Econ 551 Government Finance: Revenues Winter 2018faculty.arts.ubc.ca/kmilligan/teaching/ECON551/551-slides-2a.pdf · Government Finance: Revenues Winter 2018 ... Top 10 percent 92,800

ECON 551: Lecture 2a 1 of 40

Econ 551

Government Finance: Revenues

Winter 2018

Given by Kevin Milligan

Vancouver School of Economics

University of British Columbia

Lecture 2a: Redistribution and Social Choice


Agenda:

1. How unequal are incomes?

2. Does government have a role?

3. Social welfare functions

4. Axiomatic approach: Arrow’s impossibility theorem.


Inequality in Canada: Four trends

Two of these trends suggest: ‘this isn’t a problem’…

i) Median incomes are growing

ii) Low-income levels are improving

…but digging deeper reveals some cause for concern.

iii) Earnings stagnation

iv) Income concentration at top

Similar trends happening in some other advanced countries. (See Atkinson, Piketty, and Saez 2011

JEL)

For Canada inequality trends, see Fortin Green Lemieux Milligan Riddell (2012) or Corak (2016).


Canadian Trend #1: Median incomes moving up


Canadian Trend #2: Low income proportion: diverging measures…


Canadian Trend #3: Earnings polarization hitting median males


Role of the resource boom….


Canadian Trend #4: Income concentration at the top

What is ‘the top 1%?’

Income (2015) you need to be in the top…

Group Income needed Percentile

Top 0.01 percent 3,636,000 P99.99 Top 0.1 percent 826,800 P99.9 Top 1 percent 234,700 P99 Top 5 percent 120,100 P95 Top 10 percent 92,800 P90 Top 50 percent 33,400 P50

Total individual income. Source: CANSIM 204-0001

Income shares: How much of the total pie of income goes to people in each of these

groups?






Veall (2012): Big change in composition of top incomes

• Very big swing in wage earners vs capital earners in top 0.01%.

• Also note that proportion of wage income is ~same in top 0.01% and top 1% in 2009.

o It is ‘supermanagers’ driving the concentration trend; not capital income.


FGLMR (2012): Characteristics of the top 1% in 2005


Agenda:






Should government ‘undo’ the market income distribution?

What should government do?

• Nothing (aka anarchy)

• Enforce contracts (aka the ‘night watchman state’)

• Provide public goods

• Social Insurance

• Redistribution

In Canada, the federal government spends

• ~45% of its budget on ‘public goods’ (generously defined).

• ~55% of its budget on transfers to individuals (30%) / other governments (25%).


Concepts of fairness

Procedural Justice: what matters is a fair process.

Consequential Justice: what matters is a fair outcome.

Sen (1995 AER): You can’t separate these two concepts.

• If ‘fair’ procedure led to horrific outcome, we likely wouldn’t like that.

• If a fantastic outcome were only available through something horrible like torture or death, we

might not like that.

Amartya Sen


Perceptions of fairness: Alesina and Angeletos (2005 AER)

See also Lefgren et al. (2016) and Weinzerl (2017) for experimental/survey evidence.


Perceptions of fairness: Luttmer and Singhal (2011 AEJ-Policy)


The Rawls (1971) experiment

John Rawls “A Theory of Justice” (1971)

• A book about a ‘social contract’.

• Imagine we chose how much redistribution there would be in society before we got to see our

own position in the distribution.

• In Rawls’s language, imagine we are behind a ‘veil of ignorance’ in the ‘original position.’

• Rawls deduced that in this case, we should choose ‘maxi-min’, which maximizes the

outcomes of those at the bottom.


Rawls’s critics

Nozick “Anarchy, State, and Utopia” (1974) offers point-by-point rebuttal along libertarian lines.

• Incomes belong to individuals; not ‘society’.

• ‘Society’ has no right to redistribute because

‘society’ doesn’t own anything.

• If outcomes are unequal, that doesn’t matter.

• What matters is the process that generates the outcomes. If process is fair, then outcomes are

fair. (i.e. procedural justice)

Also:

• How much do we know behind ‘veil of ignorance’? Our abilities? The distribution of abilities?

The distribution of outcomes? How much is ‘luck’ how much is ‘hard work’?


Redistribution might be efficient: Boadway and Keen (2000)

Boadway and Keen (2000) offer a survey of theories of redistribution.

They also offer some reasons why redistribution can be efficiency enhancing.

• Incomplete markets for insurance—redistribution acts as insurance to fill missing markets;

improve efficiency.

• Risk-sharing induces more risky investment

o Government is ‘silent partner’.

o Needs full loss-offset for the math to work, though…

Other arguments have been made as well:

• Inefficient investment in children; human capital. See e.g. Corak (2013)


Agenda:






Social Choice

• There are lots of points on the contract curve: They are all efficient. o How to choose among them?

• Subfield of ‘Social Choice’ draws on philosophy, mathematics, and economics.

• For deeper treatment of the topics, see Mueller (2003) ch. 23 and Blackorby and Bossert

(2004).


Real-valued Social Welfare Functions

Basic form was developed by Bergson (1938) and Samuelson (1947)

Say we have

• Individuals ℎ, from 1 to H.

• Each individual has a utility function 𝑈ℎ.

Definition:

A social welfare function is a function W such that: 𝑊 = 𝑊(𝑈1, 𝑈2, … , 𝑈𝐻)

That’s it.


Comments on real-valued Social Welfare Functions

(See Mueller ch. 23 for criticisms)

• How do we evaluate 𝑈ℎ? Interpersonal utility comparisons? Is that informationally possible?

If so, is it ethical?

• An omniscient ruler might be able to see all of our 𝑈ℎ and plug them in. Who gets that job?

• Alternative interpretation: it’s all one person, just in different states of the world. Now it’s just

intrapersonal utility comparisons.

• Note that we can abandon the Pareto criterion and explicitly trading off individuals here.

• How to choose which functional form for W?

o Several have been proposed…..


Benthamite / Utilitarian Social Welfare Function

Bentham and Mill most strongly associated with utilitarianism.

Bentham: we can use a ‘hedonic calculus’ to ascertain the sum total of pleasure and pain produced

by an act.

In math, 𝑊 =1

𝑁∑ 𝑈ℎℎ .


Benthamite / Utilitarian Social Welfare Function

𝜕𝑊 = 𝜕𝑈1 + 𝜕𝑈2 = 0 implies 𝜕𝑈2

𝜕𝑈1= −1.

Graph on ‘social indifference map’

Here, individuals are ‘perfect substitutes’. (Sen 1995: any weight on liberty? Is slavery ok?

Violence? Torture?)

U1

Slope= -1

U2


‘Rawlsian’ Social Welfare Function

The Rawlsian result: maxi-min.

𝑊 = maxminℎ

𝑈ℎ

Here, people are ‘perfect complements’. Society not better off unless the ‘min’ guy gets more, no

matter how much other guy is getting.

U1

U2


Atkinson’s Generalized Social Welfare Function

𝑊 =1

1 − 𝛾∑[(𝑈ℎ)1−𝛾 − 1]

ℎ

When 𝛾 = 0, this collapses to Benthamite SWF.

When 𝛾 = ∞, this collapses to Rawlsian SWF.

In between those points, 𝛾 governs the degree of curvature; of trade-off between individual utilities.


Atkinson and Stiglitz Question Mark Diagram

45 ° line

P

E

R

W

C N

J

T

•

𝑁′

•

•

•

• •

•

•

Utility Person 1

Uti

lity

Per

son 2

Slope = -1


Atkinson and Stiglitz Question Mark Diagram

• Traces ‘utility possibilities curve’ for persons 1 and 2.

• PT is the ‘technical frontier’, given instruments at government’s disposal.

• N is initial endowment. • Between N and C are potential Pareto improvements.

• If we had started at N’, no Pareto improvements could have been available.

• E is the egalitarian solution. Equal utilities for each guy. Many points Pareto-dominate E.

• What about utilitarians? Their SOC’s are linear with slope -1. So, they like a tangent point

like W. This maximizes the sum of utilities.

• What about Rawls? Guy 2 is the ‘max’ guy and guy 1 is the ‘min’ guy. So, the goal is to give

guy 1 the most he can get. This is at point R.


Agenda:






The problem with SWFs:

Who gets to choose the SWF we use to aggregate preferences?

• One individual could do it, but that would be a dictatorship. (Perhaps Plato’s philosopher king;

a benevolent dictator).

• Maybe we can have a ‘constitutional convention’ to choose a SWF that would satisfy some

general properties.

• For individuals in microeconomics, we build up preference orderings from a set of axioms:

o E.g. completeness, transitivity and reflexivity are sufficient for individual rationality.

• Can we do the same for ‘social’ preference orderings?


Arrow’s approach:

Kenneth Arrow tried to lay out a set of very general axioms

that a social preference ordering should satisfy.

Unfortunately, he found that it was impossible to satisfy his

set of five general axioms.

For a more technical version and the proof you can look in

Mueller Ch. 24, or read Arrow (1951). Below, we follow

Mueller ch. 24.

http://en.wikipedia.org/wiki/Kenneth_Arrow


Arrow’s five axioms:

1. (T) Transitivity. The social ordering should be consistent over all alternatives. xPy and yPz

implies xPz.

2. (U) Unrestricted domain. No restrictions on individual preference orderings. Individuals can

have any preferences. I can rank apples>bananas>pears and you can do whatever you want to.

3. (P) Pareto principle. If xPy for all people individually, then society should prefer xPy.

4. (I) Independence of irrelevant alternatives. Social ordering over x and y depends only on the

individual orderings of x and y, not their orderings of other alternatives.

5. (D) No Dictator. No one gets his way all the time.

(Note that these five axioms spell ‘TUPID’, which makes a nice memory device.)


Statement of Arrow’s Impossibility Theorem:

Theorem: (loosely) When there are at least three possible choices available, no social choice

mechanism (or SWF) that satisfies all five axioms is possible.

Corollary: A social choice mechanism that satisfies the first four axioms only exists in a

dictatorship.

Proof: See Mueller, or Geanakoplos (2005) for three brief proofs.


Implications of Arrow’s result:

Many find this very depressing. Are there no ‘perfect’ voting systems?

• There is no way to make social decisions without violating one of these seemingly weak

axioms. There is no way of structuring our elections or other ways of choosing that can do it.

• This means there is NO social analogue to the concept of individual rationality and preference

orderings.

• We may be faced with the choice of either (a) making coherent social choices or (b) living free

from rule by a dictator.


Can we just relax one of the five axioms?

(T) Without transitivity, we will end up in voting cycles. Arrow argues that the social choice

process will be path-dependent and arbitrary.

(U) We could put structure on individual preferences. We’ll talk about this soon.

(P) Pareto criterion. If we relax this, then we move away from the game we’re playing here.

We’re trying to choose among points on the frontier. Interior points are just not interesting for this

game.

(I) IIR: Relaxing this axiom opens up the possibility of strategic behaviour (not reporting your

true preferences). This opens the door to agenda manipulation.

(D) Plato would say that a dictator would be great, so long as we found a perfect philosopher king.

If we get a bad one, changing dictators is costly. And maybe we have other fundamental reasons to

prefer democracy, too.


Summary of Social Choice:

• The question is: How do we choose among efficient allocations?

• If we want to make interpersonal utility comparisons, then we can use Bergson-Samuelson

SWFs. These can take many forms, from utilitarian to Rawlsian to whatever.

• Arrow’s impossibility theorem suggests that making social decisions is difficult. There is no

perfect social choice process; no magic voting method.

• This brings us into examining the properties of different voting methods….the topic of the

next lecture.

Econ 551 Government Finance: Revenues Winter 2018faculty.arts.ubc.ca/kmilligan/teaching/ECON551/551-slides-2a.pdf · Government Finance: Revenues Winter 2018 ... Top 10 percent 92,800

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