Econ 551 Government Finance: Revenues Fall 2019 Given by Kevin - - PowerPoint PPT Presentation

ECON 551: Lecture 2a 1 of 42

Econ 551 Government Finance: Revenues Fall 2019

Given by Kevin Milligan Vancouver School of Economics University of British Columbia Lecture 2a: Redistribution and Social Choice

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Agenda:

• 1. How unequal are incomes?
• 2. Does government have a role?
• 3. Social welfare functions
• 4. Axiomatic approach: Arrow’s impossibility theorem.

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Inequality in Canada: Four trends

Two of these trends suggest: ‘this isn’t such 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).

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Canadian Trend #1: Median incomes moving up

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Canadian Trend #2: Low income: diverging measures…

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Canadian Trend #3: Earnings polarization hitting median males

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Role of the resource boom….

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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 11-10-0055-01

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

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ECON 551: Lecture 2a 10 of 42 266.7 150.0 215.0 145.0 157.7 127.7 117.8 93.4 95.8 75.0 100.0 125.0 150.0 175.0 200.0 225.0 250.0 275.0 300.0 1982 1983 1984 1985 1986 1987 1988 1989 1990 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 2013 2014 2015 2016 Income Share indexed to 1982=100

High Income Shares 1982-2016 Indexed to 1982=100

P99.99 P99.9 P99 P95 Bottom 95 Source: CANSIM 11-10-0055-01

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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.

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

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

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Agenda:

• 1. How unequal are incomes?
• 2. Does government have a role?
• 3. Social welfare functions
• 4. Axiomatic approach: Arrow’s impossibility theorem.

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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%).

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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

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Perceptions of fairness: Alesina and Angeletos (2005 AER)

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

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Perceptions of fairness: Luttmer and Singhal (2011)

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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

• utcomes of those at the bottom.

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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

• utcomes 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’?

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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

• Government is ‘silent partner’.
• 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)

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Agenda:

• 1. How unequal are incomes?
• 2. Does government have a role?
• 3. Social welfare functions
• 4. Axiomatic approach: Arrow’s impossibility theorem.

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Social Choice

 There are lots of points on the contract curve: They are all efficient.

• 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).

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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 𝑉ℎ. Definition: A social welfare function is a function W such that: 𝑋 = 𝑋(𝑉1, 𝑉2, … , 𝑉𝐼) That’s it.

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Comments on real-valued Social Welfare Functions

(See Mueller ch. 23 for criticisms)  How do we evaluate 𝑉ℎ? Interpersonal utility comparisons? Is that informationally possible? If so, is it ethical?  An omniscient ruler might be able to see all of our 𝑉ℎ 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?

• Several have been proposed…..

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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, 𝑋 =

1 𝑂 ∑ 𝑉ℎ ℎ

.

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Benthamite / Utilitarian Social Welfare Function

𝜖𝑋 = 𝜖𝑉1 + 𝜖𝑉2 = 0 implies

𝜖𝑉2 𝜖𝑉1 = −1.

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

• k? Violence? Torture?)

U1 Slope= -1 U2

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‘Rawlsian’ Social Welfare Function

The Rawlsian result: maxi-min. 𝑋 = max min

ℎ 𝑉ℎ

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

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Atkinson’s Generalized Social Welfare Function

𝑋 = 1 1 − 𝛿 ∑[(𝑉ℎ)1−𝛿 − 1]

ℎ

When 𝛿 = 0, this collapses to Benthamite SWF. When 𝛿 = ∞, this collapses to Rawlsian SWF. In between those points, 𝛿 governs the degree of curvature; of trade-off between individual utilities.

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Atkinson and Stiglitz Question Mark Diagram

45 ° line P E R W C N J T

• 𝑂′
• Utility Person 1

Utility Person 2 Slope = -1

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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.

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Agenda:

• 1. How unequal are incomes?
• 2. Does government have a role?
• 3. Social welfare functions
• 4. Axiomatic approach: Arrow’s impossibility theorem.

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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:

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

rationality.  Can we do the same for ‘social’ preference orderings?

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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.

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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.)

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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.

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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.

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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) IIA: Relaxing this axiom opens up the possibility of strategic behaviour (not reporting your true preferences), randomness of outcomes, and centralized decision

• making. Arrow argues all these are undesirable.

(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

• ther fundamental reasons to prefer democracy, too.

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More on Independence of Irrelevant Alternatives

Arrow (1951) provides several motivations for the IIA condition. Here are three things that may arise if IIA is not satisfied. 1) Introduces randomness (p. 26): choice shouldn’t depend on perhaps random presence/absence of an option not chosen. Consider choice over candidates, where one has died. “Surely the social choice should be made by taking each of the individuals’ preference lists, blotting out completely the dead candidate’s name, and considering only the

• rderings of the remaining names…to assume otherwise would be to make the result of

the election dependent on the obviously accidental circumstances of whether a candidate died before or after the date of polling.”

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More on Independence of Irrelevant Alternatives

Arrow (1951) provides several motivations for the IIA condition. Here are three things that may arise if IIA is not satisfied. 1) Introduces randomness (p. 26): choice shouldn’t depend on perhaps random presence/absence of an option not chosen. 2) Cardinal utility comparisons are bad (p. 9-11; 109-111): Introducing an outside alternative acts as a numeraire against which we can score the included choices. This introduces cardinal rankings. Cardinal rankings allow centralization of decisions which opens social choice to abuse. Also, it is difficult and contentious to measure. 3) Strategic behaviour (p. 27): With point-based systems (e.g. Borda count), you can construct situations where IIA

• fails. This gives an incentive to misrepresent preferences to game the count. Arrow views

this as a bad property of a social choice mechanism.

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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

• f the next lecture.