Econ 551 Government Finance: Revenues Fall 2018 Given by Kevin Milligan Vancouver School of Economics University of British Columbia Lecture 2a: Redistribution and Social Choice ECON 551: Lecture 2a 1 of 42
Agenda: 1. How unequal are incomes? 2. Does government have a role? 3. Social welfare functions 4. Axiomatic approach: Arrow s impossibility theorem. ECON 551: Lecture 2a 2 of 42
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). ECON 551: Lecture 2a 3 of 42
Canadian Trend #1: Median incomes moving up ECON 551: Lecture 2a 4 of 42
Canadian Trend #2: Low income proportion: diverging measures ECON 551: Lecture 2a 5 of 42
Canadian Trend #3: Earnings polarization hitting median males ECON 551: Lecture 2a 6 of 42
Role of the resource boom. ECON 551: Lecture 2a 7 of 42
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? ECON 551: Lecture 2a 8 of 42
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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. o It is supermanagers driving the concentration trend; not capital income. ECON 551: Lecture 2a 13 of 42
FGLMR (2012): Characteristics of the top 1% in 2005 ECON 551: Lecture 2a 14 of 42
Agenda: 1. How unequal are incomes? 2. Does government have a role? 3. Social welfare functions 4. Axiomatic approach: Arrow s impossibility theorem. ECON 551: Lecture 2a 15 of 42
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%). ECON 551: Lecture 2a 16 of 42
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 ECON 551: Lecture 2a 17 of 42
Perceptions of fairness: Alesina and Angeletos (2005 AER) See also Lefgren et al. (2016) and Weinzerl (2017) for experimental/survey evidence. ECON 551: Lecture 2a 18 of 42
Perceptions of fairness: Luttmer and Singhal (2011 AEJ-Policy) ECON 551: Lecture 2a 19 of 42
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. ECON 551: Lecture 2a 20 of 42
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? ECON 551: Lecture 2a 21 of 42
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) ECON 551: Lecture 2a 22 of 42
Agenda: 1. How unequal are incomes? 2. Does government have a role? 3. Social welfare functions 4. Axiomatic approach: Arrow s impossibility theorem. ECON 551: Lecture 2a 23 of 42
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). ECON 551: Lecture 2a 24 of 42
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 U h. Definition: A social welfare function is a function W such that: W = W(U 1, U 2,, U H ) That s it. ECON 551: Lecture 2a 25 of 42
Comments on real-valued Social Welfare Functions (See Mueller ch. 23 for criticisms) How do we evaluate U h? Interpersonal utility comparisons? Is that informationally possible? If so, is it ethical? An omniscient ruler might be able to see all of our U h 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.. ECON 551: Lecture 2a 26 of 42
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 Uh h. ECON 551: Lecture 2a 27 of 42
Benthamite / Utilitarian Social Welfare Function W = U 1 + U 2 = 0 implies U2 U 1 = 1. Graph on social indifference map U 2 Slope= -1 U 1 Here, individuals are perfect substitutes. (Sen 1995: any weight on liberty? Is slavery ok? Violence? Torture?) ECON 551: Lecture 2a 28 of 42
Rawlsian Social Welfare Function The Rawlsian result: maxi-min. W = max min h U h U 2 U 1 Here, people are perfect complements. Society not better off unless the min guy gets more, no matter how much other guy is getting. ECON 551: Lecture 2a 29 of 42
Atkinson s Generalized Social Welfare Function When γ = 0, this collapses to Benthamite SWF. When γ =, this collapses to Rawlsian SWF. W = 1 1 γ [(Uh ) 1 γ 1] h In between those points, γ governs the degree of curvature; of trade-off between individual utilities. ECON 551: Lecture 2a 30 of 42
Utility Person 2 Atkinson and Stiglitz Question Mark Diagram T N N Slope = -1 C W 45 line R E P Utility Person 1 ECON 551: Lecture 2a 31 of 42
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. ECON 551: Lecture 2a 32 of 42
Agenda: 1. How unequal are incomes? 2. Does government have a role? 3. Social welfare functions 4. Axiomatic approach: Arrow s impossibility theorem. ECON 551: Lecture 2a 33 of 42
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? ECON 551: Lecture 2a 34 of 42
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. ECON 551: Lecture 2a 35 of 42
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.) ECON 551: Lecture 2a 36 of 42
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. ECON 551: Lecture 2a 37 of 42
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. ECON 551: Lecture 2a 38 of 42
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 other fundamental reasons to prefer democracy, too. ECON 551: Lecture 2a 39 of 42
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 orderings 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. ECON 551: Lecture 2a 40 of 42
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. ECON 551: Lecture 2a 41 of 42
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: Lecture 2a 42 of 42