The compulsory taxes of government introduce an excess burden of taxation If income transfers are financed by government borrowing, the taxes and excess burdens are in the future

Hillman 2009 Social justice Chapter 7 21

The efficiency losses of redistribution (the leaky bucket)

The leaky bucket of redistribution and the taxpayer The transfer recipient and the leaky bucket of redistribution

• People personally bear efficiency losses of the leaky bucket
• They take into account the efficiency losses when, behind

a veil of ignorance, they choose redistribution

O Z J

V

L22 L2 SL2 w2 w2(1 + s) Hours worked Wage O C D B L11 L1 SL w1 w1(1 – t) Hours worked Wage

Hillman 2009 Social justice Chapter 7 22

The leaky bucket defines feasible redistribution People are anonymous behind the veil of ignorance but we can label two people as person 1 and person 2

Incomplete insurance at points 1 or 2 with a leaky bucket of redistribution

45o S V E A 1 2 F1 F2 W0 W1 W2

W

U1 U2 O

Hillman 2009 Social justice Chapter 7 23

• C. Choice of social insurance behind a veil of

ignorance Maximizing a social welfare function behind the veil of ignorance implies choosing a social insurance contract to be implemented when people will have emerged from behind the veil of ignorance Two cases of social welfare and social insurance:  Jeremy Bentham  John Rawls

Hillman 2009 Social justice Chapter 7 24

Jeremy Bentham (1748–1832): “the greatest good for the greatest number.”

1 n i i

W U





. For two people

1 2

W U U  

.

Bentham’s social welfare function The Bentham incomplete social insurance contract

45 450 45 450 U1 U2 W1 W2 O

45 450

1 A

F1

F2 W0 W1 2 U1 U2 O

Hillman 2009 Social justice Chapter 7 25

John Rawls (1921–2002) and the weakest link

 

W max min U 

Rawls’ measure of social welfare Complete insurance with Rawls’ social insurance contract

The Rawls objective is not equality but maximization of the utility of the worst-off person

4 5 0 S

V

E A F1 F2 W0 W1 W2 U1 U2 O O 2 4 5 0 W1 W2 1 3 U1 U2

Hillman 2009 Social justice Chapter 7 26

Bentham and Rawls as limiting cases

Limiting cases of social welfare and social insurance contracts The slope of a social welfare contour expresses relative social weights

Bentham and Rawls are limiting cases of aversion to inequality

Bentham Rawls General symmetric social welfare function O U1 U2 45o

450 450 H B A D U2

U1 O

Hillman 2009 Social justice Chapter 7 27

With no leaky bucket, Bentham and Rawls provide complete insurance An extremely leaky bucket: Rawls continues to provide social insurance but Bentham provides no social insurance

With no leaks in the bucket of redistribution, aversion to inequality does not affect social insurance Any symmetric social welfare function provides complete insurance and ex-post equality

A Rawls

45o

F1 F2 B U1 U2 O Bentham 4 5 o F1 F2 E U1 U2 O Bentham Rawls

Hillman 2009 Social justice Chapter 7 28

The reason for different social insurance provided by different social welfare functions is different sensitivities to the efficiency costs of redistribution through the leaky bucket Bentham is the most sensitive to efficiency costs of redistribution through the leaky bucket Rawls is not sensitive to efficiency losses at all as long as the worst-off person is not harmed

Hillman 2009 Social justice Chapter 7 29

The Laffer curve and income redistribution The Laffer curve limits the amount of tax revenue that is available for redistribution of income

The Laffer curve as a constraint on redistribution Social insurance with a revenue constraint

tM Tax revenue R Tax rate t

O

Max R at point G1 or G2 Both the taxpayer and the transfer recipient lose when the tax rate exceeds tM. G1 4 5 0 S

V

E A F1 F2 W0 W1 W2 U1 U2 O B2 B1 Bentham Rawls G2

Hillman 2009 Social justice Chapter 7 30

The Laffer curve can prevent complete insurance when Rawls is chosen Bentham social insurance is never hindered by the revenue constraint of the Laffer curve

Hillman 2009 Social justice Chapter 7 31

The choice of the social insurance contract Behind the veil of ignorance, will people choose Bentham or Rawls? The case for choosing Bentham Rational behavior under uncertainty is maximization of expected utility Expected utility is defined by giving weights to different

• utcomes equal to the objective probabilities of the

different outcomes arising

Hillman 2009 Social justice Chapter 7 32

n people behind a veil of ignorance know that

H L

n n n  

After the Bentham social insurance contract has been implemented through taxation and income transfers

H L

U U 

H H L L

W n U n U  

H H

n p probability of having highincome n  

L L

n p probability of having lowincome n  

.

H H L L

W p U p U EU n   

Hillman 2009 Social justice Chapter 7 33

Choice of a Bentham social welfare function behind the veil of ignorance is rational in maximizing expected utility Rawls gives positive weight in social welfare to whoever will be the worst-off person and gives zero weight to everybody else Bentham rationally accounts for the likelihood that, after emerging from behind the veil of ignorance, an individual will not be the worst-off person

Hillman 2009 Social justice Chapter 7 34

Bentham’s lottery and Rawls’ certainty in life Bentham offers a lottery through incomplete insurance Rawls offers certainty in life after people emerge from behind the veil of ignorance and discover who they are

• We cannot compare levels of social welfare measured

by the different Bentham and Rawls social welfare functions

• We can use a common utility function to compare

personal utility

Hillman 2009 Social justice Chapter 7 35

Possible social insurance contracts when the Laffer curve does not restrain income redistribution

The trade-off between ex-post equality and efficiency Choice of the social insurance contract through choice

• f a social welfare function is a choice between greater

ex-post equality and greater efficiency

C The Bentham lottery UH for person 1 UL for person 2 4 5 o S V B A F1 F2 B2 B1 UC U1 U2 O UC C2 C1 EU EU The Bentham lottery UH for person 2 UL for person 1 Rawls’ certain

• utcome in life

at A if the Laffer curve allows The intermediate social welfare function gives a lottery with

• utcomes at C1 or C2

and average utility at C

Hillman 2009 Social justice Chapter 7 36

A society may decide not to accept Bentham’s lottery and the associated ex-post inequality Political parties take positions on the trade-off between efficiency and ex-post equality – that is, on the spectrum between Bentham and Rawls

Hillman 2009 Social justice Chapter 7 37

A general representation for choice of social welfare functions between Bentham and Rawls:

L L H H

W p U p U   

Social welfare functions obtained by varying 

A O

45o

U1 U2 Bentham  =1 Intermediate 0 < <1 Below the 45o line, person 2 has high utility and person 1 has low utility Above the 45o line, person 1 has high utility and person 2 has low utility C1 C2 Rawls  = 0 B1 B2 C B As  decreases, UL after taxation and redistribution increases As  decreases, UH after taxation and redistribution declines In the Rawls outcome at A, there is no difference between UH and UL after taxation and redistribution

Hillman 2009 Social justice Chapter 7 38

Choosing a social welfare function with α <1 is a decision to subjectively increase the weight on experiencing a bad outcome and correspondingly a decision to discount subjectively the likelihood of experiencing a good outcome In the limiting case of Rawls where α = 0, the likelihood

• f a good outcome is altogether ignored

Hillman 2009 Social justice Chapter 7 39

W hy deviate from the objective probabilities of Bentham ? The reason for deviating from Bentham cannot be risk- aversion with respect to income because the utility function is the same in either case

Hillman 2009 Social justice Chapter 7 40

Prospect theory Daniel Kahneman and Amos Tversky (1937-1996) in 1979 defined “prospect theory”, from behavior in experiments People subjectively evaluate personal gains and losses from a specified reference point or status quo An implication of prospect theory is behavior that exhibits loss aversion

• People place larger than objectively justified

weights on low-probability events that would bring large losses

• This results in  < 1

Prospect theory was inferred by psychologists from

• bserved human behavior

Hillman 2009 Social justice Chapter 7 41

Regret Departure from Bentham can be explained by the wish to avoid regret If the outcome is L, there is regret that Rawls was not chosen Choosing Rawls minimizes regret from experiencing an adverse outcome. Maximize “happiness” rather than utility from consumption

• r material wealth

Regret affects happiness, including regret that Bentham was chosen

Hillman 2009 Social justice Chapter 7 42

How does a work ethic affect social insurance? There are no leaks in the bucket of redistribution, if all people have work ethic: When a work ethic is present, people work because of the intrinsic value of work and because of a feeling of disutility if they do not work In a society without a work ethic, the personal risk of experiencing an adverse outcome in Bentham’s lottery is balanced against the risk of having equal but perhaps no meaningful income under the complete insurance of Rawls

Hillman 2009 Social justice Chapter 7 43

A welfare state

• The objective of the welfare state is, in principle,

complete insurance

• Why have voters in high-income welfare states

persistently supported the high taxes and extensive income redistribution that approach Rawls-type social insurance?

• High personal incomes have been sustained: A work

ethic has been present

• With a work ethic, unfortunate people attempt to be

self-reliant but have been unlucky

• There is no resistance by taxpayers to paying high

taxes to finance redistribution to people who have been unlucky

Hillman 2009 Social justice Chapter 7 44

The foundations for a work ethic Max Weber (1864-1920) studied how religion has influenced economic behavior The Protestant Ethic and the Spirit of Capitalism (1905) Bentham and a work ethic A Bentham social welfare function would call for extensive social insurance, if leaks in the bucket of redistribution are small Bentham and the rule of law Maximization

• f

Bentham summation

• f

utilities is restrained by the rule of law

Hillman 2009 Social justice Chapter 7 45

• D. Adverse selection and tim e inconsistency

After emerging from behind the veil of ignorance, people will know whether they have experienced H or L

• There is asymmetric information
• There is no uncertainty
• There is no demand for insurance

Asymmetric information and adverse selection Adverse selection occurs when low-risk people leave an insurance pool

Hillman 2009 Social justice Chapter 7 46

Resolving the adverse-selection problem through different contracts

• Low risk people with good prospects in life want

insurance only within a group of their own “type”

• A contract with a low insurance premium and low

payout will be accepted by low-risk types

• A contract with a high insurance premium and high

payout will be accepted by high-risk types

• The two types of individuals identify themselves

through the type of insurance contract they choose

• Both types of persons gain from pooling risk in the

separate insurance pools

• The asymmetric information problem is resolved and

voluntary insurance is possible with no adverse selection

Hillman 2009 Social justice Chapter 7 47

Should the government offer separate insurance contracts? Compulsory social insurance is not insurance but systematic subsidization of high-risk people by low-risk people The case for enforcement by government of a single insurance pool is based on a time-inconsistency problem A time-inconsistency problem arises when optimal present decisions about future behavior are no longer

• ptimal when the future arrives

In enforcing compliance with the social insurance contract, governments respond to a time-inconsistency problem and avoid adverse selection

Hillman 2009 Social justice Chapter 7 48

7 .2 MORAL HAZARD

• So far only pure luck has determined personal
• utcomes through H and L
• We now recognize that personal outcomes depend on

a person’s effort at self-reliance

• H and L become endogenous consequences of

personal decisions

• Personal incentives to be self-reliant introduce moral

hazard

Hillman 2009 Social justice Chapter 7 49

• A. Moral hazard and insurance

Moral hazard occurs when the presence of insurance affects personal decisions in ways that make payouts from insurance more likely The hazard is moral, because people exploit the presence

• f insurance

Hillman 2009 Social justice Chapter 7 50

Moral hazard and personal effort Moral hazard introduces personal effort as a personal decision variable

H L

e high effort toavoid thebad outcome  .

L L

e low effort toavoid thebad outcome 

1 1

( , ) ( , )

H L

U y e U y e 

Hillman 2009 Social justice Chapter 7 51

Two types of effort decisions

• Taxpayers reduce work effort in response to taxes by

substituting leisure or free time for work: the leaky bucket of redistribution

• There is no uncertainty when taxpayers make this effort

decision: taxpayers know that they are taxpayers For prospective recipients of income transfers:

• Effort decisions affect the likelihood being self-reliant
• This decision about effort to be self-reliant is made under

conditions of uncertainty about future personal income

Hillman 2009 Social justice Chapter 7 52

Voluntary insurance

• Voluntary insurance does not involve payment of

taxes and so does not affect work effort of taxpayers

• The effect of voluntary insurance is on effort to be

self-reliant through moral hazard Asymmetric information

• Moral hazard involves asymmetric information
• People have private information about whether they

have chosen high or low effort to avoid adverse

• utcomes
• Others (including a private insurance company or the

government) can observe an outcome yH or yL but cannot observe whether a person chose eH or eL

Hillman 2009 Social justice Chapter 7 53

Effort and luck

Pr( | ) Pr( | ) 1, ,

H i L i

e e i H L      Pr( | ) Pr( | )

H H H L

e e    Pr( | ) Pr( | )

L L L H

e e   

Whether a person has high or low income depends on both luck and effort Because of asymmetric information, whether low income is due solely to bad luck or also to low effort is not known to other people

Hillman 2009 Social justice Chapter 7 54

The prisoners’ dilemma and moral hazard in a voluntary insurance contract

• We consider income transfers made in accord with a

voluntarily agreed contract

• There is no taxation and no excess burden of

taxation

• Government is present only to provide the legal

framework for the voluntary insurance contract

Hillman 2009 Social justice Chapter 7 55

With incomes shared through the insurance contract, personal outcomes for incomes are:

• When both people choose high effort eH, the likelihood

is maximized that, after income sharing, each person will have high income yH

• When both people choose low effort eL, the likelihood is

maximized that, after income sharing, each person will have low income yL

• If one person chooses high effort eH and the other

chooses low effort eL, the likelihood is maximized that the two people will share (yH + yL) and have

2

H L H A L

y y y y y    

Although personal incomes are shared through insurance, the cost of exerting high effort is personal and is not shared

Hillman 2009 Social justice Chapter 7 56

The sharing of incomes and the personal cost of effort give rise to a prisoners’ dilemma The prisoners’ dilemma and moral hazard

Person 2 chooses high Effort Person 2 chooses low effort Person 1 chooses high effort 3,3 1,4 Person 1 chooses low effort 4,1 2,2

In the Nash equilibrium with moral hazard, the likelihood is maximized that everyone will have low income People “free ride” by choosing low effort

Hillman 2009 Social justice Chapter 7 57

The common-pool problem (as in the tragedy of the commons) Earned income is a common pool When n people share a common pool of income:

1 n i a i

y y n



 

2 1 n i a i

y y y n n



             



Person 1 keeps y1/n of own-earned income

Hillman 2009 Social justice Chapter 7 58

Self-deprivation and moral hazard The Nash equilibrium of prisoners’ dilemma has resulted in self-deprivation People choose to place themselves in personal circumstances where there is a high likelihood of personally earning low income

Hillman 2009 Social justice Chapter 7 59

Moral hazard and the failure of voluntary insurance

• With participation in an insurance contract voluntary,

exit from the contract ends the common pool problem

• f pooling and sharing of incomes
• Without pooling of incomes, there is high EU from

exerting personal effort because high income does not have to be shared

• Everyone is better off without the disincentives of the

common pool problem of shared incomes and without moral hazard

• In terms of the tragedy of the commons, incomes are

privatized Moral hazard results in the failure of voluntary insurance

Hillman 2009 Social justice Chapter 7 60

• B. Behavior w ithout m oral hazard

When is there no moral hazard problem? No random component of income

• Effort alone determines personal income
• Information about effort is no longer asymmetric
• There is no role for insurance because there is no

uncertainty about why income is low There is no asymmetric information and no moral-hazard problem if personal effort choices are observable

• The insurance contract specifies the necessity of having

been observed to have chosen high effort to receive payouts from insurance if there is low income

Hillman 2009 Social justice Chapter 7 61

How does a society maintain insurance in the face of the moral-hazard prisoners’ dilemma? Moral hazard and a work ethic A person who behaves according to a work ethic systematically chooses high effort to be reliant even though insurance is available when income is low There is no moral hazard and no prisoners’ dilemma when all people have a work ethic Everyone chooses high effort, notwithstanding the pooling

• f incomes through insurance

Hillman 2009 Social justice Chapter 7 62

• C. Moral hazard and adverse selection in diverse

populations What happens when populations are diverse and are composed of both people with a work ethic and people subject to moral hazard? Because of asymmetric information about choice of effort at self-reliance, unlucky people who exerted effort to be self-reliant are indistinguishable from people who did not attempt to be self-reliant  People subject to moral hazard choose low effort to be self-reliant when insurance is available  People with a work ethic choose high effort to be self- reliant whether or not there is insurance

Hillman 2009 Social justice Chapter 7 63

Two norms of behavior in a population

Person 2 has no work ethic and chooses high effort Person 2 has no work ethic and chooses low effort Person 1 with a work ethic chooses high effort 4,3 3,4 Person 1 with a work ethic chooses low effort 1,1 2,2

• The dominant strategy of person 1 with a work ethic

is to choose high effort

• Person 2’s best response to person 1’s choice of high

effort is to choose low effort

• The Nash equilibrium is at (3, 4)

Hillman 2009 Social justice Chapter 7 64

In a diverse population, people with a work ethic systematically subsidize people whose behavior is subject to moral hazard The objective of self-reliance of person 1 with a work ethic allows person 2 to maximize utility by choosing not to be self-reliant

Hillman 2009 Social justice Chapter 7 65

Sources of different norms regarding a work ethic

• A work ethic may be expressive and confirmation of

self-identity

• Some people feel uncomfortable or personally

inadequate if they were to take advantage of insurance as a source of income

• A work ethic may also be due to stigma – family and

peers may be able to observe a person’s effort decision

• Individual ability and human capital affect whether a

work ethic is present

• High human capital (or being educated) is the

consequence of a work ethic, applied to studying

• Is the work ethic related to religion (Max Weber)?

Hillman 2009 Social justice Chapter 7 66

How do societies that begin with a work ethic come to have diverse social norms? (1) Change in norms from within The model of the family (2) Change in norms from outside

• There is adverse selection when people without a work

ethic locate in a welfare state

• Local residents may view immigrants as victims of

exogenous bad luck

• If sufficient immigrants do not integrate into self-reliant

economic activity, the social insurance contract of the host welfare state may become unsustainable

Hillman 2009 Social justice Chapter 7 67

Why do the self-selected immigrants who choose location in a welfare state not have a work ethic? In immigrants’ home countries:

• Personal property rights were not protected (a

Nietzschean society)

• There was a personal danger from having a work

ethic (rulers feared that accumulated private wealth will be used to challenge their control)

• The ruler may distribute charity, to preempt or to

quell unpopularity and unrest The western welfare state replaces the ruler

Hillman 2009 Social justice Chapter 7 68

Adverse selection through emigration Adverse selection occurs when taxpayers leave the welfare state Slavery and a work ethic A work ethic cannot be present under slavery Common property and a work ethic A work ethic is not rewarded when because private property and personal wealth cannot be accumulated Discrimination and a work ethic Adverse discrimination diminishes the motivation to look for work

Hillman 2009 Social justice Chapter 7 69

Presumption and incentives

• There may be a presumption that people do not have

a work ethic because they have been observed not to be self-reliant – and because they are supported by income transfers from the government

• When the income transfers cease, people look for

and find work and become self-reliant Changes in incentives bring us to public policy responses to moral hazard

Hillman 2009 Social justice Chapter 7 70

• D. Public policy responses to m oral hazard

Savings as voluntary self-insurance The optimal personal response to income uncertainty is not saving but risk pooling through voluntary insurance If adverse selection and moral hazard prevent voluntary insurance, saving as self-insurance is the sole voluntary means of protection against adverse personal future

• utcomes

Hillman 2009 Social justice Chapter 7 71

Objective verification: A third case of asymmetric information Moral hazard and adverse selection are two reasons why markets for voluntary insurance fail due to asymmetric information There is third source of asymmetric information that results in failure of voluntary insurance markets Voluntary insurance requires means of objective verification of outcomes against which insurance is sought

Hillman 2009 Social justice Chapter 7 72

The failure of voluntary insurance

• If the insurance contract and income pooling are

voluntary, people with a work ethic can simply exit the insurance pool

• If all people with a work ethic leave the insurance

pool, the people subject to moral hazard who behave strategically in choosing low effort have no one from whom to systematically receive income transfers

• The circumstances revert to the symmetric prisoners’

dilemma where the behavior of everyone in the insurance pool is subject to moral hazard

• Everybody then leaves the insurance pool because of

moral hazard

Hillman 2009 Social justice Chapter 7 73

Voluntary insurance has failed, first because of adverse selection and then because of moral hazard If there is to be insurance, the insurance needs to be provided by government as compulsory social insurance from which people cannot exit

Hillman 2009 Social justice Chapter 7 74

Social insurance when there is moral hazard The moral-hazard problem is solved through incomplete insurance that makes earning high pre-tax income and being a taxpayer preferable to earning low income and receiving an income transfer The moral-hazard problem is solved if

( , ) Pr( | ) ( ) Pr( | ) ( ) ( , ) Pr( | ) ( ) Pr( | ) ( ).

H H H H L H L L H L H L L L

EU y e e U y tax e U y incometransfer EU y e e U y tax e U y incometransfer             

Hillman 2009 Social justice Chapter 7 75

Solving the moral hazard problem also solves the adverse selection problem If incomplete insurance has made choosing high effort everyone’s best choice, no one has an incentive to leave the insurance pool With incomplete insurance providing incentives for everyone to choose high effort, any person observed to have low income has been genuinely unlucky and so is a victim of fate who deserves help

Hillman 2009 Social justice Chapter 7 76

Impediments to helping people who deserve help

• Incomplete insurance limits the assistance that is

given to people who experience bad outcomes

• A society may want to help such people more,

because they exerted high effort to be self-reliant but were unlucky

• If help could be given as a surprise after a person

has experienced an adverse personal outcome, there would be no moral hazard

• There is a repeated game

Moral hazard is re-introduced when people take advantage of asymmetric information to choose low effort in response to the high social insurance benefits – which are no longer a surprise

Hillman 2009 Social justice Chapter 7 77

The social dilemma of resolving the moral-hazard problem

• Non-generous

income transfers

• f

incomplete insurance eliminate moral hazard

• Because of the non-generous income transfers for

people who experience bad outcomes, everyone chooses high effort

• However,

some people nonetheless experience random unfortunate outcomes through no fault of their own

• High income transfers to the people who experienced

the genuinely random unfortunate outcomes cannot be made without reintroducing moral hazard

Hillman 2009 Social justice Chapter 7 78

The two cases for incomplete insurance We now have two cases for incomplete social insurance (1) Behind a veil of ignorance where people have no information about their future selves (2) Moral hazard when, after emergence from behind the veil of ignorance, information is asymmetric, because people have private information about whether they have chosen high or low effort to be self reliant How incomplete should social insurance be, when the no- information and asymmetric-information cases for incomplete insurance are combined?

Hillman 2009 Social justice Chapter 7 79

Type-1 and type-2 errors and political sensitivities Incomplete insurance introduces two types of errors A type-1 error People in genuine need through no fault of their own are insufficiently helped by social insurance. A type-2 error People who could be self-reliant choose low effort at self-reliance and benefit from the income transfers of social insurance.

Hillman 2009 Social justice Chapter 7 80

Sensitivity to type-1 errors can expand insurance beyond Bentham’s incomplete insurance Sensitivity to type-2 errors can make choice of social insurance more incomplete than Bentham.

• The left is less willing to make a type-1 error
• The right may be less willing to make a type-2 error

Hillman 2009 Social justice Chapter 7 81

Disagreement over whether type-2 errors exist We have viewed luck and effort at self-reliance as separate influences on a person’s income. Could effort at self- reliance also be consequence of luck? Do people choose low effort at self-reliance or do they have no choice The left:

• Through unequal opportunities in life, people with low

incomes are victims of fate and unfairness The right:

• Low incomes in the presence of insurance are the

consequence of moral hazard.

• Overly generous social insurance creates low incomes

through moral hazard

Hillman 2009 Social justice Chapter 7 82

7 .3 SOCI AL JUSTI CE W I THOUT GOVERNMENT

Can social justice be achieved without government?

• A. Altruism and charity
• Altruistic income transfers are voluntary
• There are no efficiency losses because of leaks in the

bucket of redistribution

• Altruism and charity do not eliminate moral hazard

Hillman 2009 Social justice Chapter 7 83

Adam Smith on altruism Adam Smith in his book Theory of Moral Sentiments (1759) observed that human nature led people to be altruistically concerned about the well-being of others: However selfish soever man may be supposed, there are evidently some principles in his nature, which interest him in the fortune of others, and render their happiness necessary to him, though he derives nothing from it, except the pleasure of seeing it

Hillman 2009 Social justice Chapter 7 84

Interdependent utilities

1 2

Y y y  

1 1 1 2 2 2 2 1

( , ), ( , ) U U y y U U y y  

1 2 2 1

0, U U y y      

Interdependent utilities and Pareto-improving voluntary income transfers

4 5 0 A E D C B max U1 max U2 U1 U2 O

Hillman 2009 Social justice Chapter 7 85

A three-person society

1 1 1 3 2 2 2 3

( , ), ( , ) U U y y U U y y  

3 3 3

( ) U U y 

The income of the unfortunate person y3 has the characteristics of a public good

Hillman 2009 Social justice Chapter 7 86

The prisoners’ dilemma of private income transfers when each person prefers that the other give

Person 2 gives Person 2 does not give Person 1 gives 3,3 1,4 Person 1 does not give 4,1 2,2

Hillman 2009 Social justice Chapter 7 87

Public policy because of the prisoners’ dilemma: taxation and publicly financed income transfers Asymmetric information:

• When

preferences

• f

donors differ, there is asymmetric information

• A government can only take a best guess about the

taxes to levy on the two donors to finance an income transfer

Hillman 2009 Social justice Chapter 7 88

Expressive voting for voluntary redistribution Through expressive voting, people derive utility from confirmation of identity It may be sufficient to vote in favor of income transfers to

• btain the benefit of utility from feeling generous

Hillman 2009 Social justice Chapter 7 89

A two-person example U(voting for transfers)=1 U(paying for transfers)=-2 U(if veto)=0

Person 2 votes against income transfers Person 2 votes in favor of income transfers Person 1 votes against income transfers 0,0 0,1 Person 1 votes in favor of income transfers 1,0

• 1, -1

Nash equilibria in pure strategies are (1, 0) and (0, 1) Nash equilibrium in mixed strategies: 0.5 for either

Hillman 2009 Social justice Chapter 7 90

Sequential decisions

• The first person votes in favor
• The second person vetoes
• A person who can credibly commit to vote in favor of

the incomes transfers gains from expressive voting Large numbers of voters

• Voters know that their vote will not be decisive under

majority voting

• They take the positive utility that is available from

voting expressively in favor of the income transfers

• The income transfers take place if a majority votes

expressively (or genuinely) in favor

• Each voter would veto the income transfers if he or

she could Expressive voting favors voluntary decisions by donors to provide income transfers

Hillman 2009 Social justice Chapter 7 91

Pleasure from giving Charity when the act of giving increases utility and highest utility is achieved by being the sole donor Person 2 gives Person 2 does not give Person 1 gives 8, 8 10, 5 Person 1 does not give 5, 10 0, 0 The dominant strategy is to give

Hillman 2009 Social justice Chapter 7 92

Charity when the act of giving increases utility and highest utility is obtained by giving together with others Person 2 gives Person 2 does not give Person 1 gives 10, 10 8, 5 Person 1 does not give 5, 8 0, 0

Hillman 2009 Social justice Chapter 7 93

Exploitation of charitable intentions We have been considering interactions among donors We now consider the interaction between a donor and a beneficiary of income transfers who does not have a work ethic There is no moral hazard because there is no asymmetric information: the donor can observe whether the recipient is making an effort to be self-reliant

Hillman 2009 Social justice Chapter 7 94

The exploitation of charitable feelings The recipient (person 2) exerts effort to be self-reliant The recipient (person 2) does not exert effort to be self-reliant The donor (person 1) does not give 2, 2 1, 1 The donor (person 1) gives 4, 3 3, 4 The Nash equilibrium is (3, 4) The donor is unhappy with the outcome What can the donor do?

Hillman 2009 Social justice Chapter 7 95

Misrepresented preferences by the donor The recipient exerts effort to be self- reliant The recipient does not exert effort to be self-reliant The donor does not give 2, 2 4, 1 The donor gives 3, 3 1, 4

• No dominant strategy for donor or the recipient and no

Nash equilibrium in pure strategies

• The recipient does not want to die of starvation and

recipient adopts a maxi-min strategy (makes the decision that results in the least potential self-harm)

• The outcome is at (3, 3)

Hillman 2009 Social justice Chapter 7 96

• Based on the donor’s true preferences, this is the
• utcome that the donor wants

Is the donor’s claim of willingness to allow the donor to starve to death credible? Rules and not discretion The role of a government bureaucracy that follows rules, not discretion

Hillman 2009 Social justice Chapter 7 97

Degrees of charity Maimonides (1135-1204) also known as the Rambam distinguished 8 levels of charity Social status

• Thorstein Veblen (1857-1929), in The Theory of the

Leisure Class (1899), described conspicuous consumption

• Conspicuous giving to charity displays wealth
• The contest for status is similar to a rent-seeking

contest: status is achieved relative to the status of

• thers
• There is a prisoners’ dilemma similar to the rent-

seeking prisoners’ dilemma

• The contest for status has social benefits when status

is achieved by visible charitable activities

Hillman 2009 Social justice Chapter 7 98

Other questions

• Can the quest for social status also be an impediment to

voluntary charitable transfers?

• Does public assistance decrease the incentive to give

private charity?

• Are declarations of intent of charitable expressive?
• The amount of private charity depends on how many

people are prepared to actually give, rather than expressively declaring that “something should be done to help the needy”

• Does the behavior of the some beneficiaries of private

charity affect overall willingness to give?

• People are unwilling to give if they perceive moral

hazard

Hillman 2009 Social justice Chapter 7 99

7 .3 B. Experim ental evidence on norm s of fairness The ultimatum game Outcomes of the ultimatum game indicate how conceptions

• f fairness influence behavior in a society

In general, donors propose that they keep 60 percent and

• ffer 40 percent to the recipient

Hillman 2009 Social justice Chapter 7 100

Outcomes of the ultimatum game in different locations

USA Japan Israel Indonesia Amaz. tribe Ca Penn Arizo na High sum Low sum Numbers (pairs) 15 27 24 29 30 37 94 21 Value $160 $10 $10 $10 $10 $80- 120 $10- 15 $160 Mean 0.48 0.45 0.44 0.45 0.36 0.44 0.44 0.26 Mode 0.50 0.50 0.50 0.50 0.50 0.50 0.40 0.15 Rate of rejection 0.22 0.08 0.24 0.33 0.08 0.19 0.04 8 Rejected if >20%

• ffered

0/0 0/1

• 2/4=

50% 5/7= 71% 0/0 9/15 = 60% 1/10 = 10%

• Standards of fairness as near-equal division are universal
• An interpretation: people chosen to be donors should

understand that luck could have gone the way

• We see the relation to the veil of ignorance

Hillman 2009 Social justice Chapter 7 101

The aberration: a tribe in Peruvian Amazon Generous offers

• In an experiment in China, a university student

rejected a generous offer because the person

• ffering the money was “using the mind of a petty

man to measure the heart of a gentleman”

• Chinese middle school students were concerned that

they were being offered money that they had done nothing to deserve

• The usual response among the students was to

divide the money equally because no one deserved the money and certainly no one deserved more money than anyone else

Hillman 2009 Social justice Chapter 7 102

The dictatorship game

• Less in general is given in dictatorship games than in

ultimatum games

• People are prepared to incur a personal cost in order

to punish perceived selfish behavior

• Sharing is consistent with cultural transmission from

a hunter-gatherer society

• Self-image and social approval
• Anonymous situations: there is less sharing when no
• ne, including the experimenter, observes their

behavior

• A collective decision by a group usually results in

more generous sharing than an individual decision

• People are less generous when they feel they have

earned the money rather having received as a gift

Hillman 2009 Social justice Chapter 7 103

Comparisons between the ultimatum and dictatorship games

• In the ultimatum game, people fear retribution
• In the dictatorship game, there is no fear of

retribution and donors give less to recipients

• In

dictatorship games, effort

• f

recipients is rewarded

• Not in ultimatum games

The role of social justice therefore changes between the two games

Hillman 2009 Social justice Chapter 7 104

Gender differences in ultimatum games

• Sometimes men offer more to women than to men
• Women also tend to offer more to women than men
• Other studies show that in ultimatum games both men

and women make lower offers when the recipient is known to be a woman

• Women are more inclined than men to take the money

that is offered, which is rational behavior

Hillman 2009 Social justice Chapter 7 105

Gender differences in dictatorship games

• The generosity of men depends more on how much

generosity costs (the loss or price of making the transfer)

• Women are more insensitive to loss or the price of

giving

• Men are more generous when the cost of giving or

efficiency loss is low

• Women are more generous when the cost of giving

(or efficiency loss) is high – because women tend to give independently of the price of giving Evidence on personal choice of social welfare functions

• More men maximized the sum of benefits and so

chose Bentham

• More women indicated a preference for ex-post

equality expressed in Rawls social welfare function

Hillman 2009 Social justice Chapter 7 106

• C. I ntergenerational econom ic m obility

High economic mobility in general requires equal

• pportunities for personal improvement – or ex-ante

equality. Social justice can be defined as high intergenerational economic mobility How do people fare in life relative to their parents?

Hillman 2009 Social justice Chapter 7 107

Estim ates of intergenerational econom ic m obility

child parent

Y a bY    

When incomes are in logarithms, the coefficient b is an elasticity If the variances of the distributions of Ychild and Yparent are equal, b is the correlation coefficient between children’s and parents’ incomes If b = 0, there is complete economic mobility If b = 1, there is complete social immobility

Hillman 2009 Social justice Chapter 7 108

If 0 < b < 1, there is regression to the mean in income inequality

• parents with high incomes do not necessarily have

children who will have high incomes

• parents with low incomes do not necessarily have

children who will have low incomes Francis Galton (1822 – 1911), who studied inherited human characteristics (Galton, 1889), predicted an equalizing process through regression to the mean of the population Studies for different countries suggest convergence of incomes to the mean over a small number of generations

Hillman 2009 Social justice Chapter 7 109

Comparisons of economic mobility fathers and sons, value of b U.K. 0.42, 0.57 U.S. 0.40 Canada 0.23 Sweden 0.13,0.14,0.28 Norway 0.155, 0.13 Germany 0.11, 0.34 Finland 0.13, 0.22

Hillman 2009 Social justice Chapter 7 110

Should economic mobility be maximized? To maximize economic mobility

• income consequences of inherited traits would have

to be neutralized

• inheritances would have to be taxed completely or all

wealth and income would need to be collectivized

Hillman 2009 Social justice Chapter 7 111

Characteristics other than income U.S. intergenerational economic characteristics (Mulligan 1999)

Economic characteristic Range of estimates Average Years of schooling 0.14–0.45 0.29 Earnings, wages 0.11–0.59 0.34 Family income 0.14–0.65 0.43 Family wealth 0.27–0.76 0.50 Family consumption 0.59–0.77 0.68

Hillman 2009 Social justice Chapter 7 112

Assortative mating Assortative mating occurs when there are systematic rather than random tendencies when males and females sort themselves into couples

• Tendencies for inequality arise, and reversion to the

mean does not take place

• Reversion to the mean is within subgroups of the

different sorted groups A ssortative mating decreases economic mobility Fertility Social immobility increases, if high-ability, high-income women have fewer children

Hillman 2009 Social justice Chapter 7 113

Economic mobility of women

• Women seemed to have shown lower economic

mobility than men

• Associative sorting is revealed in high correlations

between the husband’s income and the incomes of a woman’s father and the her husband’s father

• The time from which the data were taken matters

Hillman 2009 Social justice Chapter 7 114

Meritocracy in labor markets Economic mobility requires meritocracy in labor markets There is no point in investing in education and indeed being one of the most successful of students, if jobs are

• btained on the basis of privileged family connections

Social instability Economic mobility promotes social stability Economic mobility and social insurance Economic mobility does not end the demand for social insurance – because of different time dimensions

Hillman 2009 Social justice Chapter 7 115

Income distribution and economic mobility 2 people have incomes of 100 and 200 The children switch incomes There has been no change in income distribution but there has been perfect high economic mobility

• For economic mobility, it matters whose incomes

changed

• Income distribution is independent of the identities of

the people who have the different incomes High economic mobility does not necessarily imply a more equal income distribution

Hillman 2009 Social justice Chapter 7 116

If b<1, inequality declines and converges to a constant level Economic mobility is a means of achieving a more equal income distribution – without the need for taxation and public spending on income transfers

Hillman 2009 Social justice Chapter 7 117

• D. Global social justice

Social justice without government includes global social justice because there is no global government In some countries, the social insurance contract is non- existent A global insurance contract behind the veil of ignorance Behind the veil of ignorance we would want a global insurance contract that applies wherever we would be

Hillman 2009 Social justice Chapter 7 118

The World Bank and global insurance The World Bank, other international aid agencies, and governments provide aid to governments in poor countries

• Insurance in principle compensates for random

adverse events

• The foreign assistance provided because of adversity

has not been random

• Aid has been given systematically to the same

countries over the course of time

Hillman 2009 Social justice Chapter 7 119

Moral hazard The ineffectiveness of aid: Data shows conclusively that aid has been ineffective in promoting growth and economic development in poor countries The hostage problem: Governments in poor countries keep the poor in their countries poor so that aid will continue

Hillman 2009 Social justice Chapter 7 120

The dilemma of foreign aid

Government in the poor country helps the poor Government in the poor country does not help the poor Donor gives aid 4,1 3,4 Donor does not give aid 2,2 1,3

• The dominant strategy of the donor is to give
• The government of the poor country has a dominant

strategy of not helping the poor

• The Nash equilibrium is at (3, 4)
• The aid is given and is appropriated.

Hillman 2009 Social justice Chapter 7 121

Why does the donor persist in giving the aid, given that that the dominant strategy of the government is to not use aid resources to help the poor?

• The donor feels obligated to be a donor and to give
• The appropriation by the recipient government has

the form of a tax on helping the poor imposed on the donor

• The World Bank would be in a difficult position if

there were no one to try to help

• The aid is expressive

Hillman 2009 Social justice Chapter 7 122

Global government could in principle implement a global social insurance contract Is global government desirable? How would global government look?

• The United Nations is the closest institution to global

government

• Corruption

in many UN member countries is extensive and institutionalized

• Norms of personal behavior are retained when

government

• fficials

join the United Nations bureaucracy