Distributional Justice: Theory and Measurement (Routledge Frontiers of Political Economy, 47)

Distributional Justice

The late John Rawls’s Theory of Justice, published in 1971, was the start of a lively debate among moral philosophers. The debate has not spilled over into empirical studies of income distribution and rates of poverty. This book attempts to connect the philosophical debate and empirical studies. Introducing the main theories of distributional justice the book covers utilitarianism and welfare economics, moving on to Rawls’s social contract and the Sen/Nussbaum capability approach with a refreshingly readable style. There is a chapter covering the position of mothers and children in theories of justice. The book then studies empirical methods used in analysing the distribution of economic goods, covering Lorenz curves and inequality measures. The concepts of income, wealth and economic goods are comprehensively discussed, with a particular view to their role in theories of justice. This book is an important read for economists and other social scientists, as well as philosophers who want to quantify social and economic justice. Its readable style combined with its original approach mean that it will prove popular across a range of levels, from student to researcher. Hilde Bojer is Associate Professor at the Department of Economics, University of Oslo.

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Distributional Justice Theory and measurement

Hilde Bojer

First published 2003 by Routledge 11 New Fetter Lane, London EC4P 4EE Simultaneously published in the USA and Canada by Routledge 29 West 35th Street, New York, NY 10001 Routledge is an imprint of the Taylor & Francis Group

This edition published in the Taylor and Francis e-Library, 2005. “To purchase your own copy of this or any of Taylor & Francis or Routledge’s collection of thousands of eBooks please go to www.eBookstore.tandf.co.uk.” © 2003 Hilde Bojer All rights reserved. No part of this book may be reprinted or reproduced or utilised in any form or by any electronic, mechanical, or other means, now known or hereafter invented, including photocopying and recording, or in any information storage or retrieval system, without permission in writing from the publishers. British Library Cataloguing in Publication Data A catalogue record for this book is available from the British Library Library of Congress Cataloging in Publication Data Bojer, Hilde, 1939– Distributional justice: theory and measurement / Hilde Bojer p. cm. – (Routledge frontiers of political economy ; 47) Includes bibliographical references and index. 1. Distributive justice. 2. Welfare economics. 3. Utilitarianism. I. Title II. Series. HB523.B65 2003 330–dc21

ISBN 0-203-98788-8 Master e-book ISBN

ISBN 0–415–29824–5 (Print Edition)

2003041388

Contents

List of figures List of tables Preface

xi xiii xv

1 Introduction

1

PART I

Theories of justice 2 About distributional justice Economic goods 8 Global and local justice 8 Principles of justice 9 About theories of justice 10 Egalitarianisms 12 The social contract 13 Libertarianism and Marxism: two special cases 14

5 7

3 Deserts and the fruits of our labour Deserts 15 Rewards according to contribution 16 The fruits of our labour 17

15

4 Welfarism: utilitarianism and welfare economics Utilitarianism 21 Welfarism and equality 24 Social evaluation functions 26 Welfarism and ethics 31

20

viii

Contents

5 John Rawls’s theory of justice The original position 37 The difference principle 39 Illustrations of the difference principle 39 The difference principle and the theory of uncertainty 41 Primary goods 42

36

6 Equality of what? Resources and capabilities Approaches to economic equality 46 Dworkin and equality of resources 47 Capabilities 48

46

7 Libertarianism and Marxism Libertarianism 51 Marxism 54

51

8 Children and their mothers What is special about children? 57 Welfarism and children 58 Libertarianism and children 59 The Rawlsian social contract 60 The good of children 62

56

PART II

Measuring inequality 9 Income and wealth Economic goods 65 Income 66 Components of income 69 Extended income 70 Full income 73 Lifetime income 74 Wealth 76 Access to economic goods 77 10 Household income Equivalent adult scales 78 The cost of living function and economies of scale 79 The cost of children 81 Estimating equivalent adult scales 83 The unit of analysis 85

63 65

78

Contents

ix

11 What should we measure? Household or individual income? 87 Standard income, extended income, full income? 89 Lifetime income or annual income? 90

86

12 Lorenz curves and inequality measures The distribution function 92 The Lorenz curve 96 Inequality measures 99 The theory of inequality measures 100 Ordinality of inequality measures 103 Some properties of different inequality measures 104

92

13 Social evaluation of inequality Lorenz dominance and inequality aversion 107 Ethical inequality measures 108 Atkinson’s inequality measure 109

107

14 Some inequality measures The Generalised Entropy class of inequality measures 112 The M-curve and the A-measure 113 Kolm’s inequality measure 114 Choosing an inequality measure 115 Inequality in some OECD countries 116

112

15 Poverty Relative poverty 118 Measuring poverty 120 The importance of equivalence scales 121

118

16 Decomposition of inequality measures Decomposition by group 123 Decomposition by group: an example 125 Decomposition by income component 126 Decomposition by component: an example 131

123

Appendix A: uncertainty and expected utility Appendix B: sampling errors Notes Suggested further reading References Index

134 137 139 140 142 147

Figures

4.1 Utility and marginal utility as functions of income 4.2 Welfare egalitarian distribution of income 4.3 Utilitarian distribution of income 4.4 The utilitarian social welfare function 4.5 A Sen function 4.6 Equality and wealth 5.1 The difference principle in action 1 5.2 The difference principle in action 2 5.3 The difference principle in action 3 9.1 Income and wealth 9.2 Income by age, men and women 9.3 Income, consumption and wealth 10.1 The budget share of food and the Engel method 12.1 Parade of dwarfs 12.2 Inverse distribution functions of income 12.3 Distribution functions of income 12.4 Frequency distributions of income 12.5 A Lorenz curve 12.6 Lorenz curves before and after an equalising transfer 12.7 Lorenz dominance 12.8 Generalised Lorenz curves 12.9 Crossing Lorenz curves 12.10 Lorenz curves of women and men 13.1 The social cost of inequality 14.1 An M-curve 15.1 Distributions with and without relative poverty 15.2 Composition of the Norwegian poor in 1996 by equivalent adult scale 16.1 Interaction curves: capital income and transfers, employees 16.2 Interaction curves: capital income and transfers, pensioners A.1 Utility and risk aversion A.2 Second order stochastic dominance

24 25 26 28 29 30 40 40 41 68 74 75 84 93 94 95 96 97 97 98 99 104 105 108 114 119 122 128 128 135 136

Tables

9.1 12.1 12.2 12.3 14.1 15.1 16.1 16.2 16.3 16.4 16.5 16.6 16.7 A.1 B.1

Composition of income, Norway 1996 Composition of decile groups Inequality, Norwegian men and women Changes in inequality 1982–90 Inequality in selected OECD countries 1994/95 Poverty rates in selected countries by equivalent adult scale Population and group Ginis Inequality by occupational group Group decomposition of inequality Inequality by occupational group Decomposition of the Gini coefficient Decomposition of the coefficient of variation Capital income, transfers and inequality Expected income and expected utility Gini coefficients and their standard deviations

70 95 100 104 117 121 124 125 126 131 132 132 133 134 138

Preface

This book has been in the making for more years than I care to remember. During this period, I have received help and encouragement from a number of institutions and people. I am happy to be able to thank them all formally at last. The Research Council of Norway financed a fruitful year abroad. During this year I first received the hospitality of the Humboldt Universität Berlin, for which I thank Professor Bengt Arne Wickström and Frau Sonja Boden. I spent the autumn of 1999 as a guest scholar at the then Radcliffe Institute for Public Policy Research, and thank the whole staff there for the ideal working conditions. Various parts of the text have been read at various stages of production by Tony Atkinson, Christian Brinch, Alexander Cappelen, John K. Dagsvik, Andreas Føllesdal, Aanund Hylland, Jo Thori Lind, Diderik Lund, Agnar Sandmo and Steinar Strøm. I thank them all for their time and their comments, and apologise for sometimes doing things my own way in spite of their advice. The Department of Economics has been generous with grants for research assistance. For their assistance with the drawing of figures and otherwise relieving me from tedious chores, I owe thanks to Stian Holter, Fredrik Hauge, and especially to Pål Magnus Lykkja. I owe a special debt to inquisitive and critical students at the Universities of Oslo and St Petersburg. I thank Feminist Economics and The Nordic Journal of Political Economy for permission to use extracts from articles published in them. Unless otherwise stated, numerical examples in tables and figures as well as in the text are from my own computations on data from the Norwegian Surveys of Income. The data were supplied by Statistics Norway through the Norwegian Social Science Data Services (NSD). Neither of these institutions is in any way responsible for the use I have made of the data. A special ‘thank you’ goes to the ever friendly and helpful Helene Roshauw of NSD. I set out to write the book that I wished were available when I started doing research in income distribution. My reach exceeded my grasp. But as Winnie-thePooh said: ‘It’s come different from what I thought it would, but it’s come. Now I must go and sing it to Piglet’. Hilde Bojer Oslo, March 2003

1

Introduction

Women work longer hours than men in nearly every country, but men receive the lion’s share of income and recognition.1 In November 2002, British firefighters threatened to strike for higher wages. One firefighter interviewed by the Guardian earned around 30,000 pounds a year after twenty-two years of service.2 An English premiership football player might well earn as much in a week, while a care assistant had yearly earnings of 10,000 pounds.3 These are some examples of differences in economic circumstances, and I know in my heart that they are unjust. For many years, I did not realise that I could use my reason to explain why. When I studied economics in Oslo in the beginning of the 1960s, a truth universally acknowledged in the profession was that justice in distribution is not, and cannot be, the subject of academic research. There is, to be sure, the social welfare function. But the social welfare function is for the politicians to determine and for the economics profession to put it into practice unquestioned. Accordingly, when I first began doing research on income distribution, I started off by learning what I could about empirical methods, inequality measures and the intricacies of concepts and definitions in income statistics. But increasingly I found myself becoming more interested in the why than the how of the analysis. Why is the distribution of household income more interesting than the distribution of individual income? Why should we be interested in measuring the degree of inequality in either of them? So I tentatively started to read Rawls and Sen, and made two discoveries, one of them delightful and the other rather disheartening. The delightful discovery was that academic research into questions of justice in distribution is not only possible and legitimate, but also a flourishing academic discipline with an increasing number of practitioners. The disheartening discovery was that I did not understand the literature. I found it dense, abstruse, impenetrable. As I slowly began to understand something of the content, I made a third discovery, namely of the gap between what the philosophers write and what is studied in empirical analyses of income distribution.

2

Introduction

Researchers working with empirical methods seem to take for granted that the ultimate aim of public policy is to increase individual welfare, and the task of the empirical analyst is to find the level and distribution of welfare. On the other hand, such outstanding moral philosophers as Ronald Dworkin, Martha Nussbaum, John Rawls and Amartya Sen are not at all concerned with welfare, but with opportunities, resources, rights and capabilities. According to them, achieving individual welfare and happiness is the person’s own responsibility. The state has the moral duty to further the means to, and remove constraints on, the pursuit of happiness, but not to secure that happiness itself. But then again, these same philosophers seem quite unconcerned with how their concepts can be made operational for empirical analysis. So I decided to write this book to bridge the gap between moral philosophy and empirical research. I have not succeeded; the bridge is still unbuilt. But here at least is a book where moral philosophy and empirical methods coexist between the same two covers, and with some attempts at interaction between the two parts. The book is addressed to those students of the social sciences who are interested in both the why and the how of studying income distribution. Perhaps it may also be of some interest to researchers on either side of the divide who want to learn something about how the other half thinks. Moral philosophy cannot, of course, prove that one way of organising society and arranging the distribution of economic goods is ‘objectively’ better than another. But it can make our ideas of justice more precise, help us to reason logically about justice and to find areas of agreement and disagreement. I also think that knowledge of moral philosophy could make empirical research more relevant to people’s concerns about justice in distribution. I know Norwegian income statistics fairly well, which accounts for the numerical examples in this book. Here is one: by the end of the 1990s, the average woman in Norway received about 60 per cent of the income of the average man. (The percentage varies slightly with the definition of income used.) Is this difference in income unjust? To answer the question, we have to know the reasons for the difference. These are reasonably well known. About half the difference is due to different wage rates. Some part of these 20 per cent may be due to women receiving lower wages than men for the same work, but this part is probably fairly small. It is also very difficult to identify, because women on the whole do not do the same work as men. And the kinds of paid employment that women tend to undertake, are also the kinds that are not very well paid. The remaining difference of 20 per cent is either due to women working part-time or not being in paid employment at all. Most people now agree that it is wrong and unjust to discriminate against women by giving them lower pay than men for the same work. (But trade unions in Norway negotiated separate wage rates for women and men until about 1960.) The greater part of the difference in incomes, however, does not stem from discrimination, but from men and women making different choices in the labour market. In Norway, it is a long time since any profession or education was formally closed to women.

Introduction

3

Women’s choices of education and profession are made of their own free will. So it seems is their choice of part-time work. At this point in my lectures, I usually ask the students to suggest why so many women work part-time. Invariably, the answer is given by one of the female students: women spend time taking care of the children. Disagreement about the justice of women’s low incomes then stems from disagreements on two points. The first concerns the question of just wages in the typical women’s professions, like nursing. The second concerns the justice of women doing most of the domestic unpaid work, particularly child care. There are also those who feel that the difference in incomes of men and women is of no importance because of income sharing between married couples. (I have never yet met a woman who agreed with this last statement.) All the empirical research from which the above example was drawn was carried out in the last twenty to thirty years. (Before 1970, Statistics Norway did not even publish separate tables on the income of women and men.) The research was grounded in moral concerns about women’s economic and social position. The use I have made of it stems from what I have learned in moral philosophy about the importance of free choice and contingent circumstances. It has led me to question the widespread practice of basing empirical analysis on household income alone. In spite of this example, the present book is not a feminist treatise. It contains no specific feminist methods or analyses. But it is written by a woman concerned about justice to women. The book is in two parts: Theories of Justice and Measuring Inequality. Part I is an introduction to some important theories of justice. It starts with an overview of the theories considered in the following chapters. Chapter 3 discusses the idea of rewards according to deserts. I have tried to present welfarism (Chapter 4), Rawls’s social contract (Chapter 5), Dworkin’s equality of resources and the Nussbaum/Sen capability approach (Chapter 6) both critically and, I hope, fairly. But I found it impossible to hide my lack of enthusiasm for libertarianism and Marxism (Chapter 7). Chapter 8 contains my own ideas on children and motherhood in relation to distributional justice. I had to develop my own ideas because I found very little about children and women in the theories presented in the first seven chapters. It should be emphasised that Part I is an introduction to the subject, aimed at social science students, not students of political philosophy. And it is my hope that the text can be read by social scientists in general and not only economists, even though there are some (very simple) formulas in Chapter 4. Students of economics may find parts of this same chapter wordy and lacking in rigour precisely because the mathematics is missing. The first two chapters of Part II contain a detailed discussion of various ways of defining and measuring access to economic goods. I have tried to make clear that such access is more than cash income, and that therefore justice in distribution of economic goods concerns not only distribution of income. In Chapter 11, I have tried to make a connection between theories of justice and empirical measurement by regarding income as a constraint rather than as a measure of welfare.

4

Introduction

Chapters 12–14 and 16 contain the theory of inequality measures, and a discussion of their properties. I have tried to avoid unnecessary formalisation. But it is impossible to compute measures of any kind without taking the trouble to understand at least a few formulas. Measuring inequality is not altogether a straightforward business, and it is important to understand why. I have given no proofs, only assertions. Those interested will find references to more rigorous expositions, containing references to the original articles with proofs, in ‘Suggested further reading’ at the end of the book. Chapter 15 is a minimalist treatment of the definition and measurement of poverty. There are a number of examples from Norwegian income statistics in Part II, because these are statistics I know well and have access to. They have been included to illustrate the methods and not because I imagine conditions in Norway to be of absorbing interest. As for the vexing problem of ‘he’, ‘she’ or ‘they’, I have addressed this issue by sometimes writing ‘he’ and sometimes ‘she’ more or less at random.

Part I

Theories of justice

2

About distributional justice

Justice is the first virtue of social institutions, as truth is of systems of thought. (John Rawls)

Distributional justice is justice in the distribution of economic goods between the members of a society. For Plato and Aristotle justice was a personal virtue, the highest virtue of man. For the contemporary philosopher John Rawls, justice is a virtue of social institutions, that is of society. Not all authors distinguish between these two meanings of the term ‘justice’. In the present book, the distinction is regarded as important. I shall follow Rawls in considering justice and injustice as characteristics of society, not of the individual conscience. Being a virtue of society, distributional justice presupposes the existence of a society. Traditionally this society is the nation state, and just distribution concerns distribution between the citizens of a nation state at a certain point in time. This is the class of theories of distributional justice that will be presented here. Therefore, two important issues of our times will not be considered: distribution between nations and distributions between generations, over time. Distributional justice is only one of several aspects of the just society. The following exposition will not be a treatise of justice in the law courts, nor will it discuss the political organisation of society in general, such as the rights and duties of citizens, democratic institutions, the extent of freedom. The issues of justice in distribution will be treated in isolation from other aspects of justice in so far as such partial treatment of the subject is possible. Some excursions into wider issues is nevertheless unavoidable. Justice in distribution is a societal concern and the provision of justice in distribution is the responsibility of the state. There may be conflicts between justice in distribution on the one hand and individual rights and freedom on the other. Whoever demands justice in distribution must of necessity accept that the state be given the power to implement such justice. Several of the theories to be discussed in the sections that follow deal with theories of justice in distribution as a part of a wider theory of the just society.

8

Theories of justice

Economic goods Distributional justice is justice in the distribution between persons, of goods that are scarce and transferable; which I shall call economic goods. It is about scarce goods because the question of just distribution does not arise where there is abundance: enough for every one. Moreover, the concept of distributional justice only makes sense for transferable goods: goods that it is possible to take from one individual and give to another. Many goods that we regard as important are neither scarce nor transferable. Health, intelligence, musicality and other talents are not transferable, nor is happiness. But some non-transferable goods may be acquired by means of goods that are transferable. Good nutrition as well as medical care fosters health. There is a well-established connection between poverty and ill-health. The effects of a physical disability such as blindness may be mitigated by the transfer of economic goods, for example the means to keep a guide dog and to acquire books in Braille. Conceivably, a lack of non-transferable goods may also be compensated for by transferable goods. The distribution of economic goods is not the same as the distribution of monetary income. The distribution of income decides the distribution of goods that can be bought with money in the market, but there are important economic goods that are not so available. In all modern countries, some economic goods are distributed in kind by the government to the citizens. This distribution varies from state to state, from nation to nation. Defence, courts of law and police are the responsibilities of government everywhere (for good or ill), as is at least some part of the physical infrastructure such as roads, harbours and airports. The provision of other parts of the infrastructure (water, energy) as well as the provision of education, health care, social insurance are available from the public and/or the private sector in varying combination. The extent to which economic goods should be provided in kind by the government, and how they in this case should be distributed, is an issue of distributional justice. In all economies, there is also a so-called informal sector of varying size and importance: production, exchange and distribution of economic goods outside the monetary economy. Housework, subsistence farming, child care are examples of activities wholly or mainly outside the monetary economy. These are also, as it happens, activities mainly carried out by women all over the world. So, distribution of economic goods is not purely a question of the distribution of monetary income. Even so, the distribution of monetary income is of particular significance. First, because money is technically easy to transfer. Second, because money buys a large class of goods. The connection between economic goods and income and wealth will be considered in more detail in Part II, Chapter 9.

Global and local justice Some authors distinguish between global and local distributional justice. A global principle of justice is meant to apply to all or a large class of distributional

About distributional justice

9

problems; it corresponds, roughly, to the distribution of income and wealth. A principle of local justice applies to the distribution of just one scarce good. Examples of local problems of distribution are the assignment of kidneys for transplantation and other priorities in health treatment, allocation of places in universities, and many others. Jon Elster (1992) points out that different principles of justice are, in fact, applied to these and other cases. All scarce goods might have been allocated by buying and selling. Problems of local justice arise because there are scarce goods that ought not, in justice, to be bought and sold for money. The question then arises: which goods, if any, should be exempt from the global rule of just distribution? Rules of local justice may also arise as second-best solutions, because it is thought to be unrealistic to achieve justice in global distribution of income and wealth. In order to limit injustice, or limit inequalities, certain goods are taken out of the global mechanism and distributed separately. Typical examples are health care, education and social security. There is no general agreement about this simple dichotomy between global and local justice. Walzer (1983) maintains that there are different spheres of distribution with separate principles of justice for each sphere. Kolm (1996: 75) argues that global and local problems of justice must ultimately be solved by the same method of justice. The theories of justice presented in this book are all global in nature.

Principles of justice Brian Barry (1989) classifies theories of justice according to whether they are based on impartiality or on mutual advantage. This classification addresses the question, not of which distribution is just, but of why it is just. Is there a set of first principles which are self-evident and to which we can all agree, such that finding a theory of distributional justice is ‘merely’ a matter of deducing their logical consequences? The short answer is that there seems to be many such first principles, and no general agreement either on what they are or on their implications. Theories of mutual advantage consist of various attempts to apply bargaining theory to deduce distributional justice from the outcome of various bargaining situations. I belong to those who do not consider bargaining outcomes as theories of justice, and they are not included in the survey in this book. The theories I do present are all in some sense built on the principle of justice as impartiality. That is not to say that self-interest is excluded. One method of deducing principles of justice is based on the theory of rational choice in enlightened self-interest. A thought experiment is developed to help us cleanse our conception of justice from the biases created by our own immediate interests and circumstances, such as bargaining power. We are asked to reflect on, and decide on, which distribution of economic goods we would prefer if we did not know what our own place in the distribution would be. This thought experiment is called choosing a distribution from behind the veil of ignorance. Now, there is agreement neither on how thick the veil of ignorance ought to be to create the correct situation of choice, nor on what the result of such an imagined choice would be.

10

Theories of justice

As we shall see, rational choice from behind the veil of ignorance is believed to lead to utilitarian principles of distribution by some, while it leads to a complete break with utilitarian principles for John Rawls. John Rawls proposes a method of thinking about justice which he calls reflective equilibrium. Reflective equilibrium is the equilibrium between our abstract principles and our concrete intuitions about justice. We may, for instance, maintain the widely held abstract principle that justice in distribution is rewards according to effort. Now, consider what this principle entails in some concrete cases. One such case may be that of elderly persons who are no longer able to work. The principle of rewards according to effort might on the face of it seem to entail that these non-working elderly should receive no income. Perhaps we agree. Then there is equilibrium between our principles and our intuition in this case. On the other hand, we may not be willing to accept this consequence (as indeed the majority of people are not). The abstract principle will then have to be modified. A suitable modification might be that rewards should be according to effort for those able to work, supplied by publicly provided old-age pensions. This modified principle must then be confronted with other special cases, and if our intuition in these cases do not fit the new principle, either the principle or our intuition must be modified. When we have an abstract principle that agrees with our intuitive opinions in concrete cases, we are in reflective equilibrium. To a certain extent, all systematic reflection on justice uses a combination of logic and intuition, as I shall in this book.

About theories of justice All the theories presented in this book have some traits in common. They are secular, humanist and individualist. They have their roots in the period of the Enlightenment in Europe (seventeenth and eighteenth centuries) and their concerns and methods can be traced back to the great philosophers of that period (Hobbes, Hume, Kant, Locke, Rousseau). The theories are secular, in that they do not take their ethical prescriptions as given by God or revealed in a Holy Writ. They are concerned with humanity here and now, not in afterlife, and no deity is available to mete out rewards or punishments. The sources of justice must be found in our own conscience and intellect. They are humanist in that justice concerns justice to human beings, and in some sense have the well-being and interests of humanity as their goal, not that of animals or nature. They are individualist: justice is justice to the individual, and principles of justice are based on the interests of individuals. Society consists of individuals, bound together, perhaps, by strong ties of solidarity and common interests, but in the last resort, the common good, the good of society, must be traceable to the good of one or several individuals. There is no such thing in these theories as the good of a class, a race, a sex or a nation as such, in isolation from the good of the individual members of that class, race, sex or nation. Such an approach is called ethical individualism.

About distributional justice

11

The theories are also all what Serge Kolm (1996) calls respectful. That is, they respect the individual’s own conception of what she or he wants from life; their life plan in Rawls’ theory, their preferences in utilitarianism and related theories. They are also all liberal and democratic in that they are based on the rule of law, arguing against discrimination on the grounds of sex, race or class, and for the freedom of the individual. Another, less attractive trait common to the great majority of philosophers presented (with the notable exception of Amartya Sen), is that by the words ‘mankind’ and ‘man’ they mean literally that: the adult male. Indeed, older philosophers like Hobbes and Rousseau, let alone Aristotle and Plato, are explicit on this point: justice to man is the concern of society, justice to women and children is the concern of the patriarchal head of family. Even a contemporary philosopher like John Rawls conceives of the just society as consisting of heads of families, although he does not specify that they are all men. Contemporary philosophers do not explicitly limit themselves to discussing justice to men. This makes no substantial difference as long as they also do not explicitly examine the implications their theories have for the experiences and social situation of women and children. More particularly, they do not address the fact that we are all born as children, and that some part of humanity must necessarily occupy themselves in bearing, rearing and nurturing children in order for humanity to survive. The place of women and children in theories of justice is considered in Chapter 8. This was what theories of distributional justice discussed in this book have in common. There is no simple way of classifying them according to their differences, as they not only give different answers, but ask different questions and use different methods and concepts. One well-known dichotomy is the distinction between procedural justice and consequential justice. In procedural theories of justice, the outcome is just if the procedure is just. In consequential justice, the procedure is just if it leads to just outcomes. But all ethical theories are at some level or other concerned with consequences. The justice of procedures may be based on the normal or expected consequences of following the rules. One theory that is purely procedural is the libertarianism of Robert Nozick. But the libertarians Hayek and Friedman, with almost entirely similar views on the just organisation of society, base their arguments pragmatically on the favourable consequences of libertarianism. Welfare economics, on the other hand, is almost purely consequentialist. All other theories and philosophers, Dworkin, Rawls and Sen, to mention just a few, are concerned with both procedural and consequential justice, with rights and consequences and of the relationship between them. Theories of justice may also be classified according to whether they are welfarist or non-welfarist. By welfarism is meant the belief that the state of a society should be judged solely by the subjective sense of well-being of its members. Welfare economics and utilitarianism are welfarist schools of thought. A welfarist theory is consequentialist and entirely concerned with outcomes, but is not necessarily outcome egalitarian. Indeed, both utilitarianism and welfare economics may be said to be neither egalitarian nor non-egalitarian. Their consequences for distribution are discussed in Chapter 4.

12

Theories of justice

Egalitarianisms Then if what is unjust is unequal, what is just is equal; as is universally accepted even without the support of argument.1 (Aristotle: Nichomachean Ethics) Another well-known dichotomy is that between egalitarians and nonegalitarians. Egalitarians are supposed to be in favour of equality, the others are not. But as several thinkers, among them Sen (1992) and Kolm (1996) have pointed out, in modern, Western discourse on distributional justice, all participants are in favour of equality in some sense. We might well ask ourselves why equality is seen as an essential attribute of justice in the first place. Is equality a good in itself, or is equality necessary in order to obtain some other good? And if equality is instrumental for some other good, which good is that? This question is a very profound one in moral philosophy, and I shall leave it unanswered. Let us just take as given that there seems to be consensus in Western moral philosophy after the Enlightenment that human beings are morally equal, and that this moral equality entails equal liberty and social and political equality at least in some respects. There is no consensus, however, that moral equality entails economic equality, that is, equality in access to economic goods. If we reserve the term egalitarian for proponents of economic equality in some sense, there are still several different equalities proposed in the literature: equality of opportunities, equality of resources, equality of primary goods, equality of income, equality of capabilities, equality of welfare. A well-known distinction between equalities is that between equality of opportunity and equality of outcome, where outcome is sometimes taken to be cash income. Economic egalitarianism is sometimes taken to mean being in favour of equality of incomes. Now, equality of incomes is on the one hand not consistent with equality in hourly wage rates, on the other hand not consistent with equality in consumption. If wage rates are equal, earnings will differ because of differences in working hours. With part-time work continually becoming more usual, differences in working hours explain an increasing part of earnings differentials.2 In particular, since the majority of part-time workers are women, equality of wage rates between men and women does not imply equality of earnings between men and women. Moreover, even with equal working hours per year, equality in wage rates would imply inequality in lifetime earnings because of differences in length of education, and therefore in the number of working years. Nor does equality of individual incomes imply equality of consumption. Some people live together in households, pooling their incomes and taking advantage of economies of scale within the household. Living alone is more expensive than living in a household, as any divorcee will know. Then there is the question of provision for children. A couple with children needs a higher income than a couple without children to achieve the same level of consumption.

About distributional justice

13

Thus, an outcome egalitarian will have to choose one of several definitions of outcome. Equality in one dimension necessarily implies inequality in the other dimensions. This would not be so if all persons were similar and behaved identically. If everyone had the same needs and lived in the same kind of household, equality of income would secure equality of welfare. Equality of wages would secure equality of income if everyone had the same length of education and identical working hours. In modern Western societies, differences in education and working hours are on the face of it results of the free choice of the individual. The individual is also free to choose between cohabiting and living alone. Arguably, having children is also in our time a matter of free choice, although, as everyone knows, in this respect there is an element of uncertainty. So, inequalities in outcome seem to be the result of people’s own free choice. Now, another firm principle in Western discourse on justice is that the consequences of free choice should be respected. If all differences in economic outcomes were due to free choice, a majority would be of the opinion that the differences are not unjust. That is why a discussion of freedom, and an analysis of the conditions for free choice, is such an important part of theories of justice. The demand for equality of opportunity is the demand that choices should be made in conditions that make the outcomes just, and is therefore not perhaps as different from the demand of equality in outcomes as one might think. One reason for demanding equality of outcome is that opportunities are not equal, outcomes are therefore unjust and should be corrected by transfers from the rich to the poor. I believe this is a common basis for theories that are commonly called egalitarian, and within this discourse we in particular find the discussion of what should be meant by equality of outcome.

The social contract The state differs from other organisations and institutions in society in that it may legally use coercion. But coercion is in itself an ill, and should be avoided. Therefore it is reasonable to ask when and for what reasons governmental coercion is legitimate. One way of considering this question is by asking: if we as free and equal citizens had been able to choose whether we wanted to be a part of society or not, in which circumstances would we be willing to accept coercion from the state? The question is of course purely hypothetical, there is no such thing as a human being outside society. But several philosophers through the ages have found this hypothetical approach to be fruitful. The answer may be formulated as a social contract. The social contract is an imaginary contract between the state and each citizen, specifying the rights and duties of the state in relation to the individual citizen, and of the citizen towards the state. For contractarians, the social contract defines the just society. It may also specify the principles of just distribution. The concept of a social contract was created by the philosophers of the Enlightenment, in particular by Thomas Hobbes and Jean Jacques Rousseau. Unsurprisingly,

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Theories of justice

these two philosophers arrived at very different conclusions concerning the contents of the social contract. Prominent contemporary contractarians are John Rawls and Thomas Scanlon. The theory of Rawls will be presented in Chapter 5.

Libertarianism and Marxism: two special cases There are two ideologies, ironically enough at either end of the right–left political axis, which maintain that theories of distributional justice are futile, namely Libertarianism and Marxism. For Marxists, justice in distribution is impossible in a capitalist society, since capitalism is based on the exploitation of the working class. According to Marxist theory, the working class is exploited because their wages represent only a part of the values produced by them. The proletariat is in other words robbed of part of the fruits of its labour. Here, Marxist theory implicitly builds on the very broadly held principle of distributional justice that every person has the right to possess what he himself produces, to enjoy the fruits of his labour, as Hume writes. The same tenet is held by libertarians, but not by other theorists presented in this book. Libertarians argue that liberty of action has absolute priority, and that whichever distribution of income is just that results from the exercise of liberty and of property and other rights. Libertarianism is a theory of procedural justice: if the procedure is just, the result is just. Robert Nozick claims that the demand for any pattern whatever of distribution is unjust in the very nature of things. Another well-known libertarian, Friedrich Hayek has written a book titled: The Mirage of Social Justice (1976). But even so, libertarians maintain equality of rights, and libertarianism is therefore egalitarian in this sense. Libertarianism and Marxism will be discussed in Chapter 7. For the reasons that they both refuse to discuss just patterns of distribution, the Marxist theory of exploitation and the libertarian advocacy of absolute freedom should perhaps not have been included in this book. But both Marxism and Libertarianism play an important part, acknowledged or not, in political discussions of issues of distributional justice, which seems to me to be a reason good enough for their inclusion.

3

Deserts and the fruits of our labour

Use every man after his desert, and who should ’scape whipping? (Hamlet) Every person, if possible, ought to enjoy the fruits of his labour, . . .1 (David Hume)

Deserts Our most basic idea of a just, or fair, distribution, seems to be that each one of us ought to get what we deserve. Evolutionary psychologists claim that human beings have developed something called reciprocal altruism, and that ‘. . . the demands of reciprocal altruism are probably the source of many human emotions. Collectively they make up a large part of the moral sense’ (Pinker 1997: 403). Samuel Bowles and Herbert Gintis quote several surveys of attitudes to welfare policies in the United States, and conclude: ‘. . . egalitarian policies that reward people independent of whether they and how much they contribute to society are considered unfair and are not supported, even if the intended recipients are otherwise worthy of support . . .’ (Bowles and Gintis 2000: 47). They call these attitudes ‘reciprocity’, and refer to a wealth of anthropological studies as well as American opinion surveys. They also quote from one study: ‘Politics is often viewed, by elites at least, as a process centred on the question “who gets what”. For ordinary Americans, however, politics is more often about who deserves what . . .’ (Gilens 1999: 12).2 In this context, being deserving seems to be the same as either working, and so contributing to society, or being unable to work due to circumstances outside one’s own control, like old age or handicaps. My own casual impression of the ongoing debate about inequality and welfare in Norway gives the impression of similar attitudes. One example is the overwhelming majority for increasing government old-age pensions. The argument in favour of the increase often is that today’s old-age pensioners created the country’s present wealth by their labour when they were active. Old people as a group are therefore seen as deserving.

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Theories of justice

Another example showing the importance of individual merit turns up in the various opinions about the benefits that are paid to single mothers in Norway. The opinions are backed up by different stories, leading to different conclusions about whether single mothers deserve benefits or not. One story is the traditional tale of woe: She was poor, but she was honest Victim of the squire’s whim First he loved her, then he left her . . . (Anon.) The innocent wronged girl deserves our help. Another, and quite different, story is the one about the lazy girl who lets herself become pregnant to make an easy living and jump the queues for council housing. A third variant is the careless girl who indulges in sex without taking precautions, and then expects society to pay for the consequences. Both these two last stories are of a girl who has herself to blame for being burdened with a child, and who therefore is not deserving of financial assistance from society.

Rewards according to contribution The quotation from Hume at the beginning of this chapter expresses a fairly commonly held view of what is meant by distribution according to desert: we have the right to receive the fruit of our labours. The English philosopher John Locke was one of the first to formulate the idea of labour as a source of rights: ‘Though the water running in the fountain be everyone’s, yet who can doubt that in the pitcher it is his only who drew it out?’ (Locke 1993: 129). The founding father of modern economics, Adam Smith, wrote: ‘The Produce of labour constitutes the natural recompense or wages of labour’ (1961: 72). And the French socialist Louis Blanc coined the slogan: ‘From each according to ability, to each according to effort’. A more modern formulation might perhaps be that we deserve rewards from society according to how much we ourselves contribute to society. When discussing rewards according to deserts, it is necessary to distinguish between rewards according to effort on the one hand and rewards according to results on the other. Rewarding hard work means rewards according to effort. The right to keep the fruits of one’s labour implies rewards according to results. Now, I believe the principle of rewards according to deserts receives such broad backing because of the general belief that results on the whole reflect effort. But some people work very hard without achieving very much, while others obtain rich fruit without seeming to make much effort. There is also the problem of finding out what the results of one person’s labour are. Production in human society is built on cooperation and division of labour. We all depend for our results on the efforts of countless others. Moreover, the fruits of our labour depend not only on how much we produce, but also on the value of what we produce. The two questions, who produces what? and what is the value of

Deserts and the fruits of our labour

17

their produce? were important issues for the classical economists of the nineteenth century. There are no consensual answers: the subject is highly ideological. As a principle of just distribution, the principle of rewards according to contribution is surely incomplete, since it can only apply to able-bodied adults in the active working population. It excludes children, the aged, the infirm. I do not mean to say that those who maintain that rewards should be according to contribution also maintain that children, the aged, the infirm should, in justice, receive nothing. But in order to resolve the just share of the economically inactive, we need a principle other than ‘rewards according to contribution’. The argument for increased old-age pensions cited above could be interpreted to imply that, in old age, we deserve income according to what we did contribute while active. But this principle cannot be applied to the congenitally disabled or to children. Children present a problem to all principles of just distribution that depend on merit, effort, production. So does the bearing and nurturing of children, as George Bernard Shaw brings out in his comment: the clearest case in the world of a person providing something herself by her own painful, prolonged and risky labour is that of a woman who produces a baby; but then, she cannot live on the baby: the baby lives greedily on her. (Shaw 1932: 21) So, rewards according to contribution is a principle which can only be applied to a part of the population, roughly the part that is productive in the sense that they are able to produce goods and services that can be sold in the market.

The fruits of our labour But even with this restricted application, not every one will agree that rewards according to contribution is a just principle. Let us imagine that it is possible to identify the fruit of every person’s labour, and that every one has the right to keep all his fruit, but nothing else. (I like to think of the fruit as apples.) Consider then which factors may contribute to unequal crop, and which, if any, of these factors would make the ensuing inequality just, or unjust. Free choice Some differences occur because people choose differently. Some work night and day, others prefer to have some leisure. If things go according to plan, the crop of apples will vary correspondingly. This is the situation where we feel that keeping the fruit of one’s labour is reward according to merit and that this is a just principle. The ant is not obliged to share with the grasshopper. Ownership of natural resources In agricultural societies, inequality in ownership of land is the main source of economic inequality, and land reform is seen as the key to fighting poverty. In many countries, ownership of, and access to, water is of equal importance. Possession of other scarce natural resources creates inequalities between countries as well as between persons: inequalities that are difficult to regard as merited. It is hardly reasonable to consider the wealth accruing

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Theories of justice

to Norway from the oil deposits in the North Sea as in any sense merited by the efforts of the Norwegian people. Ownership of capital Capital is a resource created by human efforts, unlike the resources that are Nature’s bounty. But today’s stocks of capital were created, at least in part, by past generations, and bequeathed to the present generation through inheritance. The role of private ownership of capital in creating economic inequalities between persons is, of course, highly contentious. But there seems to be a consensus that riches acquired through inheritance are not merited (which is not to say that there is consensus that inherited wealth is unjust). Human capital By human capital is meant the competence and ability of the individual person, acquired by formal education and practical training. Our human capital is certainly at least partly part due to our own efforts. But it is also partly due to our environment as children. It is well known that poverty and a deprived background is a grave handicap for children at school. Human capital, once acquired, cannot, like resources and physical capital, be redistributed from one person to the other. But the means of acquiring human capital, access to education and a nurturing environment, can be distributed by the government. Talents John Rawls writes: ‘It seems widely agreed that no one deserves his place in the distribution of native endowments any more than one deserves one’s initial starting place in society’ (Rawls 1999a: 170). Nonetheless, many people feel that talents should be rewarded. On the other hand, we may feel differently about the lack of talents, and agree that nobody has deserved to be born blind or with any other handicap. Therefore, they do not deserve punishment. It may also be worth noting that what counts as talents on the one hand and handicaps on the other, depends on the kind of society we live in. Legend has it that Homer was blind. He may not have been rich, but he is certainly famous. Being blind was not necessarily a handicap for bards in preliterate society, and may even have been an advantage in memorising their long epics. Also, reading Homer, or the Norse sagas, we may well feel that some of their great heroes would have cut less imposing figures in modern politics or business. Equally, we may feel that some of our contemporary great men would not have shown up to their advantage in the Trojan war. Uncertainty and luck In one sense, our lives, our successes and failures are almost entirely due to luck, because we do not choose where and when we are born, or as who. In most of the world, it is, for example, a misfortune to be born a woman. But luck is also a factor in the course of the rest of our lives. Napoleon is reputed to have considered luck the most important personal quality of his generals. In agriculture, it is clear that the luck of the weather influences the crop. In industry, it is acknowledged that capital is needed for risky ventures, and luck certainly is of importance when playing the stock exchange. One of the great Victorian entrepreneurs in Britain said that, ‘to succeed, you need to take risks, and you need a great deal of luck’ (Atkinson 1983: 183). Even so, we find the winners often reluctant to acknowledge that they have been lucky.

Deserts and the fruits of our labour

19

Most of the circumstances listed above are outside our individual control. Our success in life will in practice be a mixture of free choice and various contingent circumstances, and it is difficult, to say the least, to disentangle what is what in an individual career. Contingencies may also interact with each other, and with free choice in various ways. A person born in difficult circumstances may for instance choose to make little effort, since the chance of being rewarded is in any case small. A person with the same mentality, but from a more favourable background, will choose to make an effort in the near certainty of obtaining a suitable reward. The part played by luck and uncertainty is particularly complicated. Some random events are completely outside our own control, like the weather. And even the most careful motorist is exposed to accidents through the carelessness of others. On the other hand, some risks are taken willingly, like buying and selling shares, gambling and engaging in dangerous sports. Ronald Dworkin has coined the term brute luck for random events like the weather and option luck for risks undertaken deliberately. But he also writes: ‘Obviously the difference between these two forms of luck is one of degree, and we may be uncertain how to describe a particular piece of bad luck’ (Dworkin 1981b: 293). Even more to the point: it is in many cases impossible for others to know whether my luck is brute luck or option luck in a particular case. Take the case of single mothers. Since no contraceptives are 100 per cent effective, there is always an element of chance in conception. We have no way of knowing whether an individual’s unwanted pregnancy is due to carelessness, bad luck or a mixture of the two. There are many who agree with John Roemer, when he writes: justice requires the equalization of some kind of advantage insofar as that advantage is the consequence of circumstances and traits for which persons should not be held responsible, but allows differentiation of advantage insofar as it results from circumstances and trait regarding which the person should be held responsible. (Roemer 1996: 8) The problem is how to distinguish between the two kinds of traits and circumstances in practice.

4

Welfarism: utilitarianism and welfare economics

The greatest happiness of the greatest number is the foundation of morals and legislation. (Jeremy Bentham)

The term welfarism was coined by the British economist John Hicks (1981: 136). It has been introduced into contemporary debate about social justice by Amartya Sen. Welfarism is a term denoting all theories that demand that we judge the state of a society in general, and just distributions in particular, by the welfare of the people concerned, and by their welfare only. Welfare is an emotional state, subjectively experienced by the person herself. More or less synonymous to welfare are the terms well-being, happiness, desire fulfilment, utility. Utility (from Latin ‘utilis’: useful) is the preferred term in economic analysis, and it is also the root of the word ‘utilitarianism’. In Chapter 2, I wrote that the concept of distributional justice only makes sense for transferable goods: goods that it is possible to portion out and transfer to individuals. Now, welfare is obviously not transferable in this sense. Nor is it clear that welfare is a scarce good. It is far from obvious that my welfare can only be increased at the expense of the welfare of another person. On the other hand, it is also obvious that welfare is influenced by economic goods. Man does not live by bread alone, but the welfare of a hungry person increases when she is given bread to eat, or money to buy bread. So, distribution of economic goods is up to a point distribution of welfare. Welfarism implies that the distribution of economic goods is evaluated by the effect it has on the welfare of the persons concerned. There are several welfarist schools of thought. Two notable examples of welfarist theories are utilitarianism and welfare economics. While utilitarianism is a school of moral philosophy, most economists would claim no more for welfare economics than its being a practical tool for analysing ‘economic issues, that is, the problem of allocating scarce resources, and the associated question of the proper distribution of income’ (Hammond 1982: 85). A typical statement from an economist is: The measurement of welfare forms the foundation of public policy analysis. A full consideration of taxes, subsidies, transfer programs, health care reform,

Welfarism: utilitarianism and welfare economics

21

regulation, environmental policy, the social security system, and educational reform must ultimately address the question of how these policies affect the well-being of individuals. (Slesnick 1998: 2108) The quotation above is from a survey of methods for measuring welfare. Now, we may well ask how ‘an emotional state, subjectively experienced by the person herself’ can be quantified, measured with a number. The short answer is that it cannot. What Slesnick means by ‘measuring welfare’ is measuring proxies for welfare, that is, some variable or variables that are correlated with welfare. For instance, if we can assume that the welfare of an individual increases when income increases, ceteris paribus, income can be used as a proxy for welfare. Then, if a certain policy increases income, we know that welfare also increases, and this knowledge is sufficient to evaluate the policy for many practical purposes. But when analysing ‘the proper distribution of income’, it is not sufficient to know that welfare and income are correlated. Suppose two people have the same incomes. Can we conclude that their welfares are also equal? This question raises two distinct problems. The first problem is that of different tastes and needs, what in the literature is called preferences. The second is that of interpersonal comparability. If two people have identical preferences, we may tentatively conclude that equal incomes will provide them with equal welfares. The conclusion is tentative, because of the second problem. Many thinkers claim that it is meaningless, impossible, to compare the emotional state of different persons. Others claim that it is possible, by empathy, for one person to put herself in the other’s place, and so judge what the other person’s feelings are. In this chapter, welfarist theories of justice will be discussed as if individual welfares are both fully measurable and comparable from one person to the other. The reason is that mathematical analysis is a useful tool for investigating the logical implications and other properties of welfarism, and mathematical analysis presupposes that welfare can be meaningfully expressed in real numbers. When practising welfarist policies, we do not in general need the high level of precision of some of the following analysis. No distributional policy is tailored to the exact needs of the single individual. Taxes and public benefits are designed to fit the approximate needs of broadly defined groups such as families with children, senior citizens and wage-earners.

Utilitarianism Utilitarianism is a philosophical and ethical system covering both personal ethics and social justice; however, only those aspects that have a bearing on distributional justice are being considered, here. Jeremy Bentham who is quoted at the beginning of this chapter is considered to be the founder of utilitarianism. Bentham’s famous declaration was apparently first formulated by Francis Hutcheson: ‘. . . that action is best, which procures the greatest happiness for the greatest numbers; and that, worst, which, in like

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manner occasions misery’ (Hutcheson 1725).1 Another well-known advocate of utilitarianism is the economist and philosopher John Stuart Mill. The contemporary formulation of Bentham’s declaration is that the goal of public policy should be to maximise the total welfare of the population, total welfare being either the sum or the average of all individual welfares. Mathematically, maximising total welfare in the utilitarian sense is equivalent to maximising either W = U1 (·) + U2 (·) + · · · + Un (·)

(4.1)

or W =

1 [U1 (·) + U2 (·) + · · · + Un (·)] n

(4.2)

where the symbol Ui (·) represents the welfare of person i, and we do not specify which variables actually determine her welfare. Note that the welfare of every individual contributes equally much to total welfare; in this sense, utilitarianism treats all persons as equals. The above two formulations of utilitarianism are equivalent when the population number is constant, but may lead to different conclusions about population policy. In the following, I shall let utilitarianism be represented by the version in equation (4.2). Within this framework, there are also several versions of utilitarianism. One distinction is that between rule utilitarianism and act utilitarianism. Rule utilitarianism concerns, as the name makes clear, the basic principles and rules of society. Act utilitarianism analyses concrete actions here and now. A well-known example may illustrate the difference. It is not difficult to think of situations in daily life where the consequences of lying are beneficial and increase the welfare of everybody concerned. It is equally clear that the only beneficial rule must be to tell the truth. There are also different ways of defining what is meant by happiness or welfare. The most widespread version of modern utilitarianism is preference utilitarianism. When defining welfare, the preference utilitarian respects the individual’s own tastes and opinion of what determines his welfare. A leading modern utilitarian, John C. Harsanyi, writes: More fundamentally, preference utilitarianism is the only form of utilitarianism consistent with the important philosophical principle of preference autonomy. By this I mean the principle that, in deciding what is good and what is bad for a given individual, the ultimate criterion can only be his own wants and his own preferences. (Harsanyi 1982: 55) Preference utilitarianism is in accordance with the definition of welfarism, on p. 20: ‘Welfare is an emotional state, subjectively experienced by the person herself’.

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23

Preference utilitarianism is not based on specific assumptions about what determines the welfare of an individual. In particular, it does not assume that individuals are egoistic, or that welfare is decided purely by economic goods. Also, a preference utilitarian does not, or not necessarily, assume that people always act so as to maximise their own welfare. Why should a government aim to maximise the sum of individual welfares? One answer may be that it goes without saying that a government should act for the good of the inhabitants of the country, at least in a democratic society. Furthermore, it is self-evident that in a democratic society, the good of every citizen should count equally much. But, as we shall see, it is not self-evident that the good of the citizens should be their subjective sense of welfare. Nor is it self-evident that the good of society should be a simple sum of the good of each citizen; there are other ways of ensuring that each person counts the same as every other person. Another answer is that utilitarianism is what every citizen would choose as the basis of government policies in his own enlightened self-interest if he had to choose a policy from behind a veil of ignorance. This way of justifying utilitarianism was developed by John Harsanyi and is described in Harsanyi (1982). To explain the reason behind this manner of thinking, assume that individual welfare is determined by income only, and imagine a citizen choosing how income should be distributed if she did not know where in the distribution she herself would end up. In a society consisting of n persons, there are n incomes, and there is a probability equal to 1/n of receiving one particular income. As explained in Appendix A, a citizen behaving according to the principles of rational choice under uncertainty would choose to have income distributed so as to maximise average welfare: W =

1 [U (Y1 ) + U (Y2 ) + · · · + U (Yn )] n

(4.3)

In equation (4.3) the symbol U (Y1 ) represents the preferences of our citizen, in this case the welfare she obtains from an income equal to Y1 . Equation (4.3) is different from equation (4.2) in that there is no subscript marking the difference in preferences between different persons. A self regarding person would wish the government to act so as to achieve the highest possible welfare according to her own preferences. In order to obtain the rule that government should respect the different preferences of citizens, the terms of the choice have to be put in a slightly different way. Harsanyi introduces the concept of moral preferences as distinct from the preferences describing a person’s own taste. The moral preferences are those of a benevolent and impartial observer of society. Being benevolent, the observer would favour the welfare of every citizen; being impartial, he would give the welfare of all citizens equal weight. Harsanyi then proves that, under certain technical assumptions, the observer would decide that society should maximise average individual welfare, as described by equation (4.2), which respects the differences in preferences. Another basis for equation (4.2) is given by Serge Kolm (1996: 194, 195). Kolm postulates a society consisting of n individuals with different, but given,

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preferences, and that each person has to choose how income should be distributed if he knows neither which preferences he will turn out to have, nor what his income will be. Note that both the Harsanyi and the Kolm justifications of utilitarianism as the result of a rational choice under uncertainty, lead to that version of utilitarianism which maximises average, not total utility. Their way of formulating the problem is very similar to that of John Rawls. The problem and possible solutions will be further discussed in Chapter 5.

Welfarism and equality In order to clarify some logical and mathematical concepts used in the analysis of distribution from a welfarist point of view, I shall consider a greatly simplified situation where welfare is determined solely by income, and the distribution of income therefore determines the distribution of welfare. In economic analysis, the welfare of the individual is called utility, U for short. The connection between income and utility is described by a utility function written as U = U (Y ). The utility function is the mathematical representation of a persons’s preferences and is usually assumed to be of the shape shown in Figure 4.1. As income increases, utility increases, but the higher the income the smaller is the increase. The increase in utility due to an increase in income of one unit, is called the marginal utility of income. The utility curve in Figure 4.1 implies that the marginal utility of income (MU ) is decreasing, as shown. From now on I shall use the term individual welfare as synonymous with utility in the economist’s sense. There is unfortunately no agreed terminology. The so-called pure distribution problem is the problem of how to distribute a given total income among several persons. It is solved differently by different welfarist principles. In the section ‘Egalitarianisms’ of Chapter 2, I wrote that there are several egalitarianisms. Three of them are possible in the simple case presented here: equality of welfare, equality of income and utilitarian equality.

MU

U U (Y )

MU (Y ) Y

Figure 4.1 Utility and marginal utility as functions of income.

Y

Welfarism: utilitarianism and welfare economics

25

UI (YI)

Ivar’s utility

Kari’s utility

UK (YK)

YI

YK Income

Figure 4.2 Welfare egalitarian distribution of income.

The implications for the distribution of income of two egalitarianisms, welfare egalitarianism and utilitarianism, will be considered. A welfarist egalitarian holds that welfare should be equally distributed. The ensuing distribution of income depends on the shape of the utility functions. If two persons have identical utility functions, equality of welfare always implies equality of income. If not it does not. Figure 4.2 shows the distribution when the utility functions are different. In the figure, the width of the horizontal axis equals the size of the income to be distributed. Ivar’s income is measured from left to right, Kari’s income from right to left. The corresponding utility functions are UI (YI ) and UK (YK ), where YI is Ivar’s income, YK is Kari’s income and total income equals Y = YI + YK . Kari’s welfare increases faster with income compared to that of Ivar. Equality of welfare therefore implies that Ivar’s income should be greater than Kari’s, since he needs more to achieve a given level of welfare. A utilitarian wants total welfare in society to be as large as possible, which is equivalent to maximising the sum W = UI (YI )+UK (YK ) subject to Y = YI +YK . The solution to this maximising problem is to distribute income so that the marginal utilities of Ivar and Kari are equal. If the marginal utilities were unequal, say Ivar’s were larger than Kari’s, it would be possible to increase total welfare by transferring one unit of income from Kari to Ivar. By assumption, such a transfer would increase Ivar’s welfare by a larger amount than the corresponding decrease in Kari’s welfare. The distribution of income maximising total welfare is shown in Figure 4.3. The utility functions are the same as in Figure 4.2, but the graphs shown are of the marginal utilities, not the total utilities, of Ivar and Kari. We see that equality of marginal utilities implies that Kari’s income should be greater than that of Ivar. Kari is, to use Amartya Sen’s expression, a more efficient utility machine than Ivar. Favouring Kari increases social welfare more than favouring Ivar. A fortiori, when Kari’s income is larger than Ivar’s, her welfare is higher than his.

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MUK Kari’s MU

Ivar’s MU

MUI

YK

YI Income

Figure 4.3 Utilitarian distribution of income.

We have seen then, that when utility functions are different, equality of welfare implies neither equality of income nor maximum welfare. A necessary and sufficient condition for equality of welfare, equality of income and maximum welfare always to coincide is that everyone has the same preferences. Neither the welfare egalitarian nor the utilitarian cares how it comes about that Ivar and Kari have different preferences. But many people would find the reasons behind their differences to be ethically relevant. Let us say that Ivar has a physical handicap, he is blind for instance. In that case, many would find unjust a distribution of income which gave him less than Kari because he needed more. On the other hand, Ivar may have expensive tastes and be unable to achieve welfare without enough money to pay for luxury cars and hand-made shoes. In that case, equality of welfare between Ivar and Kari might well seem ethically unacceptable.

Social evaluation functions The utilitarian rule W =

1 (U1 + U2 + · · · + Un ) n

(4.4)

is a rule for evaluating the state of society by calculating the average individual welfare of its citizens. It is an example of a social evaluation function. Such functions are widely used by economists when analysing distributional issues. A social evaluation function is any rule ranking the outcomes of the economy by means of a real number. In welfarist analysis, the outcomes are evaluated by their effects on individual welfares, and the social evaluation function serves to weigh the individual welfares against each other. The evaluation function is then usually called a social welfare function, and its values are called social welfare, W , as distinct from the individual welfares U . The utilitarian rule in equation (4.4) is a utilitarian social welfare function.

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27

In the expression ‘social welfare’, the word welfare cannot have the same meaning as in ‘individual welfare’ if we accept the definition: Welfare is an emotional state, subjectively experienced by the person herself. Expressions such as ‘emotional state’ and ‘subjectively experienced’ do not make sense applied to society as a whole. I therefore prefer the term social evaluation function, and shall try to avoid the expressions ‘social welfare’ or ‘the welfare of society’. Also, a social evaluation function does not have to be defined on individual welfares, as we shall see in Part II, Chapter 13. In the present chapter, we shall study welfarist social evaluation. The concept of social welfare functions was introduced by the economist Abram Bergson (1938). There is no agreement among economists that social evaluation functions are useful. One criticism is that they are meaningless, since individual welfares are neither measurable nor comparable. Another, and a more general, line of criticism is that there is no basis for postulating that a democratic government should, or would, base its policies on a social evaluation function. The foundation for the latter opinion was laid by Kenneth Arrow (1951), and is called Arrow’s possibility theorem. Arrow showed that, given some very weak assumptions that should apply to any democracy, there is no way of decision-making among citizens that would lead them to adopt a social evaluation function whatever their preferences. This means that for every democratic procedure, it is always possible to imagine individual preferences that would block a social evaluation function. Arrow’s possibility theorem should not, however, be understood to imply that a social evaluation function, democratically arrived at, can never exist. The members of a society may well have preferences and procedures that result in a social evaluation welfare function; Arrow has proved that this cannot always be the case. For the reasons outlined above, many economists feel that their discipline should not concern itself with issues of justice in distribution. On the other hand, many economists do address issues where questions of just distribution arise, and when they do, their analysis is based on a welfarist social evaluation function more often than not. Such functions therefore represent a widely used way of thinking about distributional justice. A useful way of studying the properties of social evaluation functions is by diagrams like Figure 4.4. For practical reasons, we again assume that there are just two persons in the economy. The curves are so-called social indifference curves: along a social indifference curve, no point is socially preferable to any other. The social indifference curve therefore shows all possible distributions of individual welfare which are equally socially acceptable. The straight lines in Figure 4.4 are the indifference curves of the utilitarian social welfare function. The greater the individual welfare, the better, or more preferred, is the state of society, so W 3 > W 2 > W 1 . An increase in the welfare of one person while that of the other is unchanged, is called a Pareto improvement. The straight line A–B illustrates a Pareto improvement in favour of Ivar. We see that a Pareto improvement increases utilitarian social welfare. The technical term is that the utilitarian social welfare function fulfills the Pareto principle.

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U⬘

Ivar’s welfare

E

B E* A

W2 W1 Kari’s welfare

W3

Figure 4.4 The utilitarian social welfare function.

It is also symmetrical: a distribution of welfare giving 5 to Kari and 7 to Ivar is equally as good as 7 to Kari and 5 to Ivar, since 5 + 7 = 7 + 5. It is in this sense that utilitarianism treats all persons as equals. Now, imagine that society disposes of a given amount of welfare, and that individual welfare may be freely transferred from one person to the other. The utilitarian social indifference curve represents points where the sum of individual welfares is constant. It follows that any transfer or redistribution of individual welfares will leave the utilitarian social evaluation of society unchanged. The utilitarian social welfare function is inequality neutral (in individual welfares). The state of society can only be improved by increasing the individual welfare of one or more of its members. The inequality neutrality of utilitarianism has been criticised by John Rawls and Amartya Sen, among others. John Rawls, in particular, writes that utilitarianism is in contradiction to the Kantian principle that men should treat one another as ends in themselves, never as means to an end: ‘. . . it treats them as means by allowing higher life prospects for some to counterbalance lower life prospects for others who are already less favourably situated’ (Rawls 1999a: 157). Note that here, Rawls implies that a transfer of welfare from the well off to the worse off does not contradict the Kantian principle. The general class of social evaluation functions most frequently studied in economic welfare theory is written: W = W (U1 , U2 , . . . , Un )

(4.5)

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U

Ivar’s welfare

E

A

E* W2 W1

O

U⬘ Kari’s welfare

Figure 4.5 A Sen function.

They are called Bergson–Samuelson social welfare functions. They are normally assumed to fulfill the Pareto principle, but may otherwise be of any shape. For the purposes of studying distributional justice, inequality averse and symmetric social evaluation functions are of special interest. These do not have any particular name in the literature, for convenience I shall call them Sen functions. The social indifference curves of a Sen function are shown in Figure 4.5. As before, W 2 > W 1 . The line O–E represents all equal distributions of individual welfare, while the straight line U –U
represents points where the sum of individual welfares is constant. Like the utilitarian social evaluation function, the Sen function is symmetrical round the equality line, and so treats all persons as equals. It also satisfies the Pareto principle, as is easily verified. In point A, Ivar’s welfare is greater than Kari’s. The line U –U
through A represents all possible transfers of welfare between Ivar and Kari when the sum of welfares is unchanged. Moving downwards and to the right from point A along U –U
towards the equality line O–E represents transfers that decrease Ivar’s welfare and increase Kari’s until equality of welfare is reached in point E ∗ . Such transfers are called equalising transfers. Starting from point A, the U –U
line crosses social indifference curves that represent states preferred to A, and equalising transfers result in states that are socially more and more preferable until perfect equality is reached in E ∗ . A Sen function is therefore said to be inequality averse.

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When social outcomes are evaluated by a Sen function, the state of society can be bettered in one of two ways: by making the distribution of individual welfare more equal, and by increasing the sum of individual welfares. The shape of the function decides how the two possibilities of social improvement should be weighed one against the other. To the extent that individual welfare depends on wealth, the social evaluation function is an instrument for measuring the trade-off between wealth and equality. In the case of only two individuals, the degree of inequality aversion is easy to read off graphically by the degree of curvature of the social indifference curves. In the more general case, measuring inequality aversion is more complicated. Note also that the degree of inequality aversion of a given evaluation function does not have to be the same in all states of society. It is sometimes claimed that policies to increase economic equality make the economy less efficient, and therefore result in there being less to distribute. The claim that greater equality leads to a decrease in the size of the pie is contentious. However, even if the claim is true, a social evaluation function may well prefer an equally distributed small pie to a bigger pie distributed unequally. The trade-off is illustrated in Figure 4.6. The figure illustrates the distribution between Ivar and Kari. Kari is the economically active person, producing society’s wealth. Ivar is a disability pensioner, say, and dependent on the income generated by taxing Kari. The analysis is built on the assumption, usual in economic models of optimal taxation, that Kari works

UK + UI = U

Ivar’s welfare

E

R S W

U

O

L Kari’s welfare

Figure 4.6 Equality and wealth.

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less the more she has to pay in taxes. On this assumption, transfers from Kari to Ivar decrease total wealth. Ivar’s individual welfare is shown along the vertical axis, Kari’s along the horizontal axis. The curve shows all possible distributions of welfare between Ivar and Kari, L being Kari’s welfare when she is allowed to retain the whole pie for herself. Increasing taxation makes Kari produce less. As taxes (and hence also transfers to Ivar) increase, Kari’s welfare decreases while Ivar’s increases up to the point R. Beyond R, both Ivar’s and Kari’s welfares decrease. A utilitarian social evaluation function will decide that U is the best state achievable. The result of a Sen evaluation depends on the degree of inequality aversion; a moderate inequality averse function chooses the point S. Note that neither the utilitarian nor the Sen evaluation function ranks the point of maximal production, L as the best. The assumption that sharing with Ivar acts as a disincentive for Kari’s working is of course decisive for the results. If Ivar were Kari’s son, say, she might well work harder in order to provide for him than if she were responsible for herself alone.

Welfarism and ethics Some consequences of welfarism contradict several fairly widespread ethical intuitions. I shall first describe some ethical properties of welfarism, properties that are logically implied when the good of society is determined by individual welfares only. Then some ethical criticisms of welfarism will be presented and discussed. Ethical properties of welfarism Individualism Welfarism is individualist; it is based on normative or ethical individualism. The welfare of the individual, and the individual’s welfare only, determines the state of society. Nothing can influence the state of society unless it influences the welfare of at least one individual. Society, the community, the nation have no intrinsic value for welfarism, and there is no such thing as the common good, existing independently of individual welfare. Humanism Most versions of welfarism are also humanist, or as some would put it, anthropocentric. Only the welfare of human beings count. Nature, the environment, the rights of animals, do not in themselves influence the state of society. Effects on the environment will be of importance to the state of society to the extent that environmental conditions determine the individual welfare of human beings, but only to that extent. Respect for preferences Most versions of welfarism, and especially welfare economics, respect the preferences of the individual. In economics, this principle is called consumer sovereignty. In utilitarianism, as we have seen, it is called preference utilitarianism.

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Consequentialism Welfarism is consequentialist. The state of society is assessed entirely by outcomes. Ethical principles, rights, liberties, have no intrinsic value, but are deduced from their effects on the welfare of individuals. What counts is individual welfare, not how that welfare is obtained. It should be emphasised that none of the above implies that welfarism assumes human beings to be anthropocentric, or individualist in the sense of being egoistic or unconcerned with society and the common good.

Critique of welfarism A respectful welfarist does not try to determine what is good for people, but relies on people deciding that for themselves. Whatever the individual herself regards as good for her, and for whatever reason, is good for society. Tobacco is a good as long as there exist persons who prefer smoking to not smoking. It is up to the smoker herself to weigh the pleasure of smoking against the harmful effects as far as her own health is concerned. A respectful welfarist will recommend that measures be taken against smoking only in so far as smoking adversely affects others than the smoker herself. This respect for preferences may create ethical problems. There are people who have repulsive and ethically unacceptable preferences. One extreme example is sadism. Welfarist ethics will not normally accept sadistic behaviour. But the prohibition is based on the assumption that the pleasure of the sadist is not sufficiently great to outweigh the sufferings of the victim, and not on an ethical absolute. Envy is a less extreme but in some ways more problematic example. When distributing income between an altruistic person and an envious person, an inequality averse welfarist may plausibly decide to compensate the envious one for the loss of welfare caused by envy. Another much discussed problem is that of expensive preferences, thoroughly analysed by Ronald Dworkin (1981a). Some people are content with a simple life, others are unhappy without vintage champagne and caviar. The latter group clearly need a higher income than the former to achieve the same level of welfare. Is such a distribution just? The consequences for distribution of economic resources of repulsive preferences or expensive tastes depend on how these traits affect the mathematical shape of the utility function as well as on the shape of the social evaluation function applied. For the utilitarian, the only aspects of preferences that count when distributing income are those that affect the marginal utility of income. Expensive tastes may be equivalent to having a small marginal utility of money, to being an inefficient utility-producing machine. In that case, we saw in the section ‘Welfarism and equality’ that a utilitarian would award the luxury-loving Ivar, less than his equal share of income. But an inequality averse social evaluation function would tend to increase Ivar’s share until he obtained equal welfare with the other members of society.

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On the other hand, there may be other reasons than a penchant for luxury goods why a person needs extra money to achieve a given level of welfare. Physical illness may lead to needs for medical care, medicines and/or an expensive diet. One may well find it just that people should receive extra income to cover the costs of a medically prescribed expensive diet, but not frivolous expensive tastes. Some of these ethical problems may be tackled by modifying the absolute respect for peoples’ preferences in various ways. Harsanyi (1982) proposes two methods. One method is to distinguish between irrational and true preferences, where the true preferences: are the preferences he would have if he had all the relevant factual information, always reasoned with the greatest possible care, and were in a state of mind most conducive to rational choice. Given this distinction, a persons’s rational wants are those consistent with his true preferences and, therefore, consistent with all the relevant actual information and with the best possible logical analysis of this information, whereas irrational wants are those that fail this test. (Harsanyi 1982: 55) The second method is that of excluding antisocial preferences: But I think we have to go further than this: some preferences, which may well be their ‘true’ preferences under my definition, must be altogether excluded from our social-utility function. In particular, we must exclude all clearly antisocial preferences, such as sadism, envy, resentment and malice. ··· Utilitarian ethics makes us all members of the same moral community. A person displaying ill will toward others does remain a member of this community, but not with his whole personality. That part of his personality that harbors these antisocial feelings must be excluded from membership, and has no claim for a hearing when it comes to defining our concept of social utility. (Harsanyi 1982: 56) However, Harsanyi’s distinction between acceptable and antisocial preferences raises some further problems. One seems purely technical, but may nevertheless be serious: how is it possible to cleanse a person’s preferences of his antisocial tendencies? The second problem is: who decides which preferences are antisocial, and by which criteria? Harsanyi’s ‘sadism, envy, resentment and malice’ seem straightforward. Other cases are less clear. There are many instances of disagreement and serious public debate about which preferences should be allowed and which prohibited, and concerning what kind of preferences have ethical relevance. Sexual harassment is one example. One person’s sexual harassment is another’s friendly flirt or harmless joke; one person’s righteous anger is the other’s paranoia. The disagreement concerns which person shall have the right to define the other’s behaviour as antisocial and malicious.

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The opposite of envy is altruism. The altruist obtains welfare from the well-being of one or more other persons. Even if none of the others is envious, an inequality averse welfarist distribution of income will be unfavourable to the altruist. So, the weeding out of envy is not sufficient to ensure an ethically acceptable distribution: welfarism would still tend to reward egoism and punish altruism economically. Also, the problem of expensive tastes, which may be either frivolous or due to physical or mental ailments, is not solved by excluding antisocial preferences; a taste for vintage champagne can hardly be considered antisocial. Some people may be efficient producers of utility simply because they have a sunny disposition, or – perhaps – because their system creates plenty of endorphins. In the literature, this is called the problem of Tiny Tim, after the little crippled boy with a gift for happiness in Charles Dickens’s A Christmas Carol. A utilitarian would give Tiny Tim a higher income than others less fortunate while a welfare egalitarian would give him less: both distributions seem equally arbitrary. A related problem stems from what is called adaptive preferences. A famous example is given by Sen. He cites an Indian survey from 1944 which showed that just 2.5 per cent of the widows questioned, but as many as 48.5 per cent of the widowers, considered themselves to be ‘ill’ or in ‘indifferent health’. The survey was carried out in Bengal the year after the Great Bengal Famine. Sen writes: ‘. . . the condition of women in India outside elite groups – and of widows in particular – is nothing short of scandalous, and the position of women in terms of nutrition tends to be particularly bad. . . . Quiet acceptance of deprivation and bad fate affects the scale of dissatisfaction generated, and the utilitarian calculus gives sanctity to that distortion’ (Sen 1984a: 309). The survey showed, not that the widows were in good health, but that they had resigned. Their expectations had adapted to their surroundings. What is needed are criteria for which preferences to respect and which to ignore, and these criteria cannot be based on the same preferences that they are to judge. One way of tackling the ethical problems of welfarism is suggested by the distinction between rule utilitarianism and act utilitarianism. We can think of justice as being decided on in two stages. In the first stage, long-term rules about individual rights and which preferences to accept are decided. These rules are then binding constraints on the social evaluation in the short run. This kind of procedure has been suggested by Y.-K. Ng (1990). It corresponds perhaps to John Rawls’ distinction between choosing the basic design of society on the one hand, and decision in individual cases on the other (see Chapter 5). But then again, we meet the problem of which preferences to apply to the long-term decision about rules. Our preferences are, at least to some extent, shaped by the society we live in. If these same preferences are then used to judge this society, a circularity arises. An even more fundamental critique of welfarism is the following. Not every person sees the pursuit of her own individual welfare as the ultimate purpose of her life. She may pursue goals like doing her duty, carrying out the will of God, contributing to the good of humanity or writing the Great American Novel. If this is so, welfarism, even preference welfarism, is not truly respectful of the individual’s own conception of what she wants from life. But then, a truly respectful theory

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35

of distributional justice needs another concept of the good to be justly distributed. Various attempts to define such a respectful good will be discussed in the following two chapters. Welfarism need not be respectful. The opposite of respectful welfarism is paternalism: the relevant authorities decide what is good for you. But paternalistic welfarism can easily become more authoritarian than benevolently paternal. The problems of welfarism are well illustrated by the nightmare conditions in Aldous Huxley’s novel Brave New World. In the book’s society of rigidly segregated castes, every person is happy with the position in which it has pleased the authorities to place her, being conditioned to it not only from birth, but from the embryo stage. And any momentary unhappiness or boredom is relieved by the drug ‘soma’.

5

John Rawls’s theory of justice

John Rawls’s book A Theory of Justice first appeared in 1971. In this influential book, Rawls sets himself the task of working out the fundamental principles for the just allocation of rights and duties in society, including the just distribution of economic goods. Rawls makes clear that his intention is not to study distribution in the short term, or to specific persons. He writes: [These principles] are meant to regulate basic institutional arrangements. We must not assume that there is much similarity from the standpoint of justice between an administrative allotment of goods to specific persons and the appropriate design of society. Our common sense intuitions of the former may be a poor guide to the latter. (Rawls 1999a: 64) It is fundamental to Rawls’s thought that the common ground of a society, what creates its cohesion, should be agreement on what institutions and arrangements are just. Such a basis of society is different from a society built on common ethnicity, religion or language, factors which are more commonly assumed to create the nation state. Rawls defines a liberal society as ‘a society that allows for a plurality of different and even incommensurable conceptions of the good . . . ’ (Rawls 1982: 160). The Rawlsian society is a liberal one. But a society is also a community of citizens, a place of social cooperation, where everyone depends on everyone else: The intuitive idea is that since everyone’s well-being depends upon a scheme of co-operation without which no one could have a satisfactory life, the division of advantages should be such as to draw forth the willing co-operation of everyone taking part in it, including those less well situated. (Rawls 1999a: 13) It is often thought important that society should be organised so as to retain the voluntary cooperation of its most resourceful and gifted members. But when we put the question as Rawls does above, we see that the most successful members of any given society are the ones with the most to lose from general non-cooperation,

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while the poorest are those with the least to give up. Therefore, the important point is indeed to secure the voluntary cooperation of the least successful.

The original position Rawls bases his theory of the just society on a version of the social contract. The Rawlsian social contract is the hypothetical contract free and equal human beings would agree upon should regulate the ‘basic institutional arrangements’ of society if they were able to free themselves from the prejudices and self-interest that arise from knowing what is to their own immediate advantage or disadvantage. Since agreeing to it is a voluntary act, the contract must be such that it can be unanimously agreed upon. Rawls argues that we can deduce the contents of this contract by a thought experiment. Imagine an original position, where all members of society meet to negotiate a contract that can be unanimously adopted. In this original position, the participants are ignorant of their own position in society. A veil of ignorance hides from them their sex, talents and other genetic endowment, their place in the distribution of economic and other resources, their place of birth, the economic and social positions of their parents, even their tastes and preferences, or life plan, as Rawls prefers to put it. From behind this thick veil of ignorance, the contracting parties are to decide upon what the just distribution of goods and burdens should be in a society that they themselves would want to live in. The choice is to be made by rational persons in enlightened self-interest; the participants are ‘mutually disinterested’, as Rawls puts it. The veil of ignorance hides only the parties’ own particular circumstances from them, it must not be taken to mean that they are generally ignorant. On the contrary, Rawls writes: It is taken for granted, however, that they know the general facts about human society. They understand political affairs and the principles of economic theory; they know the basis of social organization and the laws of human psychology. Indeed, the parties are presumed to know whatever general facts affect the choice of principles of justice. (Rawls 1999a: 137) The choice of social contract, or basic social arrangements, is thus in Rawls’s imagined original position the solution to a problem of choice under uncertainty. The uncertainty concerns where in the distribution of goods and burdens each particular individual will end up as well as what kind of life she will prefer to live. The choice concerns, among other features, which form of distribution the rational individual would then prefer. Rawls’s concept of the original position has been criticised by several thinkers, among them Habermas (1995), for being ‘monological’. The basis for the criticism seems to be that there is no plurality of voices and points of view represented;

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essentially, the parties in the original position are several copies of one single human being. Feminist critics have pointed out that, in particular, no women are present. The parties in the original position do not engage in conversation or exchange points of view. The criticism is in a sense correct since the parties are without individual traits or characteristics beyond being human. On the other hand, every conceivable kind of human being is a party to the Rawlsian social contract because the contracting parties have to take into account the possibility of turning out to be of this kind. We must think of the parties as souls, as Roemer (1996: 176) calls them, souls that may be incarnated in any and every possible human shape. When choosing a society that they themselves would want to live in, it is clear to the contracting parties that they must choose a society they would want to live in whatever their place in that society turns out to be. Women are represented in the original position by the fact that the souls, when incarnated, may turn out to be women. In fact, there is a probability of almost 50 per cent of being incarnated as a woman, which should ensure a contract with equal rights and opportunities for women and men. The original position is not a description of human behaviour or of any situation that has actually occurred; it is a model or a metaphor to enable us actual living human beings to reason about the just society. Brian Barry puts it like this: There never was and never will be an original position. Talking about what would go on in it is supposed to be a way of doing moral philosophy, not a branch of imaginative literature. (Barry 1989: 207) The people actually doing the moral philosophy will represent a diversity of characters and points of view. Not being as perfectly well-informed as the imaginary souls in Rawls’s thought experiment, they will necessarily have to, or at least ought to, engage in dialogue and exchange of information and points of view with others. Indeed, this is what Rawls himself has done through the years since A Theory of Justice first appeared, partly modifying his views, partly making them more explicit and precise, in continuous dialogue with his many commentators and critics. The assumption that the parties are ‘mutually disinterested’ has also been criticised as giving too narrow a view of human nature. But, again, this assumption is not an assumption about actual human beings. In several papers, Rawls explains that his theory of justice is not, and does not imply, a specific theory about human nature. The souls, when incarnated, may turn out to be egoistic, altruistic or envious, or to possess a mixture of all these three traits. Impartial justice is justice taking the rational self-interest of every single human being equally into account. The purpose of making the contracting parties ‘mutually disinterested’ is to ensure a social contract that guarantees impartial justice.

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The difference principle Rawls argues that rational parties in the original position would unanimously agree on a social contract based on the following two principles: Each person is to have an equal right to the most extensive basic liberties compatible with similar liberties for others. Second: social and economic inequalities are to be arranged so that they are both (a) reasonably expected to be to everyone’s advantage, and (b) attached to positions and offices open to all. (Rawls 1999a: 60) Rawls maintains moreover that the principle of equal rights to extensive liberty will take lexical, or absolute, priority before the second principle. The priority follows from the fact that the parties are ignorant of which lifeplans they will prefer. Therefore they will choose to allow any lifeplan, except lifeplans that limit the liberty for others. This aspect of Rawls’s social contract makes his just society a liberal one: a society which tolerates many different conceptions of the good life and many different kinds of lifeplans. The second principle: ‘reasonably expected to be to everyone’s advantage’ is Rawls’s first version of what he calls the difference principle. It is better known in another version where point (a) in the quotation above reads: ‘to the greatest benefit of the least advantaged (ibid.: 82)’. Here, for practical reasons, the least advantaged is understood to be the least advantaged group, not individual, since the least advantaged group is the easier to identify. This last version is also called the maximin principle by many commentators, though not by Rawls himself. The difference principle is an egalitarian one, but represents an egalitarianism which accepts that the way the pie is distributed may influence how much there is of it to distribute. It is the outcome of a trade-off between absolute equality and total wealth, and accepts certain, but not all, inequalities.

Illustrations of the difference principle Figures 5.1–5.3 illustrate some aspects of how the difference principle works in practice. For simplicity, they all assume that there is only one good to be distributed, called income. The goods to be distributed in Rawls’s social contract, primary goods as he calls them, will be considered in more detail in the section ‘Primary goods’. Choosing between distributions Figure 5.1 shows the connection between Rawls’s first and second version of the difference principle. Imagine that all the persons in a society are numbered according to the size of their income, the poorest is number 1 and the richest number n. The diagram shows their incomes on the vertical axis, starting with

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Income

IE FE

Persons

Figure 5.1 The difference principle in action 1.

Income

IE FE

Persons

Figure 5.2 The difference principle in action 2.

the lowest income, then the second lowest, and so on till the highest income. Full equality appears as a straight line (FE), and is the benchmark distribution. The distribution IE is an unequal one, but where all are better off than in FE. We see immediately that, when the benchmark distribution is full equality, an improvement for the worst off is a necessary and sufficient condition for everyone to become better off. In this case, therefore, the two versions of the indifference principle give identical results, and the maximin version may be taken simply as a simplified version of the first. Figure 5.2 is the same kind of diagram. It shows a case where IE gives a worse result for the poorest than FE, but a better result for nearly everyone else. By the indifference principle, distribution FE is to be chosen as the just one. This result has bothered many critics of Rawls. It would quite obviously not be the outcome of, say, a utilitarian evaluation. On the other hand, it is a consequence of Rawls’s interpretation of the Kantian principle that one person should never be used as the means to an end of other persons. The principle is violated, according to Rawls, when a person is forced to lose something, even if very little, in order to advantage someone who is better off than himself. In the distribution IE, the situation of the majority is improved at the cost of the (admittedly very small) minority of the very poorest.

Ivar’s income

John Rawls’s theory of justice

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R E

W U Kari’s income

L

Figure 5.3 The difference principle in action 3.

When transfers decrease the size of the pie Another illustration of the difference principle is shown in Figure 5.3. It is almost the same graph as in Figure 4.6 in the preceding chapter, and illustrates the same kind of choice between total wealth and equality in distribution. The good to be distributed in Figure 5.3 is not welfare, but income. Ivar’s income is shown along the vertical axis, Kari’s income along the horizontal axis. The curve shows all possible distributions between Ivar and Kari, L being the income produced when Kari is allowed to retain the whole for herself. Increasing taxation makes Kari produce less. As taxes (and hence also transfers to Ivar) increase, Kari’s income decreases while Ivar’s income increases up to the point R. Here, the greatest possible income for Ivar is obtained. Beyond R, both Ivar’s and Kari’s incomes decrease in absolute terms while Ivar’s share increases. The point E is the point of absolute equality. Here both Ivar and Kari receive less than in R. By the indifference principle, the distribution chosen will be R. For comparison, the points U and W show the optimal distribution of a utilitarian social evaluation function and a Sen social evaluation function respectively (assuming Kari and Ivar have equal preferences). The diagram shows that the indifference principle gives shares that are unequal, but less unequal than a utilitarian distribution. Furthermore, the difference principle gives Ivar more than would both a strictly egalitarian and a utilitarian distribution, and the R distribution is indeed to both Ivar’s and Kari’s advantage compared with full equality. Figure 5.3 is very similar to figures on pp. 66 and 67 in A Theory of Justice, but not identical.

The difference principle and the theory of uncertainty In the thirty years since its appearance, Rawls’s A Theory of Justice has been the subject of a great deal of commentary and, of course, criticism. The criticisms concern both the maximin principle that Rawls deduces from his original position,

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and his way of specifying the original position itself. Some of the points that have been made were considered in the section ‘The original position’, others will be considered below. Many commentators, for instance Barry (1989), Kolm (1996) and Roemer (1996) claim that the difference principle is not the correct solution to the Rawlsian problem of choice under uncertainty. Rawls himself writes that his theory of justice is part of the general theory of rational choice. The choice to be made by the parties in Rawls’s original position can be stated in a way similar to conventional analysis of choice under uncertainty. The parties in the original position have to choose one of a class of possible distributions of economic goods without knowing what their own place in the distribution will be. The outcome for each individual is decided by the shape and location of the distribution, as visualised in Figures 5.1 and 5.2. The greater the equality of the distribution chosen, the smaller the probability of either great poverty or great riches. This choice is formally the same as the choice to be made by an investor between several investment projects with uncertain outcome. As explained in Chapter 4 and Appendix A, the investor will choose the distribution that maximises his expected utility. The corresponding choice for parties in the original position would be a social contract based on a utilitarian social evaluation function. Roemer (1996: 181) has shown that the difference principle only corresponds to the maximisation of expected utility in the special case where the person concerned is infinitely risk averse. Unless we can assume that all human beings are infinitely risk averse, there would therefore not be agreement on the choice of distribution. Rawls thus seems to appeal to the theory of rational choice under uncertainty without being willing to accept the results of that theory. I am not persuaded that this line of criticism is well taken. It is not clear to me that a social contract designing the basic institutions of society can be found with the methods of conventional uncertainty analysis. On p. 36, Rawls is quoted as saying that ‘Our common sense intuitions of’ solving short-term problems of distribution ‘may be a poor guide to’ searching for the basic design of society. Specifically, the choice of income distribution in the Rawlsian social contract entails the choice of lifetime prospects: it covers your access to economic goods, your standard of living and your position in society, literally from the cradle to the grave. Now, the choice of distribution of lifetime income would seem to be of far greater import, and to call for a far greater degree of caution (risk aversion) than a single investment project affecting only a part of your life. It seems entirely plausible that such a choice would imply a special concern for the worst possible thing that could happen.

Primary goods Rawls rejects individual welfare as the good to be equally distributed. There are several reasons for this rejection, some of them related to the problems with welfarism discussed in Chapter 4. But the most basic reason for Rawls is probably that for him, social justice must be compatible with a society that allows ‘for a plurality

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of different and even incommensurable conceptions of the good . . . ’ (Rawls 1982: 160). Social justice cannot, then, build on the assumption that individual welfare in the sense of personal happiness is the one, final good for all persons. Rawls postulates that there exists what he calls ‘primary goods’ which determine social and economic inequalities in lifetime prospects. In A Theory of Justice Rawls describes primary goods as follows: These goods normally have a use whatever a person’s rational plan for life. For simplicity, assume that the chief primary goods at the disposal of society are rights and liberties, powers and opportunities, income and wealth. . . . whatever one’s system of ends, primary goods are necessary means. (Rawls 1999a: 62) The first edition of A Theory of Justice can be read as if primary goods are biologically determined, and that they are common to all human beings whatever our social circumstances. In other words: in order to find out which goods are primary ones, we have to know something about basic human nature. In later papers, particularly in Rawls (1982) and (1997), he explains that his theory is not connected to any particular view of human nature, and that the concept of primary goods should be understood as social primary goods. The qualifier social means that primary goods are what every adult person needs in order to participate fully in society as a citizen. Primary goods are therefore understood to be connected to the public sphere of life, not the private. In the article, ‘Social unity and primary goods’, Rawls expands the list of primary goods: (a) First, the basic liberties as given by a list, for example: freedom of thought and liberty of conscience; freedom of association; and the freedom defined by the liberty and integrity of the person, as well as by the rule of law; and finally the political liberties; (b) Second, freedom of movement and choice of occupation against a background of diverse opportunities; (c) Third, powers and prerogatives of offices and positions of responsibility, particularly those in the main political and economic institutions; (d) Fourth, income and wealth; and (e) Finally, the social bases of self-respect. (Rawls 1982: 162) In the paper quoted above, and elsewhere, Rawls makes clear that he thinks of the social contract as regulating rights and duties in public life only. This means inter alia that he does not visualise children as being parties to the contract. The boundary Rawls draws between public and private life is the conventional one, with the family belonging to private life. This view of his has been criticised by several women philosophers, who have pointed out that women’s position in society is

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strongly influenced by the way the family is organised, and that Rawls therefore in practice does not tackle the subject of freedom and equality for women. I shall return to this aspect of the Rawlsian theory in Chapter 8. Rawls also makes clear that social primary goods are meant to be those of use to normal, healthy adults. Although they are supposed to serve a person’s life-prospects, that is, throughout life, they are not meant to cover periods of sickness, the period of childhood, or the possibility of disabling accidents. Many commentators feel that this makes the concept too narrow. In particular, it does not sufficiently take into account that people are different and have different needs. There is a sense in which a disabled person needs a higher income in order to function in society than an able-bodied person. Rawls (1982) defends ‘income and wealth’ against this criticism by stating that, for example, health is not a social primary good, being what he calls ‘a natural good’ and therefore not subject to government distribution. Rawls acknowledges that, since there are several primary goods, there is an index problem when weighting them together for purposes of comparison. However, several of the goods on the list are to be equally distributed separately according to Rawls; this is in particular true of all political rights and liberties and the social basis for self-respect. In the final account, only the goods ‘powers and prerogatives of position’ and ‘income and wealth’ need to be weighted together in an index. Rawls also points out that the index-problem is made considerably easier by the difference principle. Applying the difference principle, we need only somehow identify the least advantaged group, which may well be possible without the exactness of a numerical index, and then construct an index for this one group in order to measure the consequences of basic policies. Apart from these comments, Rawls does not indicate how an index should be constructed. In several papers Rawls underlines the importance of having political objectives that are open to public debate, and therefore in some sense observable and understandable: ‘a practical and limited list of things (primary goods) which free and equal moral persons, . . . , can accept as what they in general need as citizens in a just society’ (Rawls 1982: 183). I think that is the reason why he has income and wealth on his list of primary goods, in spite of the objection that equal incomes may give very different life prospects if people have different objective needs for reasons that are beyond their own control. But there are difficulties with ‘income and wealth’ as a primary good also by Rawls’s own definition of, and intention with, social primary goods. Rawls, like many other philosophers, seriously underestimates the difficulties connected not only with the practical measuring, but also of the theoretical definition of income and wealth. The concepts of income and wealth will be discussed in detail in Part II of this book. Here, I shall briefly mention some problems of the concept of income that Rawls seems to ignore. First, there is the fact that cash income, at least to some extent, is a matter of choice, namely the choice between paid work and leisure. While a certain cash income is necessary for everyone, an income over and above this minimum is not

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a primary good in the sense that Rawls means it. If income is a primary good, it must be what economists call full income: that is, earning power (determined by the real wage rate) plus unearned income (capital income and transfers). But this is not a familiar concept to most people, and is not at the moment in practice observable. Moreover, even full income is to some extent a result of choice, since it depends on the length and contents of education, among other factors. Second, there is the problem of whether income is household income or individual income. In practice, household income is the target variable for government policy in many contexts, whether taxation or family support. Empirical studies of income distribution normally analyse household income as a matter of course, without further discussion. When defining income as household income, there is a tacit assumption that it does not matter whether the income accrues to the husband or the wife. But the demand for an independent income was, and is, of course central in the struggle for women’s liberation and economic emancipation. Taking the target variable for just distribution to be household income implies that women’s economic independence is of no importance to economic justice. Third, both in government policy and empirical analyses of income distribution, account is to some extent taken of different needs, in that the size and composition of the household is usually taken into account when measuring income. But there is strong disagreement about the measuring methods, and, indeed, about the social justice of making such corrections. This last disagreement stems from different ideas about the division of responsibility between the parents and the government for the economic provision for children. It is not uncommon to maintain that parents voluntarily acquire children, and that therefore expenditure on children is no more relevant to the measurement of income than expenditure on consumption goods. Income, then, is not a social primary good in Rawls’s sense because it is not a good everyone always wants more of, whatever her preferences. Neither is income a practical concept that free and equal citizens can easily agree on: its very definition depends on one’s views on the just economic position of children and married women.

6

Equality of what? Resources and capabilities

Approaches to economic equality Economic equality in one respect implies inequality in other respects when people are different, and make different choices. In addition to the examples given in Chapter 2, we saw in Chapter 4 that equality of welfare entails inequality of income, and that equality of marginal utility can imply inequality of both income and welfare. Rawls makes it quite clear that equality of primary goods is not meant to give equality of welfare. Two other non-welfarist approaches to equality will be discussed here: resources and capabilities. These approaches are both liberal in the same sense that Rawls’s theory is liberal. Their proponents are concerned that it is not the business of the government to determine what the final good of our lives is or ought to be. Each person must decide for herself what she wants to make of her life. The business of government in the just society is to provide every person with the social and economic opportunity to pursue her own idea of the good life, whatever that may be. From the same liberal point of view, Christine Korsgaard distinguishes between three different ways of assessing proposals on what constitutes the quality of life: First, we may assess it simply as a philosophical proposal about what a good life is. Second, we may assess it for its legitimacy as a political objective: whether it is the sort of thing we ought to bring about through political means. And third, we may assess it for its utility in determining actual political and economic policy – that is, whether it provides accurate enough measures to assess the effects of policy. (Korsgaard 1993: 44) The various quantities proposed as political objectives of just distribution may perhaps roughly, and as a drastic simplification of fairly complex theories, be seen as inputs one into the other. Resources are necessary for obtaining Rawls’s primary goods, primary goods create capabilities, capabilities are necessary for functionings which in their turn determine welfare, achievement or any other final good that the individual pursues. Viewed in this way, they appear to indicate that

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various thinkers draw the boundaries between the responsibility of the government and the responsibility of the individual at different steps in the process leading from resources to the final good.

Dworkin and equality of resources Equality of resources has been proposed by Ronald Dworkin (1981b) in a wellknown article. Dworkin does not define precisely what he means by a person’s resources in contemporary society, but develops the idea in an imaginary society consisting of immigrants arriving on a desert island. The resources to be equally distributed are the natural resources of the island: the land with its water, vegetation and underground resources. It is of course not possible to provide every one with equal resources in the sense of identical resources. The different parcels of land have to be assigned a value and the values added together in order to compare the total distributed to each citizen. This is called an index problem. The index problem is not unique to the concept of resources, but it is to some degree more complicated than for primary goods and capabilities since the variety of resources is greater. Dworkin defines equality of resources as an envy-free distribution: a distribution of resources where no one envies any other person’s bundle of resources. He describes an auction process which would bring about this result. While ownership of land is, of course, of great importance in agricultural societies, private ownership of natural resources accounts for a very small part of economic inequalities in modern developed economies. Therefore, Dworkin’s concept of resources is difficult to apply in practice in a modern society. If we try to apply equality of resources to the economy described in Chapter 3, also a highly artificial construct, we see that a redistribution leading to equality of resources in Dworkin’s sense immediately raises the question of what to do with that part of the quality of the land which is due to the efforts of previous generations, the real capital part of the land as distinct from the gifts of nature. The problem is what to do with inheritance. It would seem that equality of resources must imply that bequeathing an estate to one’s children is prohibited. Dworkin mentions the problem of inheritance, but does not discuss it. Land and real capital are external and transferable resources. They can be redistributed to create equality once the problem of valuation is resolved. As explained in Chapter 3, each of us also possesses what we might call internal resources: human capital and talents. These are not transferable in themselves, but human capital can be created by access to suitable resources. Dworkin does not discuss how to avoid inequalities in human capital due to differences in the upbringing and education of children. Dworkin does, however, thoroughly discuss the justice of inequalities due to free choice, to uncertainty and to differences in talents and other genetic equipment. He introduces the idea that economic inequalities should be ambition sensitive but not endowment sensitive. These terms represent the idea that inequalities due to free choice are just, while inequalities due to differences in the endowment of internal

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as well as external resources are unjust. Now, it is impossible to make internal resources equal. Inequalities due to minor differences in talents and other internal resources can be compensated for by redistributing income, or the fruits as in Chapter 3. But full compensation for grave handicaps like blindness is impossible. Also, there is the problem of distinguishing inequalities of outcome that are due to differences in ambition and inequalities that are due to differences in endowment. Dworkin’s solution is to imagine a theoretical insurance market for the risk of low income due to these and other contingencies, including brute luck and option luck. A useful simplification of Dworkin’s highly sophisticated argument could run like this: since most people are risk averse, we would on the average choose to buy an insurance policy that secured a minimum income whatever happens. This insurance argument resembles, to some extent, Rawls’s argument of choice from behind the veil of ignorance. The difference is that Dworkin imagines adults who know their own preferences, including their degree of risk aversion, but not their talents.

Capabilities The capability approach is advocated by Martha Nussbaum and Amartya Sen. Sen writes: The capability approach to a person’s advantage is concerned with evaluating it in terms of his or her actual ability to achieve various valuable functionings as a part of living. (Sen 1993: 30) Nussbaum writes: The basic intuition from which the capability approach begins, in the political arena, is that certain human abilities exert a moral claim that they should be developed. Once again, this must be understood as a freestanding moral idea, not one that relies on a particular metaphysical or teleological view. (Nussbaum 2000: 83) The concept of functioning is central to the understanding of what is meant by capability. As examples of relevant functionings, Sen mentions being adequately nourished and taking part in the life of the community. Now, people may choose not to exercise their capability of functioning. Some people may choose to fast for reasons of religion or health, but this is different from starving because you lack the means to procure food. Again, some people may choose to withdraw from the life of their community, wholly or in part, but voluntary withdrawal is different from being forcibly excluded. One way of understanding the concept of functionings and capabilities is by stating what they are not. They are not personal welfare, nor a collection of economic goods, like income and wealth, nor resources. The focus of the capability

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approach is on what we are able to do with our resources or wealth, but stops short of claiming that achieving the greatest possible personal welfare is the ultimate good of everyone. Equality of capabilities differs from equality of economic goods because different people may need different amounts of economic goods to achieve the same capabilities. The obvious examples are people with chronic illnesses like diabetes who need medication in order to function normally and people with physical handicaps who need special equipment in order to be mobile. Sen is well aware that the number of possible functionings that are deemed desirable is almost infinitely long, that is why he writes valuable functionings (Sen 1993: 30). He deliberately does not himself propose a list of such functionings. Once the capability approach is accepted, a generally accepted list of valuable functionings must be determined by open, public debate and reflection. Martha Nussbaum, on the other hand, has proposed a list of ten types of valuable capabilities and functionings. She distinguishes between three kinds of capabilities. There are basic capabilities, like hearing and seeing and the newborn child’s innate capability for developing speech and language. Then there are the internal capabilities that are developed in the adult person, like the capability for sexual pleasure and for free speech. Finally, there are combined capabilities ‘which may be defined as internal capabilities combined with suitable external conditions for the exercise of the function’ (Nussbaum 2000: 84–5). An external condition for free speech is, of course, a society which allows freedom of speech, while a necessary external condition for the capability of sexual pleasure is the absence of genital mutilation. The last example may be used to illustrate the important difference between the capability of functioning and the functioning itself. Sexual pleasure is not necessarily a functioning that everyone chooses to achieve. Many people choose to remain celibate for a variety of reasons, religious or practical. The point of the capability approach is that there should be a free choice. Genital mutilation deprive women of that choice. Whether some of them would have chosen to abstain from sexual pleasure in any case is not to the point. Claiming the capability of sexual pleasure for every human being is different from claiming that social welfare increases with the number of orgasms per capita achieved. The concept of combined capabilities brings out the fact that capabilities depend both on the endowments of the individual and on the way society is organised. Exclusion from the social community may be due to the lack of money to participate in normal communal or societal activities on the same footing as other citizens. A well-known example is taken from Adam Smith, who points out that in England at the time a man could not appear in public without shame if he did not wear a shirt. Again, there is a considerable difference between choosing to dress informally on the one hand, and being unable to afford a shirt on the other hand. Exclusion from the social community may also be due to the formal or informal rules of the community. There may for instance exist formal rules forbidding women to appear in public unless accompanied by a male relative, or there may

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exist informal sanctions making life unpleasant for women appearing in public on their own. We see that the concept of capabilities can be used to evaluate several different aspects of society in one set of criteria. In this respect, it differs from both Dworkin’s concept of resources, which measure individual endowments only, and from Rawls’ concept of primary goods which comprises both political liberties and (external) individual endowments, but lists them separately. In my opinion, this combined property gives a considerable cutting edge to the concept of capabilities and makes it useful. Others may consider it more useful to have concepts that distinguish between individual endowments and the organisation of society. Sen proposes capabilities as criteria for evaluating society and public policy in general, not just distributional measures. Nussbaum’s list appears to have the same general purpose. She sets forth a list of minimum or threshold capabilities which can be accepted by people who otherwise differ about the degree of economic equality in the just society. almost all world societies are very far from providing the basic minimum of truly human functioning, where many or even most women are concerned; I therefore leave the debate about levels of equality for a later stage, when the differences become meaningful in practice. (Nussbaum 2000: 86) There is also the fact that no government can, or should, secure equal capabilities in so far as they depend on what Dworkin calls internal resources and Rawls calls natural goods. The government cannot make us all healthy or supply us all with equal amounts of hormones that determine sexual urges. But the government can, of course, provide a public health service and forbid genital mutilation. The government can deliver the social basis of such capabilities, the way Rawls names a primary good he calls the social basis for self respect. Nussbaum emphasises that her list, being minimum requirements, consists of separate components: We cannot satisfy the need for one of them by giving a larger amount of the other one. All are of central importance and all are distinct in quality. . . . thus, there is a tragic aspect to any choice in which citizens are pushed below the threshold in one of the central areas. (Nussbaum 2000: 81) Therefore, for threshold capabilities, there is no index problem. But above the thresholds, it may well be the case that furthering one kind of capability can only be done at the expense of another. Certainly, to the extent that capabilities are furthered by access to economic goods, it is necessary to consider the degree of equality that is considered just.

7

Libertarianism and Marxism

Libertarianism Libertarians advocate minimal state powers and maximal liberty for the citizen. The right to own private property is considered as basic as the political rights of freedom of speech and of religion. Libertarians warn against government intervention in the distribution of income and wealth and maintain that attempts to impose a Utopia, an ideal pattern, from above invariably leads to tyranny. Prominent modern libertarians are Milton Friedman, Friedrich von Hayek and Robert Nozick. That is not to imply that they have identical opinions in all respects. While Nozick develops a piece of abstract and consistent moral philosophy of the state, Friedman and Hayek advocate unfettered capitalism on more pragmatic grounds. Their argument is that the economic efficiency of free capitalism is unrivalled. Any kind of government interference impairs efficiency and hampers the creation of wealth. It is not clear to me whether Friedman and Hayek are convinced that everyone gains by the efficiency of free capitalism, at least in the long run, or whether they maintain that the poverty of a minority is outweighed by the wealth of the many. In the last case, there is an ethical problem of the kind that Rawls discusses: is it ethically defensible to benefit the majority at the cost of the sufferings of a minority, however small? As we have seen, utilitarianism answers yes, Rawls answers no. Hayek, in his book The Mirage of Social Justice also argues that the very concept of distributional justice is meaningless, at least in a free society. He writes: ‘While equality of rights under a limited government is possible, and an essential condition of individual freedom, a claim for equality of material position can be met only by a government with totalitarian powers’ (Hayek 1976: 83). It should be added that both Friedman and Hayek, but not Nozick, also favour some kind of economic safety net such as a minimum guaranteed income. Robert Nozick advocates the minimal state in his book Anarchy, State and Utopia (1974). Although he is not a contractarian, Nozick justifies the rise of the state by telling more or less the same story as Hobbes and Locke did. The story is told succinctly by Locke: Men being, as has been said, by nature all free, equal and independent, no one can be put out of this estate, and subjected to the political power of another,

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Theories of justice without his own consent. The only way whereby anyone divests himself of his natural liberty, and puts on the bonds of civil society is by agreeing with other men to join and unite into a community, for their comfortable, safe and peaceful living one amongst the other, in a secure enjoyment of their properties, and a greater security against any that are not of it. (Locke 1993: 163)

Nozick imagines a state of nature where men are free and independent of each other, and where the hunter lives off his own prey. But this state of nature would be without laws. The hunter would be exposed to other hunters trying to kill him and steal his catch. In Hobbes’s famous words, life for our hunter would be ‘solitary, poor, nasty, brutish and short’. For this reason, the solitary hunter would choose, in his own interest, to give up a part of his freedom to the state, in exchange for protection against robbery and murder. But this protection would be all he required, according to Nozick. Also, the state would not be created by an agreement, that is, a social contract, as Locke writes. It would arise through a kind of free market process, by an invisible hand, as more and more hunters voluntarily choose to pay a protection agency. The hunter would be willing to pay to finance national defence and the policing and other institutions of justice necessary to make contracts and property secure. He would be willing to respect the property of others in return for their, and the government’s, respecting his own. But he would surrender no more of his freedom than this minimum. In particular, he would insist on the right to possess and dispose of his own prey. Or, changing the metaphor from hunting to farming, he would insist on the right to keep the fruits of his own labour. In short, the solitary hunter would go for the minimal, or night watchman state. Nozick calls his theory of just distribution The Entitlement Theory: If the world were wholly just, the following inductive definition would exhaustively cover the subject of justice in holdings. 1 2

3

A person who acquires a holding in accordance with the principle of justice in acquisition is entitled to that holding. A person who acquires a holding in accordance with the principle of justice in transfer, from someone else entitled to that holding, is entitled to that holding. No one is entitled to a holding except by (repeated) applications of 1 and 2. (Nozick 1974: 151)

A man can acquire a holding in accordance with the principle of justice in acquisition, as I understand Nozick, in either of two ways: by producing it, or by appropriating property that no one previously possessed. Nozick’s reasoning here

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is based on John Locke’s theory of original acquisition, about which Locke tells this story: Nor was this appropriation of any parcel of land, by improving it, any prejudice to any other man, since there was still enough, and as good left. So that in effect, there was never less left for others because of his enclosure for himself. For he that leaves as much as another can make use of, does as good as take nothing at all. (Locke 1993: 130) When things are either acquired or produced in accordance with the principles of justice, they belong to someone who is entitled to them: Whoever makes something, having bought or contracted for all other held resources used in the process (transferring some of his holdings for these cooperating factors), is entitled to it. The situation is not one of something’s getting made, and there being an open question of who is to get it. Things come into the world already attached to people having entitlements over them. (Nozick 1974: 160) Because things ‘come into the world already attached to people having entitlements over them’, taxation is theft. Nozick’s entitlement theory is a pure procedural theory of justice: if the procedure is just, the result is just. It is also a theory of justice that takes history into account: for a distribution of holdings to be just today, it must have arisen through justice in all transfers, going back until someone originally acquired a holding with no owner, as explained by Locke. Now, it is clear to everyone, including Nozick himself, that the present day distribution of property is not the result of just transfers throughout history. Nozick concedes that a redistribution would be necessary before his rules could be put into practice. But even after a libertarian redistribution, there would be a grave problem in the entitlement theory, taking it on its own terms. The problem is whether it makes sense to claim that the producer of a ‘thing’ can be identified, whether it makes sense to claim that ‘things come into the world already attached to people having entitlements over them’. Also, the quotation above makes explicit that resources used in the process of production should be paid for. Presumably, it is crucial for the transfer to be just that the price used in the transaction is a just one. But Nozick has no theory of value, beyond stating that the price paid in transfers should be the market price. Note also that in Nozick’s theory, non-producers such as children, the aged and the handicapped, are entitled to nothing except what producers voluntarily choose to give them.

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Marxism The Marxist principle of just distribution is famously and concisely expressed in the slogan: ‘From each according to ability, to each according to need’ (Marx 1989: 87). This ideal can, according to Marx, only be realised in a communist society. For Karl Marx, justice in distribution is impossible in a capitalist society because capitalism is based on the exploitation of the working class. Marx’s main work is the three volume Capital (Das Kapital), where he analyses the capitalist economic system. The theory of exploitation is a cornerstone in the Marxian critique of capitalism. In Marxian theory, all workers are exploited because their wages represent only a part of the values they produce. The working class, or proletariat, is in other words robbed of part of the fruits of their labour. Marx deduced his theory of exploitation of the workers from the labour theory of value, which he shared with the classical economists Adam Smith and David Ricardo. He showed that, calculated in labour hours, the value of the total product equals the number of labour hours contributed by the working class. But the workers receive less than the total product in wages, the difference being profits and rent paid to the owners of capital and land. Therefore, profits and rent represent unpaid labour. The workers receive only part of the value which they create. They are exploited by the capitalists. The workers have no choice but to be exploited. Since they own neither land nor capital, they have to sell their labour at the going wage rate in order to survive. There is, according to Marx, no essential difference between wage earners forced to sell their labour for exploitation and serfs and peasants forced to deliver unpaid labour to their feudal landlords. Capitalism gives no more freedom to the proletariat than feudalism gave to the peasants. Marx presents a logically and mathematically impeccable proof of his main thesis: that the labour value of wages is smaller than the labour value of the total product. Whether his interpretation of the result holds water, is another matter. Marx nowhere states explicitly that exploitation is wrong, but its injustice is implied on every page of Capital. Marx’s theory of exploitation therefore, seems to build on the very broadly held principle of distributional justice that every person has the right to possess what he himself produces, to enjoy the fruits of his labour (see Chapter 2). Arguably, the criticism of capitalism implied in the theory of exploitation is a Marxian theory of justice, in that justice in distribution is obtained when exploitation is absent. On the other hand, Marx himself argued strongly against this principle in his much quoted ‘Critique of the Gotha Programme’. A Marxist objection to the main body of theories presented in this book is that they concern justice in the distribution of consumption, and ‘Any distribution whatever of the means of consumption is only a consequence of the distribution of the means of production themselves. The latter distribution, however, is a feature of the mode of production itself’ (Marx 1989: 87). This objection leaves, however, two unanswered questions: What is the just distribution of the means of production?

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And is the just distribution of the means of production a necessary and sufficient condition for the just distribution of consumption, or merely necessary? Neither of these questions can be answered without a theory of distributional justice. Another Marxist argument against ‘utopian justice’ is, briefly, that it is meaningless to discuss justice in isolation from the social process, class struggle, that leads towards a just society. Marx claims that in any society . . . there is no social contract that the best-off class and the worst-off will acquiesce in, except as a result of defeat in class struggle or a tactical retreat to preserve long term advantage. (Miller 1975: 209) Marxism, as a collectivist ideology, arguably falls outside the individualist tradition of the Enlightenment. But in my opinion, Enlightenment ideas of justice are clearly implicit in Marx’s criticism of capitalist society. He shows, or tries to show, that capitalist society is unjust, oppressive, does not respect the rights of the individual and is not based on freedom. Take these criticisms away, and nothing remains of Marx’s criticism of capitalism except that the capitalist system is bound in the long run to break down. But this breakdown and the ensuing communist state can only be seen as good and in this sense as progress in the light of Enlightenment ideas of the good of mankind. The collectivism of Marx consists in his claims that the only means of progressive change lie in collective action.

8

Children and their mothers

The several different theories of distributional justice presented in the preceding chapters are presumably intended to apply to all of humanity: that is, both to women and men. I am less sure that they are meant to apply to the whole lifespan: childhood, adulthood, old age. Children are very rarely mentioned. Nor has the situation of women been specifically addressed in the theories discussed in the preceding chapters, except for Martha Nussbaum’s theory of capabilities. There is no reason, in my view, to suspect contemporary male liberal philosophers of defending discrimination against women in any form. Rawls, in his 1997 paper, rightly points out that the great liberal utilitarian John Stuart Mill was a strong advocate of women’s rights. The trouble is that it is not enough to advocate equal rights for men and women: men do not bear children. In this chapter, I am going to submit the various theories to a test. I shall discuss whether they are applicable to children, and if they are, which distributional rights children are given. Since children cannot survive on their own, if children have claims, so do those who care for them, whether the carers are the biological parents or not. And if children have claims on society, so do their mothers, at least during the time when a child is physically dependent on its mother, that is, during pregnancy and breastfeeding. I do not intend to give a broad feminist critique of mainstream theories of distributional justice: the critique has been very ably and thoroughly made by several feminist philosophers, and notably by Susan Moller Okin in Justice, Gender and the Family (1989). Neither do I undertake anything like an exhaustive discussion of women’s problems and rights; again, there is a rich literature on the subject. I shall limit myself to considering which just distributional claims women have on society as mothers and as those chiefly responsible for child care. My conclusion will not be that mainstream theories give the wrong answers to questions about the claims of children. I shall argue that they are so constructed that they cannot give answers: they simply do not apply to the situation of children. In Chapter 3, I wrote that no principle of rewards according to deserts can be applied to children. If we interpret ‘deserts’ as contribution to production (the fruits of our labour), it is also hard to see how such a principle can apply to the children’s mothers. Neither Rawls’ social contract nor welfarism implies distribution of economic goods according to deserts. But Rawls, in his paper ‘The Idea of

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Public Reason Revisited’ (1997), although defending the rights of children in certain respects, specifically excludes them from being parties to his social contract. Welfarism would at first glance seem particularly suited as a framework for considering justice to children. But, as I shall argue in more detail in the section ‘Welfarism and children’, there is a problem in defining the welfare of children; we can certainly not apply a respectful welfarism based on stable preferences.

What is special about children? What makes childhood special is, of course, the fact that children are totally dependent on others. Children are also innocent, in the sense that they have no merits or deserts in relation to society. On the other hand, children are not special in the sense of constituting a separate group. Childhood is a phase of life through which we all, without exception, have to pass. Justice to children is not justice to a particular portion of humanity, but justice to all. This fact makes justice to children a different subject from justice to adults who are dependent on the care of others because of mental or physical handicaps. Such adults are a minority group. The point is well explained by John Locke: From [Adam] the world is peopled with his descendants who are all born infants, weak and helpless, without knowledge or understanding. But to supply the defects of this imperfect state, till the improvement of growth and age hath removed them, Adam and Eve, and after them, all parents were, by the law of nature, under an obligation to preserve, nourish and educate the children they had begotten, not as their own workmanship, but the workmanship of their own maker, the Almighty, to whom they were to be accountable for them. The power then, that parents have over their children, arises from that duty which is incumbent on them, to take care of their offspring during the imperfect state of childhood. To inform the mind, and govern the actions of their yet ignorant nonage, till reason shall take its place, and ease them of that trouble, is what the children want, and the parents are bound to. (Locke 1993: 142, 143) Locke, like many others, makes children the responsibility of the parents. But he does make clear that parents do not have unlimited power over their children: they hold the children, as it were, in trust. But the parents may not have adequate means to ‘preserve, nourish and educate’ the children they have begotten. On the other hand, parents sometimes have the means, but not the will, to fulfill their obligation. Moreover, nourishing and caring for children takes time, time that cannot be spent earning one’s living, while, as we saw in Chapter 3, child care is not an activity that carries fruit that the carer can live off. So we must ask the question: do children have just claims on society as a whole as well as on their parents? And to what extent are parents accountable to society and the state as well as to the Almighty for the way they treat their children?

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Furthermore, children cost the parents time and money: do the parents have a just claim on society for compensation? The rights and claims of parents should not be confused with the rights and claims of children. It is not obvious that parenthood in itself creates rights. One argument is that, in modern society, having a child is a voluntary decision: ‘If the cultivation of expensive tastes, or silly gambles, or any other intentional action, cannot give rise to distributional claims, how can procreation?’ (Rakowski 1993: 153). On the other hand, Nancy Folbre (1994) argues that children are future producers and therefore necessary also to the childless. For this reason, parents have a just claim to compensation for at least part of the time and money spent on the child. One may or may not agree with Rakowski’s or Folbre’s view of the just distributional claims of parents. Both views are equally irrelevant when we consider the claims of children, since children have no choice in the matter. Even if the parents as parents have no claims, justice may demand that society grants them the means necessary for their children to have a reasonable standard of living. Society’s contribution to the nourishment, care and education of children can be made in part by direct distribution to the children; examples are free education and free health care. But as long as parents and children live together, it is impossible to secure a certain standard of housing, say, to the children without securing it also to the parents.

Welfarism and children As we saw in Chapter 4, respectful welfarism consists of two propositions. The first is that the good of the individual is defined by her own preferences, and by these preferences alone. The second is that the good of society is derived solely from the good of the individuals. The benevolent government should always respect individual preferences; no agency has the right to overrule the judgements of the individual. But a child’s preferences cannot always define what is good for the child. We do not let the preferences of a three-year-old determine whether it is good for her to play with matches, or whether she ought to visit the dentist. This is not to say that the preferences of a child, where they exist, never define the good of the child. The point is that they cannot always define it. This being so, someone other than the child has to decide when the wishes of the child should be respected and when they should be overruled. Moreover, for respectful welfarism to make sense, each individual must possess consistent and stable preferences. Now, children may well have consistent preferences, but they are certainly not stable. For these reasons, if welfarism is to be applied to children, it must be paternalistic. The question then arises: who is the right paternalistic authority, and how does the benevolent paternalistic authority know what furthers the welfare of the child? The assumption is sometimes made that parents know what is good for their children and act on this knowledge. But the parents’ opinion of what constitutes the children’s good cannot be the definition of what constitutes the children’s good. We may conclude after empirical investigation that the majority of parents act for the good of their children. But in order to carry out such an investigation, we

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have to know in advance what is the children’s good. This good must be decided by using information beyond that contained in the preferences of the children and their parents. Nor can we deduce what is good for the child from the preferences of the adult, by imagining an adult looking back and from the advantage point of adult preferences deciding what she wishes had been done for her as a child. Adult preferences are at least to some extent formed by upbringing, and may therefore not be used as independent criteria for how that same upbringing should have been. The conclusion is that the good of children must be found outside theories based on preferences. The concept of welfare may still be useful, but the welfare in question must be decided on by someone other than the child. Welfarism cannot answer the question of who should make this decision: the parents, the government, or perhaps child psychologists or other experts. But this is the core question when we consider children’s rights. It is also a core question when shaping government policy towards children. Should government make education compulsory? And who should decide what kind of education is best for a child: the government or the parents? The answer cannot be: whatever is best for the welfare of the child. The answer depends on which agency, parents or children, should have the power to decide what the child’s welfare is. Here, again, we must be careful to distinguish between the rights of the child and the rights of the parents. It is sometimes claimed that parents should have the freedom to choose their child’s education. But the parents’ freedom to choose on behalf of the child is different from their right to choose on behalf of themselves. The child, moreover, is equally deprived of the freedom to choose whether it is the parents or the government who choose for her. If we turn from the claims of children to the claims of parents, welfarism leads to a result which strikes me as odd. Parents lose welfare from the consumption and leisure they give up to their children, but may also gain welfare from the presence of the children themselves. A welfarist has to calculate the net effect on welfare from the loss and the gain. Parents as a group have claims on society to the extent that there is a net welfare loss. In Chapter 10, we shall see that such calculations are claimed to be of practical relevance in measuring the income of households with children. Since child care in practice still is in the main carried out by mothers, it is chiefly women who lose income because they spend time caring for their children instead of being in paid work. Whether they have a just claim for compensation in welfarist terms depends on the motive for their choice. If the mothers spend time on their children because they enjoy it (have a preference for doing child care), they have no such claim. If the choice is made from a sense of duty, or because of societal pressure, the caring mother loses welfare, and so has just claim to compensation.

Libertarianism and children We saw in the section titled ‘Libertarianism’ that Nozick’s theory leaves children with no rights. On the face of it, his theory is still consistent, since it seems that he regards children as the property of their parents. On the other hand, when he

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claims that the family is a voluntary association (Nozick 1974: 167), he must have forgotten about children. Children, of course, do not choose their parents, and neither do they choose whether to be part of a family or not. And if we study the story Nozick tells to deduce the minimal state, we see that the solitary hunter must have forgotten his own childhood. Otherwise, he would surely have chosen to organise society in a way that at least guaranteed his survival to adulthood; probably also that conditions during his childhood were such as to enable him to become a fit hunter. But then, he would no longer choose the minimal state. As it stands, the libertarian theory does not, and cannot, include children. I feel it should puzzle libertarians that for the first part of your life you cannot make important choices, and you exercise no rights. Since the choices made on your behalf during childhood to a large extent condition your ability to make choices and exercise rights as an adult, logically libertarians should be more concerned than they seem to be about the rights of children. In contrast to Nozick, the more pragmatic libertarians Milton and Rose Friedman (1980: 33) argue that children do have rights.

The Rawlsian social contract The problem with Rawlsian theory is the limited scope Rawls gives his social contract, insisting as he does both in A Theory of Justice and in several papers that the social contract is a contract about the rights and duties of adults as citizens in the public sphere. In A Theory of Justice Rawls discusses what he calls the basic institutional arrangements of the just society. But he does not discuss the just organisation of the family, although he does state that the family is a part of the basic structure of society. In ‘The Idea of Public Reason Revisited’ (1997) Rawls explicitly discusses the rights of women and children. Here too, he argues that the family is outside the public sphere. But the family is government regulated and in this sense part of the public sphere in all societies. As argued by Martha Nussbaum (2002): ‘The state is present in the family from the start, . . . , it is the state who says what this thing is and controls how one becomes a member of it’. Family law defines the rules of inheritance and the duties of economic provision of parents for children, of children for parents and of spouses for one another. Moreover, the family is the main source of income for the majority of women as well as for nearly all children. Women the world over depend largely on marriage for their livelihood. Thus, the family has two functions that are essential to society: the education and nurture of children, and the distribution of economic goods between parents and children and between spouses. In particular, the family is of crucial importance in the distribution of economic goods to individuals, and therefore not to be ignored in a discussion of distributional justice based on ethical individualism. Rawls imposes, as it were, on the contracting parties in the original situation the constraint that the social contract should only include the rights and duties of adult citizens. It does not seem reasonable that the souls would accept this

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constraint if they were free to choose the scope of the contract. We should bear in mind that the souls know that they will themselves start their life as helpless infants, and that the social contract will govern their own childhood. With this knowledge, the contracting parties would surely choose to view the family and its key social functions as part of the basic institutions of society to be covered by the social contract. What should be covered are the rights and duties of parents and children on the one hand and the place of the family in the distribution of economic goods on the other. Rational souls would consider the conditions of childhood as very important indeed. Children may well be considered the weakest group in society, the group most unconditionally dependent on others. The group, children, is therefore a strong candidate for the position of the least advantaged referred to in the difference principle. It is in particular impossible to believe that rational agents would choose to face the risk of spending their childhood without rights, and without a lawful claim on society for protection from abuse, neglect and starvation. The parties in the original position will therefore agree that society has the duty to ensure a certain level of comfort and happiness in childhood for everyone. This will hold, I feel, whatever conclusions one may reach about the difference principle, and whatever weight we give to economic equality among adults. Moreover, the souls know that the probability of being a woman is approximately 50 per cent. They would therefore also choose to address the question of women’s economic position in the just society, and in particular the justice of women’s economic dependence on the family and on marriage for economic provision for herself and her children. The social contract chosen by the parties in a Rawlsian original position will guarantee equal rights for women and men to economic independence. Both women’s and children’s distributional claims and other rights will be guaranteed by the state. If these rights are guaranteed, economic justice to children and women are also guaranteed. The basic societal functions of the family will then be taken care of in a just way. There does not, therefore, seem to be any necessity for further government regulation of the family in the sense of limiting people’s choice of sexual partners, household formation and income sharing between adults. The society chosen would still be a liberal one in the Rawlsian sense of tolerating several and mutually incommensurable conceptions of the good. There would, moreover, be a civil society and a private sphere free from government intervention. But the boundary between government and civil society, between public and private spheres, would be drawn differently from that envisaged by Rawls and traditional political liberalism. It is worthwhile emphasising that the conclusions regarding the position of children and women in the social contract do not depend on the extreme degree of risk aversion which leads to the difference principle. Indeed, when considering the status of children, the contracting parties face no uncertainty at all, and the probability of being a woman is (almost) exactly equal to the probability of being a man. Moreover, when considering the claims of parents, the omniscient contracting parties also know that procreation is in no way the eccentric minority pursuit

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implied by Rakowski in the quote on page 58. More than 90 per cent of human beings are, or wish to become, parents.1 It therefore seems reasonable that the souls would also choose a social contract that secures an acceptable standard of living for parents.

The good of children The good of children has two aspects. First, well-being in some sense during childhood is of importance in itself. Second, conditions during childhood to a great extent determine our opportunities as adults, our human capital. Therefore, what we regard as the good to be distributed to children must be strongly influenced by our opinion of the proper good of adults. Resources, primary goods and capabilities are all concepts that make it possible to discuss the good of children without the circularity of respectful welfarism and without the potential authoritarianism of the paternalistic version. They are all closely related to the economist’s concept of human capital and to each other; at least if resources are meant in a broader sense than Dworkin’s concept. The concepts of capabilities and of social primary goods are closely related; first cousins, as Roemer (1996: 164) writes. Nussbaum makes the same point: ‘The capabilities approach, as I have articulated it, is very close to Rawls’s approach using the notion of primary goods. We can see the list of capabilities as like a long list of opportunities for functioning, such that it is always rational to want them whatever else one wants’ (2000: 88). Sen and Nussbaum would seem to have no quarrel with the primary goods rights, liberties, opportunities, which all are at least necessary for securing valuable functionings. The primary good ‘social basis for self respect’ also seems related to capability or capabilities. The remaining difficulty is the primary good of income and wealth. However, as explained in the section ‘Primary goods’, income and wealth are not primary goods according to what I take to be Rawls’s intentions. Rawls’s requirements are better met by something like ‘the capability to earn one’s living’, or more briefly: ‘economic capability’. Economic capability is determined partly by personal endowments (human capital), partly by social and economic features of the surrounding society. Economic capability seems to me to correspond well to women’s demands for economic independence. In short, the capability approach seems the most promising way of defining children’s good. Children’s capabilities as children must of course be conceived of as different in many ways from the capabilities as adults. There remains much work to be done in working out a suitable concept of children’s good. But let us not exaggerate the extent of our ignorance. Some general features of a society that treats its children justly can be drawn. Children need love, security, a reasonable amount of material comfort, education, health care and opportunities to grow and develop. These goods should be provided for every child without exception in the just society.

Part II

Measuring inequality

9

Income and wealth

Consumption is the sole end and purpose of all production.1 (Adam Smith)

Economic goods In Chapter 2, I wrote that distributional justice is justice in the distribution of economic goods, and that distribution of economic goods is not the same as distribution of monetary income. Economic goods are goods that are both scarce and transferable. An economic good in this sense is defined by having two properties besides being transferable. First, it is a good for someone: some person somewhere in the world wants to acquire more of it. Second, it is scarce in the sense that it can only be acquired by giving up some other good. Economic goods have a cost, that is why we have to economise on them. The opposite of a scarce good is a free good, a good of which there is abundance. Abundance means that no one has to give up some other good in order to acquire as much of the free good as they wish. In most parts of Europe, fresh air and clean water used to be considered free goods. The fact that many people are willing to spend money on bottled drinking water and air-fresheners for the home, shows that they are so no longer. The boundary between free and scarce goods vary over space and time. There are two kinds of economic goods: individual goods and public goods. Individual goods can be divided up and distributed among individuals. If one person receives more of a good, there will be less of it for other people. Public goods are not divisible in this way; more to one individual does not imply less to another. This distinction between individual and public goods is technical, not political or organisational. Public goods are not necessarily provided by the public sector (the government) while individual goods may well be. Typical examples of public goods within a country are military defence, the judiciary, public parks, roads and other kinds of infrastructure. The environment, water in the ocean, lakes and rivers, the air we breathe, are also public economic goods in the technical sense, as is the global climate. These examples also show why public goods may still be scarce goods: expenditure on military defence reduces a country’s consumption of other goods.

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The difference between individual and public goods is often a question of degree. Public parks and roads have limited capacity: they can be used by several persons without diminishing their usefulness for others within a certain limit, but above that limit they become crowded. Clean water can be both a public and a private good. When bottled and marketed it is private, but the water in rivers and lakes is public. A good can be technically public for a group of persons. The home is a public good for the persons living in it, but a private good for the economy as a whole. Access to economic goods means access to public as well as individual goods. On the face of it, access to public goods does not seem to be a problem of distribution. In fact, there are several distributional issues involved in the provision of technically public goods. Since public goods are also scarce, each public good has a cost in terms of either other public goods or individual goods. If people have different preferences, there will be political disagreements about the choice of public goods, and the choice between public and individual goods. For individual goods available in the market, the political decision is how to distribute income. Citizens then make up their own minds about how to spend the income, that is about which individual goods to buy. Decisions about public goods have to be made collectively. Income and wealth will in the following sections be considered as measures of access to economic goods that are individual in the technical sense. As we shall see, it may still be considered desirable to include access to goods provided by the government, since a government may well pay for or subsidise individual goods such as health care.

Income The terms income and wealth are parts of our everyday language, and serve us well enough without being all that precisely defined. For analytical purposes, more precise definitions are needed. Such precise analytical definitions turn out to be fairly complicated and (perhaps) tedious. No single definition is necessarily the one and only correct definition. As we shall see, the best definition depends on the purpose of the analysis, on the questions which we want answered. The generally accepted definition of income is that it is the upper limit of what we can consume in a given period without diminishing wealth. In the words of John Hicks: The purpose of income calculations in practical affairs is to give people an indication of how much they can consume without impoverishing themselves. Following out this idea, it would seem that we ought to define a man’s income as the maximum value that he can consume during a week, and still be as well off at the end of the week as he was at the beginning. (Hicks 1961: 172) This is the Hicks definition of income.

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Another much quoted definition of income is given by George Simons: Personal income connotes, broadly, the exercise of control over society’s scarce resources. It has to do not with sensations, services or goods, but rather with rights which command prices (or to which prices may be imputed). . . . In other words, it implies estimate of consumption and saving. (Simons 1938: 49) Personal income may be defined as the algebraic sum of (1) the market value of rights exercised in consumption and (2) the change of value in the store of property rights between the beginning and end of the period in question. (Simons 1938: 50) The two definitions are often considered to be identical; they are, however, slightly different. The Simons definition stresses rights: rights to consumption, rights to property. The Hicks definition concerns (possible) consumption only. Vilfredo Pareto’s discussion of income brings out the difference: Even the poorest man must be regarded as having sufficient income to keep him alive. It doesn’t matter whether this sum comes from the fruit of his work, or whether it comes to him from charity, or indeed whatever source, legal or illegal. (Quoted from Brown 1976: 75) According to Pareto the thief and the beggar both have an income. But neither has rights in consumption. They receive an income by the Hicks definition, but not by the Simons definition. The following discussion of the meaning of ‘income’ will be based on the Hicks definition: income as a measure of possible consumption. I shall return to the difference between income as a right and income as consumption in Chapter 11. It follows from both the cited definitions that income and wealth (property) are of a kind; in defining one we define the other. The difference between them is that income is a flow variable, measured per unit of time, while wealth is a stock variable, measured at a given date. The relationship between income and wealth is illustrated in Figure 9.1. The basin contains wealth. Income flows into the basin, consumption flows out of it. If consumption is smaller than income, there is positive saving, and the stock in the basin, wealth, increases. Consuming out of wealth implies dissaving, or negative saving, and the stock decreases. Thus, we might as well have defined income as the increase in wealth possible during a given period if consumption is zero. The point of the Hicksian definition of income is that it highlights consumption possibility as the main interest of both income and wealth. In daily speech, we tend to think of income as cash received during a given period. The differences between this cash income and Hicksian income are twofold.

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Income

Wealth

Consumption

Figure 9.1 Income and wealth.

First, Hicksian income includes consumption not bought with cash. Second, it includes changes in the value of capital (wealth). In order to define income, then, we begin by considering the various kinds of consumption by source. Consumption consists of: 1 2 3 4 5

Cash consumption: commodities bought for money in the market. Services from durable consumer goods. Consumption paid for by the government. Home production: consumption goods produced at home. Leisure.

The above enumeration is not complete, but will do for the essentials. On the basis of these items, we can construct various income concepts. There is no fixed terminology for the various concepts of consumption and income. Tentatively, we might call the sum of the values items 1 and 2 market consumption. Adding 3 and 4 to cash income gives extended consumption, while the sum of all 5 items equals full consumption. Noting that income equals consumption plus saving, we obtain the corresponding income concepts: • • • •

Cash income Market income Extended income Full income.

The concepts of extended income and full income will be further considered in the sections ‘Extended income’ and ‘Full income’. The income found, or at least

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aimed at, in most empirical analyses of personal income distribution corresponds more or less to what I have called market income: cash income supplemented by imputed services from durables to the extent that such data are available. I shall refer to this income concept as ‘standard income’, while the term ‘income’ without qualification may refer to any definition. Income is always defined as income during a specific period: a week, a month, a year, several years or any other time interval. The most common period of measurement is a year. In the following sections, it will be understood that income refers to income per year unless otherwise stated. Data analysing income distribution are in some countries based on tax return forms. Note that the concept ‘taxable income’ may or may not conform to the Hicksian definition of income. The assessment of income for purposes of taxation is made from a variety of considerations other than the correct definition of income.

Components of income Wage income, also called earnings, is the remuneration received by an employee for her or his labour. The remuneration may be in cash or in kind. Care must be taken to distinguish between the wage rate on the one hand and wage income on the other. The wage rate is the payment per hour, week or month as the case may be. Wage income is the wage rate multiplied by work time. Two persons working for the same wage rate may have different wage incomes if their work time differs due to, for instance, part-time work. In fact, the increasing incidence of part-time work makes differences in work time a constantly growing source of inequalities in wage income. Wage income tends to be the largest income component for persons and households in industrialised countries. Capital income is returns to assets. Examples are income from interest on savings accounts, dividends paid on shares, rent from real estate. Capital income in this sense includes the two classical income types of profits and rent. Theoretically, imputed returns from self-owned homes and other consumer durables should be included. Except for imputed rent on self-owned homes this is rarely practicable. Capital income may be negative or positive. Negative capital income is for example interest payable on debts, and capital depreciation due to a fall in share prices. Entrepreneurial income is a mixture of wage income and capital income. This category of income applies to the income of self-employed persons for whom it is not possible to identify income from work and returns to invested capital separately. Transfer income is income that does not stem from economic activity during the period in question. Transfers may be from government or private sources. The size and composition of transfer income depends on the social and economic arrangements in the country studied. In the Scandinavian countries, government transfers make up more than 20 per cent of income received by adults. These transfers are mainly old age and disability pensions.

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Measuring inequality Table 9.1 Composition of income, Norway 1996 Income component

Wage income + Entrepreneurial income + Capital income + Transfers = Total income

Per cent All

Men

Women

65 7 6 22 100

67 10 7 16 100

61 3 5 31 100

Total income: persons 18 years and older.

Transfers from private sources include payments of alimony and child maintenance, gifts from charities and inheritance. Transfers from family members working abroad should also be included. It is, however, often difficult to obtain reliable data on private transfers. Total income equals the sum of wage income, capital income, entrepreneurial income and transfers. Disposable income equals total income less direct taxes. Most people receive several kinds of income at the same time. A wage earner may receive income from savings as well as transfers, like child benefit, in addition to her earnings. A pensioner may supplement his transfers with part-time paid work. Table 9.1 shows the composition of income for Norwegian adults. Other income concepts sometimes used are primary income, which equals wage income plus entrepreneurial income and factor income, which equals primary income plus capital income. The precise boundaries to be drawn between the various kinds of income are not always clear. In Norway, unemployment benefits for employees are classified as wage income, while old-age pensions are classified as transfers. However, both kinds of income depend on rights earned by the employee while economically active. It could be argued, furthermore, that these benefits are neither transfers nor wage income, but capital income; the capital in question being the cash value of accumulated rights earned in paid employment.

Extended income The term ‘Extended income’ does not have a fixed definition in economic literature or statistics. It is often used to cover an income concept where various kinds of consumption in kind are added to total income as defined above. From the list on p. 68, cash income may be extended by adding one or more of: • • •

services from durable consumer goods; consumption paid for by the government; home production: consumption goods produced at home.

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None of these is routinely included in statistics on incomes since data are not usually available from standard sources. There are also considerable practical and theoretical problems in obtaining their values. Some of these consumption items have no market value, as there is no market for them, at least, no legal market. Also, the market value, when it exists, may not represent the value to the consumer. Services from durable consumer goods The value of services from durables is an extension of capital income. Our stock of consumer durables represents wealth. Like financial wealth, durables yield a profit, but in terms of real consumption, not money. The house yields shelter, the car transport, the TV entertainment, the kitchen equipment food. Those that do not possess these things must either go without certain kinds of consumption, or rent the equivalent equipment or services at market prices. Conventionally, a durable consumer good is defined as one which lasts more than one year. If this definition is taken literally, durables include most of our personal possessions: household furnishings, clothes, books and gadgets of every kind with which we surround ourselves in the rich part of the world. It is not worthwhile for the analyst to try to count them all. Also, goods that are durables for the less well off may well be replaced before the year is out by the rich, so there is no sharp distinction between durables and non-durables. Still, it is possible to list a few large durables that represent a sizeable investment for most of us, and that last long. First on the list is the home. Since everyone needs shelter, for all but the most destitute the alternative to ownership is to rent. The yearly value of owning a house, the profit on the investment, is the money saved on rent: the market rent of a similar home less the maintenance cost or depreciation and interest on the mortgage, if any. The practical problem may lie in finding the ‘similar dwelling’, since no two homes are exactly alike. A middle-income family in Norway spends around 25 per cent of its income on dwelling, so it is important for a good estimate of income to include this hidden income. Similar arguments could be made regarding cars and a few other large durables; in practice, the main effort when collecting data is spent on obtaining accurate measures of income from house property. Consumption paid for by the government This consumption item is an extension of transfer income. Government consumption does not, or not necessarily, consist exclusively of public goods. In many countries, the government pays for certain kinds of individual consumption, wholly or in part as subsidies. Prominent examples are health care and education. Certain money transfers may be regarded as publicly provided insurance since the alternative might have been private insurance: sickness benefits, disability benefits and public old-age pensions. For health care, too, the practical alternative to public provision is private medical insurance.

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The reason for government provision of goods that are public in the technical sense is efficiency. But the government provides private goods like health care and education largely for reasons of distributional justice.2 It is therefore reasonable to include them when analysing distribution. Some of these goods may have market value in the sense that broadly similar goods could have been bought in the private market. But they never have market value in the sense that the recipient may choose to sell her right of consumption. The recipient either takes up her right or she does not, but she may not dispose of it for money. In the case of elementary education, the child does not even have the legal right to refuse in countries where school is compulsory up to a certain age. In all cases, there are two problems: determining the quantity received by each individual, and determining the money value of the good. Determining the quantity received is not the great difficulty since the goods in question are either available to everyone, or allocated according to fairly simple, observable criteria. Free schooling, where it exists, is the right of every child, so it is a matter of knowing the number of children of an individual or household. Social insurance of various kinds is usually either available for every citizen, or allocated according to age, to level of income or to status in the work force in the case of rights connected to earnings. When assigning value, we have three choices: the market value of similar goods, the cost to the government or the value to the recipient. The market value of similar goods is normally not a good choice, because normally there are no exactly similar goods on the market. When a market for goods such as medical insurance, health care or schooling exists in addition to public provisions, it means that the private sector can offer goods that are different from those publicly provided: otherwise the private supply could not exist. We are only willing to pay for private schools or medical care to the extent that these services are better in some way than the corresponding public services. The value to the consumer can be defined as the amount she is willing – and able – to pay for the good. This value may be either larger or smaller than the cost to the government. In general, the ability to pay, hence also the will to pay, will increase with increasing income. In this sense, then, publicly provided goods represent a smaller value to the poor than to the rich. Home production Consumption from home production is an extension of work income. By home production, in this context, is not meant the owners’ consumption of marketable commodities from self-owned firms or farms. Such consumption is, or should theoretically be, included in the standard definition of income. Extending ‘income’ to include home production means including the result of housework done by a housewife, or by all of us in our spare time, as well as do-it-yourself activities such as home decoration or mending the car. One reason why efforts are made to compute extended income in this sense is the demand for recognition of women’s unpaid work at home.

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There is, however, no clear boundary between unpaid home activities and leisure. The criterion used to sort out what may properly be called home production in the sense of unpaid work is the so-called third-person criterion. An activity is unpaid work when it is technically possible to hire someone to do it for you. By this criterion, baking bread is home production while sleep is pure leisure. The third-person criterion implies that the income generated by home production does not necessarily accrue to the home producer herself. The housewife bakes bread, prepares meals and does the washing up for the whole family, not just for herself. Since much of home production consists of services (child care), measuring the output is difficult. Calculations are usually made from estimates of the time spent on various activities. The time must be then converted into money value by means of an imputed wage rate. One widely used method is to apply the wage that would have to be paid for hiring someone to do the work.

Full income Time is money and leisure is a form of consumption. The concept of full income includes the possibility of consuming leisure, and thus makes time a constraint on consumption. It was introduced by Gary Becker (1965). Becker assumed that a person could choose freely how much time to spend in paid work, the only constraint being that a day always has twenty-four hours, no more and no less. The rest of the time is divided between home production and leisure. I shall simplify by ignoring saving. Wage income equals the wage rate (w) times working time (H ). Cash consumption, C, can also be financed through nonwork income (MI): transfers and/or capital income. Total cash income then equals wH + MI. Available time is divided between paid work, H, home production HP and leisure F . Altogether, our individual faces two separate constraints, one in money and one in time: C = wH + MI T = H + HP + F The two constraints combine to produce the time and money constraint on full consumption: F I = MI + wT = C + wHP + wF

(9.1)

Here, FI is full income. Note that all we need to compute full income is the wage rate and nonwork income. In particular, it makes no difference to full income whether the time that is not spent in paid work is spent on leisure or home production. When computing home production, the time spent should be multiplied by the person’s own wage rate, not the wage rate needed to employ someone else to do it.

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Measuring inequality

Lifetime income As the name implies, lifetime income is total income received over a person’s whole life. In principle the whole life means the time span from birth to death. However, the income of a child is a fairly problematic concept. In the following pages, I shall take it that life starts with the coming of age and entering adult life at, say, 18 years. Normally, yearly income varies over the life course. The normal career of a man in modern industrialised society will start with a very small, perhaps zero, income during his education. On entering the labour force he starts earning an income. It is usually assumed that, barring mishaps, his income will increase with age until he reaches his fifties or sixties; his age at the turning point will depend on his profession. On retirement, his income decreases, and he lives on his savings, on a government old-age benefit or a combination of the two. Within this general pattern, there will be individual variations due to different lengths of education and different ages of retirement as well as unexpected interruptions because of unemployment, illness or other accidents. For women, there is at present no corresponding typical career. Women with no children tend to follow the same career pattern as men. All women with children have periods away from paid work, at the very least in connection with the birth itself. Between the stay at home housewife and the full time career woman there are any number of individual careers based on shorter and longer spells of complete withdrawal from paid labour followed by shorter or longer periods of part-time work the length of which also varies. Figure 9.2 shows income by age for Norwegian women and men in 1996. A society where everyone had the same lifetime income would in one sense be a society with perfect economic equality. But analysis of yearly incomes would show inequality. If everyone followed the same career, there would be absolute

100

Income

Men

Women

0 18

Age

Figure 9.2 Income by age, men and women.

70

Income and wealth

75

350 300 Wealth

250 200 Income

150 C

100 50 0 –50

1

0

2

3

4

5

6

7

8

9

10

11

12

Age

–100 –150

Figure 9.3 Income, consumption and wealth.

equality within age groups but inequality between age groups. With differences in life course, for instance due to different lengths of education, there would also be inequality between people of the same age. Separating inequality in lifetime income from inequality in life course raises methodological problems of some importance in analysis of yearly incomes. It is generally assumed that people wish their consumption path to be smoother than their income path. The smoothing of consumption is made by borrowing and saving. Figure 9.3 shows a stylised picture of a man’s income (I ), possible consumption (C) and wealth (W ) through his lifetime. He is assumed to start adult life with some positive wealth, W0 > 0. We see that in the beginning he first consumes his wealth and then borrows money to finance consumption. When he starts earning, he also starts saving, first by paying off his debts and then by accumulating wealth. After retirement he again consumes from wealth. Wealth and debts carry interest: he has to pay out interest while in debt, and earns interest in the periods when his wealth is positive. Because of the interest accrued, a given yearly income gives a greater long-run consumption possibility the earlier in life it comes. Therefore, lifetime income is computed as the discounted sum of yearly incomes through life: RL =


t

Rt (1 + r) t

(9.2)

where r is the rate of interest. Equation (9.2) converts the streams of income through life to the one number RL , which may be interpreted as the initial wealth which, if invested, would have yielded the given income path at the current interest rate.

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Measuring inequality

The consumption path in Figure 9.3 is drawn on the assumption that our man dies with his initial wealth intact. This consumption path equals his average lifetime income by the Hicksian definition of income. Another and higher consumption path (not drawn) corresponds to his consuming all his wealth, and dying just solvent. This is his maximal lifetime consumption, which we could also call his lifetime access to economic goods. The total consumption that he can allow himself without dying insolvent is determined not only by lifetime income, but also by initial wealth. Actual lifetime income is, of course, never known until the person has run the whole course of his life, that is, until he is dead. But the concept can nevertheless be useful, especially in bringing out the relation between income and wealth. From Figure 9.3, we see that yearly income is not necessarily an accurate guide to possible consumption in the long run. While he is earning, our man’s current annual income is larger than lifetime income, while after retirement it is smaller. Furthermore, even if he did not have to save for his retirement, there is a period during his working life where actual consumption possibility is constrained not only by his income, but also by the debts he has to repay. The actual shape of the income path through the life course depends both on the kind of career he pursues and on the social conditions in the country he is living in. Of particular importance are length of education and the way tuition fees and cost of living during education are financed. The way earnings vary with age also depends on profession; typically, earnings are expected to increase with age in white-collar jobs, while they tend to be constant after a certain age in blue-collar jobs. The consumption path in Figure 9.3 is drawn assuming what we economists call a perfect capital market: our man is able to borrow what he wants to and when he wants to at the current rate of interest. In reality, collateral is needed to obtain loans, so not everyone is able to choose the smooth consumption path drawn there. Also, the consumption path drawn is one of many theoretically possible consumption paths. The actual path chosen will depend on the man’s preferences over time among other things. Finally, as seen from Figure 9.2, the profile of women’s income over a lifetime is very different from that of men.

Wealth Wealth consists of financial and real assets. Examples of financial assets are cash, bank deposits and securities such as shares and bonds. Real assets are stocks of physical goods. A self-employed farmer or business entrepreneur has a stock of machinery, buildings, etc. for purposes of production. For a private household, examples of real assets are consumer durables, valuables like jewellery and art and, for owner–occupiers, the home. These assets are sometimes collectively called consumption capital. I shall ignore the many problems of valuing production capital and limit myself to a brief discussion of personal wealth.

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77

The value in money terms of financial wealth is in one sense well defined, it is the sales price at any given time. This is plain enough for money in the bank; but the value of securities often fluctuates from day to day. Some agreed convention is needed when we want to measure wealth for purposes of comparing the personal wealth of different individuals. As for current consumption in kind, there are three ways of valuing consumption capital: by historical cost, by market price and by use value to the owner. Because of depreciation, wear and tear, on the one hand and changes in the price level on the other, the cost of the good when it was acquired is not usually regarded as a good measure of value. As to the market price, there is the problem of finding an identical item on the market. The main item of wealth for ordinary private households is the home when they own it. There is, of course, usually a market for houses. Even so, the market price of one particular house may be uncertain if it has not been on the market for some time. There is also usually a second-hand market for other consumer durables, but that does not mean that there is a standard price, since used goods are not identical in the way new goods are. Think of buying and selling used cars. An approximation to use value would be the price of buying a new item, which may well be larger than both historical cost and estimated market price. Altogether, estimates of wealth tend to be uncertain, and are often based on rough, stereotyped measures.

Access to economic goods Access to economic goods is determined by both income and wealth; and this goes for the whole lifetime as well as for any shorter period during a life. In order to combine them in one term, either income, which is a flow concept, must be converted to a stock, or the stock concept wealth must be converted to a flow. Equation (9.2) converts flows of income to RL which is a stock and can be added to initial wealth. Thus, lifetime access to economic goods can be expressed as W0 + RL . When assessing access to economic goods for any given year, it is more convenient to convert wealth at the beginning of the year to an income flow. It seems unreasonable to convert wealth to income for just one year. Figure 9.3 indicates that wealth should be converted to income for the whole future life. If the length of the rest of life were known, T years say, the correct method would be to convert wealth at date 1 to a T -year annuity. Since length of life is, in fact, uncertain, expected length of life would have to be calculated from actuarial tables. It should be stressed that the suggested methods of conversion are purely theoretical, and are not found, as far as I know, in published analyses of the distribution of income and wealth.

10 Household income

Income is earned by individuals, but it is often spent by households whose members share income and consumption, at least to some extent. It is therefore standard procedure in analysis of personal income distribution to analyse the distribution of household income. Household income is the sum of the individual incomes of the household members. A household is a group of people living together, and sharing income and consumption. The precise details in defining a household may vary, but the whole idea of household income and household consumption is best understood by visualising a traditional Western nuclear family: mother, father and one or more children with the father as the main income earner (‘breadwinner’).

Equivalent adult scales A given household income of, say, 30,000 euros gives a larger possibility for consumption for a single person than for a couple with children. In order to obtain a measure of possible consumption per household member it is therefore standard procedure to divide household income by a measure of household size. The straightforward measure of household size is the number of persons in the household. But when people ‘keep house’ together, there will usually be goods that are public within the household: kitchen, bathroom, various consumer durables. Therefore a household of four persons, say, does not need 120,000 euros in order to obtain the same consumption as a single person with 30,000 euros. In order to allow for public goods and other household economies of scale, the size of the household is therefore measured in consumer units or equivalent adult scales. An example of equivalent adult scales is the one used in OECD income statistics: the first adult counts 1, the second and subsequent adults count 0.7 each while each child counts 0.5. The household consisting of two adults and two children equals 2.7 equivalent adults. A household income of 81,000 euros for two adults and two children is then the equivalent income of a single person’s 30,000. Although it has no official status, this scale is usually called the OECD scale. Observe that a child counts for less than an adult. The reason may be that most children live with two parents, and so economies of scale due to a third or fourth person adheres, as it were, to children. The reason may also be that children are

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79

thought to consume less than adults. The problem of ‘the cost of children’ will be considered in the section ‘The cost of children’. Many other equivalence scales have been proposed in the literature. Several of them can be shown to be encompassed by the formula ne , where n is the number of household members, while e is specific to each scale. The parameter e is called the elasticity of household economies of scale. This class of scales does not distinguish between adults and children. It was introduced in a paper by Buhmann and others (1988). This paper also showed that the choice of equivalent adult scales can make considerable difference to the results of an analysis. One of their examples is reproduced here in Chapter 15 on poverty. Dividing household income by its size measured in a suitably chosen equivalent adult scale gives household income per equivalent adult. By the OECD scale, if a household with an income of 81,000 euros consists of two adults and two children, the income per equivalent adult equals 30,000 euros. In analyses, it will be treated as four individuals, each with an equivalent adult income of 30,000 euros. The concept of ‘household income per equivalent adult’ assigns the same equivalent income to each member of the household. It is therefore implicitly based on the assumption that income and consumption are equally shared among the household members. This assumption is not necessarily realistic. Norms for sharing between spouses, between parents and children and between sons and daughters vary between cultures, and probably also between households living in the same culture. Some cultures in Africa south of the Sahara assign different spheres of economic responsibility to wives and husbands, and the idea of spouses providing for one another by pooling their income is unknown. In cultures where women have a low status, it is well-known that the women in the household take their meals after the men have eaten. When food is scarce, they make do with whatever is left. In the rich parts of the world, there is normally sufficient food for all, but the distribution of other kinds of consumption may still be unequal. When large parts of the money are spent on indivisible durables, there may be disagreement both about their purchase and their use. There may, for example, be disagreement about the kind of home chosen, or about the use of the car. While a good deal of research has been made into the internal sharing of households in the third world, there have been very few such surveys in rich countries. An econometric study from Great Britain shows that the demand for children’s clothes increased after a change to paying child benefit direct to the mother (Lundberg et al. 1997). This result at least seems to indicate that household consumption is influenced by who receives the income and how much of it.

The cost of living function and economies of scale Intuitively, it does not seem unreasonable that members of a family who live together, pool their incomes and share consumption more or less proportionately. But this intuitively reasonable idea has proved very difficult to formalise in a precise theory. There exists no canonical theory of household behaviour which leads to

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well-defined equivalent adult scales. The idea of equivalence scales is perhaps best understood by way of the so-called cost of living function, derived from economic utility theory, applied to economies of scale for adults living together. One can visualise several types of economies of scale within a household: purchases in bulk or in ‘family size’ packaging is more feasible for a large household than for a single person; in families with many children clothes and toys can be passed on from the elder to the younger and so on. One type of economies of scale is due to goods that are technically public within the household, such as kitchen equipment and other consumer durables. Chapter 4 introduced the utility function U (Y ), where Y is income. If a person obtains welfare U from an income Y , we can also say that the income Y is necessary for her to obtain welfare U : Y is the cost of living corresponding to welfare U . This inverse relationship of the utility function is called the cost of living function Y = C(U ). In the economic theory of equivalence scales, U is often interpreted as the welfare of a household, not an individual. However, the welfare of a group of persons such as a family or household is not an easy concept to interpret. In order to avoid this complication, I shall derive the household cost of living function by way of individual welfares. Consider a man who wants to marry. His cost of living function when living alone is C(U, 1). We ask the question: how large an income does he need to support a wife and retain the standard of living he had before marrying? (When defining the standard of living, we ignore the increase in welfare he may gain from acquiring a wife.) In order to answer the question, we have first of all to decide how his income is shared between himself and his wife. Assume that it is shared equally in the sense that their individual welfares are equal. Furthermore, and to simplify, assume that they have the same preferences. Having the same preferences in this context means not only needing equally much to obtain a certain level of welfare, but also having the same preferences for how their consumption should be composed. Let there be two kinds of consumer goods: public goods and individual goods. The cost of living function of the husband when single can then be divided into two parts: C(U, 1) = CP (U, 1) + CI (U, 1), where the subscripts stand for public goods (P ) and individual goods (I ) respectively. Now clearly, when husband and wife live together, they need twice as much of the individual goods as a single adult, but an unchanged amount of public goods. To achieve the welfare level U 0 for each, the married couple needs C(U 0 , 2) = CP (U 0 , 1) + 2CI (U 0 , 1) The above equation defines equivalent incomes at welfare level U 0 for a single adult and a married couple; the incomes being equivalent in the sense that they give equal levels of individual welfare. To define an equivalent adult scale corresponding to U 0 , we divide the cost of living function of the couple with that of the single man, and after a little light arithmetic obtain EAS(U 0 , 2) = 2 − aP (U 0 , 1)

(10.1)

Household income

81

Here, aP is the fraction of income spent on public goods (the budget share) at welfare level U 0 . The point of this formal exercise is to see that the scale defined in equation (10.1) depends on the level of welfare, U 0 . Therefore, it is not necessarily the same for all incomes. How the equivalent adult scale varies with income depends on how the budget share of public goods varies with income. Since the goods that are public within the household tend to be expensive consumer durables, it might seem reasonable to think of their budget share as increasing with income. On the other hand, because these goods are expensive, the well-to-do household can choose whether to treat durables as public goods or not. They can have several bathrooms and several cars. The equation (10.1) is easily generalised to any size of household, as long as preferences are identical and shares equal. It can be shown to overestimate the value of EAS(U, n), since the larger households will tend to shift consumption towards public goods. The larger the household, the more it pays, for instance, to have a private car instead of going by bus or train. The assumption of equal sharing in the sense of equality of welfare is crucial to the existence of uniquely defined equivalent adult scales. Take the example of two adults with unequal shares. In that case, it is possible to define two different scales: one for each level of welfare. Let us be gender neutral, and call the two persons A and B. Assume that A takes the larger share of individual goods. The household will then need less than the income given by equation (10.1) to ensure that A obtains a given welfare U 0 . To ensure that B obtains welfare U 0 , household income will have to be larger (and thus ensure an even greater welfare for A). Economically independent adults can, and often do, achieve similar economies of scale as the married couple described above by sharing amenities such as kitchen, bathroom, washing machine etc., but without otherwise pooling their incomes. It is therefore not always clear when the incomes of flatmates should be corrected for household economies of scale, and when the individuals concerned should be treated as independent economic units.

The cost of children The background for the idea of equivalent adult scales very much includes the welfare of children. By computing equivalent incomes, one originally wanted to compute the income necessary for a man to be able to provide in a reasonable way for his wife and his children. The scale values of children cannot be given the same theoretical foundation as those of adults, by means of a cost of living function. The cost of living function is derived from the utility function, and, as explained in Part I, Chapter 8, the utility function of a child is a problematic concept. The best basis for understanding the idea of equivalent adult scales for children is probably the purely intuitive one that children share the standard of living of their parents. Parents and children live together and normally take their meals together. It is reasonable to assume that parents buy for their children consumption goods

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Measuring inequality

of the same kind, of the same quality and in the same amounts that they buy for themselves. The norm in contemporary society seems to be that parents and children should have roughly the same standard of living, suitably modified to children’s different needs. The cost of children is usually understood to be the cost of their individual consumption. Sometimes, however, the cost of children is taken to mean the cost in terms of the parents’ welfare. The parents are then assumed to gain welfare from the pleasure of having acquired children on the one hand, but to lose welfare from having to forego consumption in favour of the children on the other. The rationale is that with modern contraception, having children is a voluntary choice which would not be made unless it increased the parents’ welfare. A distinction is therefore made between the conditional and unconditional cost of children. The conditional cost is the cost of the children’s current consumption, the unconditional cost is the loss of parents’ welfare, which is assumed to be smaller than the conditional cost. This way of thinking stems from an influential article by Pollak and Wales (1979). It is not, of course, meaningful if the purpose of our analysis is to study the welfare of children. Therefore, the majority of researchers analysing income distribution pay lip service to the Pollak and Wales paper, but prefer to base their analysis on conditional cost. But whether the primary purpose of the analysis is to study the welfare of the parents or that of the children, the two must be analysed together, simultaneously. Because parents and children live together and consume together, and since, furthermore, children are almost wholly dependent on what their parents choose to give them, it is impossible to analyse the welfare of children separately from that of the parents. A suitable interpretation of the concept of an ‘equivalent income’ is that it indicates how well parents are able to provide for their children, given that they themselves should also be able to achieve a certain level of consumption. Time cost of children Children need care as well as consumption goods. Care requires the time of one or more adults. Time costs were not included in the definition above of the cost of children, and is hardly ever referred to in the literature on equivalence scales. The reason is that the cost of time is not included in standard income, only in full income. The full income of an individual is FI = MI + wT, as we saw in Chapter 9, in the section ‘Full income’. It is determined by the wage rate, available time and non-labour income. The full income of a household is the sum of the full incomes of all members of the household. In Chapter 9, I wrote that available time is the same for everybody: 24 hours a day. Children’s need for care, however, makes a difference. Time needed for child care can be provided either by one or both parents, or by paid professionals (day-care centres, nursery schools, nannies), or a combination of all these. The time provided by the parents themselves has the same value as their other activities, namely the wage rate, while professional care is bought at the current market price.

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83

Let the time needed by a child be TCH = T0 + T1 , where T0 is the time provided by the parents, while the time bought is T1 . The full income available to the parent responsible for child care is then: FI = MI + wT − wT0 − pT1

(10.2)

Equation (10.2) ignores the complication of division of work between the parents (when both of them are present). It is just meant to give an idea of how the time cost of children can be incorporated into a definition of full household income. It is plausible to assume that both the volume and the composition of children’s needs vary with age. Newborn infants need care, or at least supervision, 24 hours a day. Their individual consumption needs, such as food and clothing, are fairly small. As the child grows older, the time needed for supervision decreases while material consumption increases. While the need for time diminishes with age, it seems reasonable that it does not become zero as long as the children are minors. But there is a sharp decrease in the need of time from parents or professionals paid by the parents when the child starts school. Elementary school is free in most countries, but parents normally have to pay for day care for younger children.

Estimating equivalent adult scales There are several ways of estimating equivalent adult scales. 1 2 3

Some scales are based on standardised family budgets, decided by experts. Some are estimated from interview surveys of peoples’ subjective evaluations of the cost of various sizes of households. Some are based on econometric analysis of data from household expenditure surveys.

These different methods tend to give different results, and no widely accepted scale has as yet evolved. A fairly abundant literature exists on the two last mentioned methods. Some references to the econometric literature on the subject will be given in the chapter on ‘Suggested further reading’. Expert evaluations of the cost of children tend to arrive at large estimates, much larger than estimates based on consumption surveys. Surveys of people’s subjective evaluation, on the other hand, tend to give fairly low estimates. It is tempting to suspect that such subjective evaluations depend on the person interviewed, particularly if there are unequal shares within the household. Even in the simple form shown in equation (10.1) above, equivalent adult scales are difficult to estimate from observed consumer expenditure. One reason is that in practice there is no clear distinction between public and individual goods. To some extent, it is a matter of choice whether to have one or more cars, for instance. Another reason is that differences in observed expenditure patterns between households of different sizes are the result of many different factors that may be impossible to disentangle. Two simplified methods of estimation from data on consumer expenditure are the so called Engel and Rothbart methods. They are old-fashioned but still useful,

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Budget share of food (a)

0.70

CC

0.60 C 0.50

0.40

0.30

0.20

∆Y (0.40)

∆Y (0.30) Income (Y )

Figure 10.1 The budget share of food and the Engel method.

and I shall describe them briefly. They also serve to demonstrate some difficulties of estimating equivalent incomes and cost of children from observed data. The Engel method relies on what is called ‘Engel’s law’ of consumption expenditure: expenditure on food is a decreasing proportion of total consumption expenditure as income increases. There is a solid body of evidence for Engel’s law, which is confirmed by studies of consumption expenditure from all countries. There is also firm evidence to show that the budget share of food increases with the size of the household for a given income. The Engel method is illustrated in Figure 10.1. The figure shows the budget share for food, a, along the vertical axis and household income, Y , along the horizontal axis. The two curves show how the average budget share for food varies with household income for a couple (C) and a couple with one child (CC). The Engel method uses incomes that have equal budget shares for food as approximations of equivalent incomes. In Figure 10.1, it is illustrated for the budget shares 0.40 and 0.30. The incomes corresponding to budget share a are Y C (a) and Y CC (a) respectively. The increase in income necessary to maintain an unchanged budget share is marked as
Y (a). We see that
Y (0.30) >
Y (0.40). In fact, the curves are drawn so that
Y (a)/Y (a) is independent of a, which implies that the proportion Y CC (a)/Y C (a) and thus the scale value of a child is constant. If the relationship between a and Y is visualised as a straight line instead of the curve in Figure 10.1, the implication would be a constant
Y (a), making the scale value of a child decrease as income increases. Now, an econometric analysis must be based on some assumption about the mathematical relationship

Household income

85

between a and Y before it is possible to estimate equivalent incomes. Therefore the possible variation of scale values depends in a crucial way on how the econometric analysis is carried out. The Engel method can be used to compute scale values for adults as well as children. The Rothbart method applies specifically to the cost of children. The researcher tries to identify items of expenditure that are consumed by adults only. A household with children is then assumed to have an income equivalent to a household without children when the adults of the two households can afford to spend the same amount of money on themselves.

The unit of analysis In the section ‘Equivalent adult scales’, I wrote that a household of four persons will, in an analysis of income distribution, be treated as four individuals with equal equivalent adult incomes. Such is indeed at present the preferred procedure of most researchers. It used to be fairly common, however, to work with the household as the unit to be counted, not the individual, and this method of analysis may still occasionally be met with.

11 What should we measure?

The preceding two chapters have introduced several different concepts and measures. There are income, wealth and the combination named access to economic goods, but also several different definitions of income. So which is the right measure of what? My answer would be that there are several answers, both to what we should measure and how we should measure it. The answers depend on which questions we want answered. This last statement is less trivial than it seems: much thought, not to mention the many reams of paper, has been spent on trying to puzzle out the one and only Correct Definition of Income. An analysis of the distribution of economic goods must in some sense and to some extent answer the questions: is the distribution just? and if not, why not? The analysis should therefore be based on some idea of distributional justice. Ideally, the variable to be measured should correspond to a good that is to be justly distributed. Since there are several such goods, the researcher should be clear in her own mind, and make clear to her readers, which good she bases her analysis on. Note that, of the theories of justice in Part I, only Rawls advocates access to economic goods (income and wealth) as a distributional end in itself. And neither Rawls nor any other moral philosopher considers access to economic goods as the one and only distributional end. Income is the chief determinant of access to economic goods. The problem when trying to evaluate concepts of income in relation to theories of justice, is that philosophers tend to be long on profundity and short on empirical measurement. Capability is not yet an operational concept, and Rawls does not seem to have considered the problems of defining the income and wealth that he wants to see equally distributed. Dworkin’s concept of resources falls far short of the human capital that is so important for chances of economic success in modern societies. Empirical work on income distribution is in the main based on welfarist approaches, inspired by the economic welfare theory. Therefore, the connection between the theoretical but unobservable concept of ‘welfare’ and empirical definitions of income is well researched. It is no accident that the concepts of equivalent incomes, equivalence scales and the cost of children considered in Chapter 10 are all defined in terms of welfare. The ideal aimed at is income as a measure of welfare or well-being, often narrowed down to so-called material or economic well-being. But the idea of income as a measure of welfare rests on fairly shaky

What should we measure?

87

foundations. No matter which income concept is used, income is a reasonable proxy for welfare only on some stringent assumptions, the most important one being that all persons have identical preferences. Note that neither the Hicks nor the Simons definition of income quoted in the beginning of Chapter 9 makes income a measure of welfare. I suggest a tentative division of approaches to measuring income into two groups: income as a measure of outcomes of choice and income as a measure of constraints on choice. Welfarism is concerned with outcomes. Resources, capabilities, primary goods represent, or are intended to represent, constraints. Theories of justice vary as to when they consider the individual responsible for her choice and its outcome. Today’s constraint may be the result of yesterday’s choice. The length and content of education determines a person’s position in the labour market, both the possibility of obtaining work, and the wage at his command. Earnings are then decided by the wage rate and choice of working hours in labour markets where such choice exists. The presence of one or more children is a constraint on time available for paid work and leisure. Having children is, however, in modern society, a free choice. For all choices described above, available options will vary with the social and economic background of the chooser. For example, no society offers exactly the same options to women as to men. Moreover, outcomes of choices are often uncertain. And sometimes we regret the choices we have made. It is then important to consider to what extent choices are reversible – in the short and in the long run. Options also depend on the social and economic conditions of the country we study. Therefore the content of the concepts used may vary according to social context. To take a simple example: the cost of children depends on whether there is free schooling, on the cost of pre-school child care and on what kind of public health service there is, if any. In countries where a dowry is demanded, daughters are more expensive to parents than sons. Above all, the choices available to women vary strongly with social conditions, as we know. With this in mind, I shall consider some of the definitions of income proposed.

Household or individual income? In Chapter 2, I wrote that all contemporary theories of distributional justice are based on the principle of ethical individualism. In Martha Nussbaum’s words: When we look at the family, whose capabilities do we look at? Here, we must repeat: we look at each person. ··· The principle of each person as an end does entail, however, that the separate person should be the basic unit for political distribution. (Nussbaum 2000: 246, 247) Nussbaum advocates capabilities as the distributional good. But her principle of the individual as an end should, under ethical individualism, apply equally to

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resources, primary goods and welfare. Therefore, no matter which distributional good we want to approximate by measuring income, it seems clear that the measure should be individual. So why is household income almost universally considered the relevant variable in standard analyses of income distribution? One strong reason is the situation of children. Income as a constraint on children’s choice is not a meaningful concept. Since children cannot live on their own, if we want to know about their standard of living, we have to know the resources of the household they live in. And since like must be compared with like, when comparing households with children and households without children, the measure must be household income, suitably corrected for household size and composition. When we consider adults, the conclusion is not so clear. As noted in Chapter 10, it is standard to assume that the members of a household pool their incomes. It is also a standard assumption that they have more or less the same level of consumption. If, then, we think of income as possible consumption only, the correct measure is household income, again suitably corrected for household size. Note that household income in this case is a measure of possible consumption in a double sense. Household income measures the possible total consumption of the household if there is neither positive nor negative saving. Household income per equivalent adult measures the possible consumption of each household member if they have equal shares. Household income per equivalent adult corresponds to the Hicksian definition of income. By this definition, children receive an income as do beggars. If we think of income more in the terms of the Simons definition, as a right and as giving the power to make decisions, individual income seems to be the relevant concept. Both theoretical and empirical analysis show that income earning power makes a difference for distribution within the household. For married women, having their own income makes a difference in several other respects, independently of the effect on consumption in the household. Of special importance is the possibility that independent earning power gives for leaving an abusive marriage. In this respect, earning power is probably better measured by full income than by cash income. In any case, individual income is the better measure of economic power and economic independence, and therefore also of economic capability. The choice, then, between household income and individual income will depend on the question asked. To my mind, a proper analysis of income distribution needs both concepts. When measuring household income, an approach based on measuring constraints rather than welfare may be a way out of the muddle of equivalent adult scales. The constraints approach would look for the moral and legal constraints on parents’ expenditure of time and money created by the presence of children. Parents have a moral and, in most countries, a legal obligation to look after their children and secure the children’s material and emotional welfare. The constraints these obligations impose are to be found in social and legal norms rather than in actual expenditure. Also, the children’s effect on a parent’s welfare is irrelevant for measuring constraints.

What should we measure?

89

The constraints approach indicates an expert appraisal of a minimum or normal cost of children rather than econometric methods of estimation.

Standard income, extended income, full income? For a person who is able to choose her working hours freely, full income is the best measure of consumption possibilities and the true constraint on choice both between work and leisure and between paid work and unpaid work. In particular, the full income of a married woman is a better measure of her options than her cash income, which may be low because she has voluntarily chosen to be a housewife. But free choice of working hours is not always possible. Indeed, the freedom of choice to work or not is not possible for every one. There are the disabled and the retired (and retirement is not always voluntary). There are, above all, the millions and millions of unemployed. For those who are employed, the choice is constrained by the working hours offered by enterprises. It used to be the case that the choice offered was full time or nothing, with perhaps some leeway concerning overtime. In many countries, however, part-time work is increasingly available. There seems to be an emerging pattern where fathers and the childless of either sex work full time, while mothers work part-time. The fact that so many mothers choose part-time work indicates that there is a further constraint on working hours, namely the time needed to look after children. Involuntary unemployment can be handled in a full income approach by setting the wage either equal to zero, or to an agreed small value which allows for the possibility of home production. Constraints due to child care can be allowed for by reducing the total time available. The data needed for measuring full income are certainly not more difficult to collect than those of the many household surveys routinely carried out in industrialised countries. Even so, it is very difficult to find analyses of the distribution of full income. In a world where everyone worked either full time or not at all, and where there were only one income earner per family, the difference between full income and cash income would not matter. For both measures, inequalities would be due to the same two factors: differences in wage rates and differences in non-labour income. For single persons with no children, this is still true. But for single parents and households with two or more adults, inequalities in income are also due to variations in working hours. It then matters for the analysis whether variations in working hours are due to free choices or to constraints. The choice of income concept here seems to depend on social conditions in the society studied: the structure of the labour market, and the provision of affordable day care for children. In Chapter 9, cash income could be extended in three ways: by including services from consumer durables, by including home production and by including consumption wholly or partly paid for by the government. Services from self-owned homes are usually included in standard income as far as practically possible.

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Including home production may be seen as a step towards working with full income. This form of extended income tends to diminish, but not eliminate, differences in income between couples due to different rates of participation in paid work.1 The differences would probably diminish even more if measured by full income. The greater part of home production is created by women working as whole time or part-time housewives. It increases the consumption of the household, but only a part of the production accrues to the housewife herself. Extending income by including household production is therefore only useful for measuring household income, not individual income. Household production cannot be observed, only estimated more or less accurately by means of time studies. For both theoretical and practical reasons, it therefore seems to me that efforts towards extending the income concept should concentrate on data for full income, which is observable. Consumption paid for by the government should ideally be included in income. If the benefits accrue approximately proportionately to standard income, including it makes no difference to measures of inequality. But if it tends to accrue proportionately more to low incomes, standard income will overestimate inequality. The error will then be of particular importance in international comparisons of inequality, since the extent of government paid consumption varies greatly between countries.

Lifetime income or annual income? Looking at Figure 9.3 in Chapter 9, it seems that annual income at no time equals lifetime income, or life prospects in Rawls’s words, at least for men. Annual income is smaller than lifetime income when he is young and when he is old, larger than lifetime income in middle age. Moreover, if our man faces a perfect capital market, his consumption will be nearer to annual lifetime income than to annual income. The life-cycle behaviour sketched in the figure therefore indicates that the variable to be measured is income over the whole lifespan, not annual income. Many households will also experience a life cycle like the one sketched in Figure 9.3. When comparing annual incomes of households, we should be aware that young families will typically be paying off debts while middle-aged families will be saving for their old age. Annual income therefore overvalues their consumption possibilities. Retired couples will typically have paid off their mortgage, and have savings to supplement their pension. Annual income therefore undervalues their consumption possibilities. In all these typical cases, actual consumption in a given year may be a better indicator of consumption possibilities than is income. And for people still alive, it is an indicator that we need: true lifetime income can only be known after death. Another indicator of lifetime income is annual income combined with a suitable annuity value of wealth, as explained in the section ‘Access to economic goods’ of Chapter 9. However, as seen from Figure 9.3, this procedure will not do for young people under education.

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91

Actual lives do not, however, always conform to the typical pattern. A promising career may be stopped by illness, disability, unemployment. Even when insured against, these accidents reduce income. For an unemployed person, the fact that he was well off when employed is no great comfort. And because the future is uncertain and accidents may happen, among other reasons, the capital market is not perfect in the economist’s sense. Even the most rational of planners is not able to even out consumption over the life course as smoothly as indicated in Figure 9.3. And, of course, we are not all perfectly rational planners of life. Also, preferences for distributing consumption over time may vary. Therefore, annual income may be a real constraint on present consumption even when it is smaller than expected lifetime income.

12 Lorenz curves and inequality measures

All happy families are alike, but every unhappy family is unhappy in its own way. (L. Tolstoy, Anna Karenina)

The distribution function We wish to study how economic goods are distributed within a group of persons. ‘Economic goods’ can be income, wealth, a combination of the two, or any other measure of access to economic goods relevant to some conception of distributional justice. The examples in the present text will all be taken from the distribution of income for the simple reason that such data are the most readily available. The variable to be studied will sometimes be called resources, sometimes income. Access to economic goods is a quantitative variable, measured by a real number. Its distribution can be described by well-known statistical measures like frequencies, mean, variance. In addition, specific methods have been developed to describe and measure the inequality of a distribution. Two key concepts are concentration curves and inequality measures. Among concentration curves, the Lorenz curve is the most well known. There are many different inequality measures. In fact there are, as we shall see, infinitely many. While there is only one way for a distribution to be equal, there are infinitely many ways for distributions to be unequal, and unequal distributions, like Tolstoy’s unhappy families, are all unequal in their own way. The theoretical study of inequality measures and their properties has shown that the concept of ‘inequality’ is a complex one that cannot be expressed in a single measure. Before introducing Lorenz curves and inequality measures, I shall briefly discuss the basic concept of a distribution function and some properties common to all distributions of economic goods. The Dutch economist Jan Pen (1974) introduced the parade of dwarfs as a way of visualising a typical income distribution. Imagine a parade of all adults, 18 years or older, say, in a country. By suitable magic, they have all been transformed: they have stretched or shrunk till their height equals their income. You stand on the platform of honour, watching them all run past. What you see, is a parade of dwarfs, all incredibly small.

Lorenz curves and inequality measures

93

Let us say that the whole parade takes ten hours. For the first hour or so, the marchers are hardly visible. Slowly, their size increases. But even after five hours, when half the parade has passed, the marchers have still not attained the average height of a man (in Norway: 180 cm). And no wonder, for during the first two or three hours, there are not many men to be seen. This parade scrupulously follows the rule: ladies first! After six hours or so the average man runs by, while the women are becoming few and far between. The height of the marchers begins to increase fairly fast after about eight hours. During the last hour, the procession has been transformed into a parade of giants – then skyscrapers – then mountains – the Alps, the Andes, the Himalayas – the very last few you glimpse may overshadow Mount Everest for all you know. You cannot see more of them than their legs, and no one really knows how tall they are. The profile of the parade in Norway at the end of the 1990s is shown in Figure 12.1 (except for the very tallest giants). Figure 12.2 shows the profile of the same parade differently organised. There, men and women march side by side, the women nearest you. The graphs show the women’s profile with the men’s above. Also, in order to get a clearer impression of the normal marchers, the top 5 per cent are not shown. The horizontal axes in Figures 12.1 and 12.2 are labelled u, and show relative positions in the parade, scaled from 0 to 1. The point on each curve corresponding to u = 0.5 shows the value of income such that exactly 50 per cent of adults receive this income or a smaller one. The income that thus divides the parade exactly in two is called the median income or just the median. The median incomes of women and men are shown as Mw and Mm in Figure 12.2.

Income

M Persons

Figure 12.1 Parade of dwarfs.

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Measuring inequality

Income

Men

Women Mm Mw

0.0

0.5 u

1.0

Figure 12.2 Inverse distribution functions of income; individual income, women and men.

Similarly, for every 0 ≤ u ≤ 1, each point on each curve answers the question: how large is the income x such that a fraction u of Norwegians receives an income of x or less? We can also turn this question around and ask: how large is the fraction of the population receiving an income equal to x or less? The curves answering this question are found by changing around the vertical and horizontal axes in Figures 12.1 and 12.2. We then obtain the inverse of the dwarf parade curves. The inverse of the curves in Figure 12.2 are shown in Figure 12.3. The curves in Figure 12.3 show the usual way of depicting the distribution of income, or any other resource, in a graph. Each curve is a graphic representation of the distribution function of a resource in a population, sometimes also called the cumulative distribution function. I shall refer to it as the distribution for short, and write it sometimes F (x), sometimes F (·) or F . It is the basic concept for describing and analysing the distribution of resources. The values of F (x) vary between 0 and 1; F (x) = 0 for the smallest income and F (x) = 1 for the maximum income. The function F has the same properties as a probability distribution. In the literature on income distribution, F is sometimes interpreted as the probability distribution for income, sometimes as the empirical distribution; often no distinction is made between the two. I shall follow this practice of allowing both interpretations. Mathematically, the curves in Figure 12.2, are the inverse of the distribution functions in Figure 12.3. The inverse distribution function is written F −1 (u). The median, M, is defined either by F (M) = 0.5 or by M = F −1 (0.5). As we have seen, the median divides the population into two equally large groups. It is a fractile

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95

1.0 0.9 0.8 0.7

Women

0.6 Men

0.5 0.4 0.3 0.2 0.1 0 Mw

Mm

Income

Figure 12.3 Distribution functions of income; individual income, women and men.

Table 12.1 Composition of decile groups Decile

1 2 5 9 10

Women

Men

All

18–25

26–66

67+

18–25

26–66

67+

27 16 5 0 0

32 28 49 25 13

2 28 4 1 0

29 14 6 1 0

11 8 27 70 83

0 5 10 2 3

100 100 100 100 100

Total income.

or quantile. Other commonly used fractiles are the quartiles, quintiles and deciles which divide the population into 4, 5 and 10 equal groups respectively. Decile or other fractile groups are useful for showing where in the distribution different kinds of people are found. Table 12.1 shows the composition of selected decile groups in the Norwegian distribution shown in Figure 12.2. We see that, in Norway, the lower groups are mainly composed of women of all ages and of young and old men, while the higher groups are dominated by men between 25 and 67 years old. Those in the lower decile groups are either not active in the labour market (young and old women and men), or work part-time (women with children). Similar tables for other societies would perhaps show different age compositions of upper and lower groups, but the tendency of women to be at the bottom of the distribution seems to be universal. A third way of depicting income distributions is the frequency curves in Figure 12.4. They show the fractions of the population having an income falling in

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Measuring inequality

1994 1982

0

100

200

300

400

500

1,000

Income

Figure 12.4 Frequency distributions of income.

certain intervals; the intervals shown are very small. The shape of frequency functions is typically asymmetric and strongly skewed towards the left. Therefore, in resource distributions M < m, the median is smaller than the mean. Most people believe they earn less than the average. Figure 12.4 shows that they are right!

The Lorenz curve Two basic tools for analysing inequality are the Lorenz curve and the corresponding relationship of Lorenz dominance. A Lorenz curve formalises the intuition that, the greater the economic inequality, the less resources will accrue to the poor and the more to the rich. It is a graph representing, for every u between 0 and 1, the proportion of resources accruing to the poorest fraction, u, of the population. The corresponding function is written L(u). By convention, L(0) = 0, while, obviously, it is always the case that L(1) = 1. If resources are distributed strictly equally, every fraction u of the population will always dispose of the same fraction u of resources, and L(u) = u for all u. The Lorenz curve will be the main diagonal in a square with area 1 (see Figure 12.5). I shall refer to this diagonal as the line of equality. If there is any inequality at all, there will always be a poorest u fraction of the population whose proportion of resources is smaller than u, so that L(u) < u except for u = 1. The Lorenz curve will then lie below the line of equality. If inequality is extreme, one person disposing of all the resources, L(u) = 0 for all u < 1. The Lorenz curve will collapse to the horizontal axis and show a discontinuous jump immediately before u = 1. Figure 12.5 shows the Lorenz curve of income for Norwegian adults in 1996. However, a single curve like the one in Figure 12.5 tells us nothing about the

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97

1.0 0.8 0.6 A 0.4 L(u) 0.2 0.0 0.0

0.2

0.4

0.6

0.8

U 1.0

Figure 12.5 A Lorenz curve. L(u)

L2 L1 0

u⬘

u*

1 U

Figure 12.6 Lorenz curves before and after an equalising transfer.

distribution except that there is not complete equality. Lorenz curves are useful only for comparing different distributions. They are tools for ranking or ordering distributions according to degree of inequality. Intuitively, it seems reasonable that the closer a Lorenz curve lies to the line of equality, the greater is the equality of the corresponding distribution. This intuition can be shown to be true. I shall just sketch the kind of proof that can be given. Let F1 be a distribution with corresponding Lorenz curve L1 (u). A transfer of 1 euro is made from one person to another with less resources, say from a person corresponding to u∗ to a person corresponding to u
< u∗ . Such a transfer is called an equalising transfer. The transfer creates a new distribution, F2 , which is clearly more equal than the first. After the transfer, the proportion of resources accruing to the population between u
and u∗ has increased slightly. Below u
and above u∗ the distribution is unchanged. The Lorenz curves before and after the transfer are shown in Figure 12.6. L2 (u) > L1 (u) for u
≤ u < u∗ and L2 (u) = L1 (u) for

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Measuring inequality

1.0 0.8

Women 1990

0.6 0.4 0.2 0.0 0.0

Women 1982

0.2

0.4

0.6

U 0.8 1.0

Figure 12.7 Lorenz dominance.

u < u
and u > u∗ . The Lorenz curve corresponding to the more equal distribution lies partly closer to the line of inequality, and is nowhere more distant. When the Lorenz curve of one distribution lies entirely above (closer to the line of equality than) the Lorenz curve of another distribution, this is called Lorenz dominance. More formally: Let F1 and F2 be two distributions with corresponding Lorenz curves L1 (u) and L2 (u). F1 Lorenz dominates F2 if L1 (u) ≥ L2 (u) for all u and L1 (u) > L2 (u) for some u. An example of Lorenz dominance is shown in Figure 12.7 which shows the Lorenz curves of the income of Norwegian women in 1982 and 1990. As will be seen in the section ‘Inequality measures’, the concept of Lorenz dominance is basic to the analysis of inequality. The Generalised Lorenz curve The Generalised Lorenz curve depicts both the level and the inequality of a distribution, and is of particular relevance when studying the social evaluation of inequality (see Chapter 13). It is the Lorenz curve multiplied with the mean: GL(u) = mL(u)

(12.1)

From equation (12.1) it follows that GL(0) = 0 and GL(1) = m. For two distributions with identical means, GL1 (u) > GL2 (u) if and only if L1 (u) > L2 (u). But if the distributions have different means, the GL-curve corresponding to the highest mean will always lie above the other after some u. Generalised Lorenz curves corresponding to the 1996-income distributions for Norwegian women and men are shown in Figure 12.8. Generalised Lorenz dominance is defined analogously to Lorenz dominance.

Lorenz curves and inequality measures

99

300,000

250,000

Men

GL (u)

200,000

150,000 Women

100,000

50,000

0 0.00

0.20

0.40

0.60

0.80

1.00

u

Figure 12.8 Generalised Lorenz curves, total income.

Inequality measures If one distribution Lorenz dominates another, it is less unequal than the distribution it dominates, as we saw in the previous section. But the Lorenz curves of two distributions may cross. In that case, the criterion of Lorenz dominance cannot be used to rank the two distributions by degree of inequality. The criterion of Lorenz dominance defines a partial ordering only of distributions. When the Lorenz curves cross, an intuitively appealing method of comparing the two distributions is by comparing the areas between the line of equality and the respective curves, the shaded area A in Figure 12.5. It is then natural to say that the distribution with the smaller area lies closer to the line of equality, and is therefore the more equal of the two. The area of the surface A is the basis of the Gini coefficient, which is defined as: G = 2A

(12.2)

When the distribution is a perfectly equal one, the Lorenz curve lies along the line of equality, A = 0 and G = 0. Perfect inequality implies that A is half the area

100 Measuring inequality Table 12.2 Inequality, Norwegian men and women Gini coefficient

1982 1990 1996

Coefficient of variation

Women

Men

All

Women

Men

All

0.42 0.36 0.37

0.34 0.37 0.45

0.42 0.39 0.51

0.79 0.67 1.00

0.97 0.88 1.91

0.99 0.89 1.79

Total income. Persons 18 years and over.

of a square with surface equal to one, A = 1/2 and G = 1. The Gini coefficient therefore varies between 0 and 1. The Gini coefficient is an inequality measure. There are several other inequality measures used in the literature, although the Gini is the measure that is the most widely used. Another common inequality measure is the coefficient of variation, v, which is the standard error divided by the mean.

v=

  1/n (Yj − m)2 m

(12.3)

When all resources are equal, v 2 = 0. There is no upper limit. Unfortunately, the Gini coefficient and the coefficient of variation do not always rank the inequality of distributions in the same way. An example is given in Table 12.2. The Gini coefficient and v tell different stories both about each separate year and what has happened over time. They both show that Norwegian women were more equal in 1990 than in 1982. But when comparing women with men in 1982, the Gini and the coefficient of variation disagree. They also disagree about the change in men’s inequality from 1982 to 1990. And, as we shall see in the following section, the disagreement cannot be resolved by deciding that one is in some sense a more correct inequality measure than the other.

The theory of inequality measures An inequality measure is a statistical measure of the deviation from equality of a distribution. An inequality measure gives a complete ordering over the set of possible distributions of resources. Let I (F ) denote an inequality measure. By the statement ‘I (F ) gives a complete ordering over the set of possible distributions’ is meant the following: for any two distributions F1 and F2 there exist corresponding inequality measures I (F1 ) and I (F2 ). Since I (F1 ) and I (F2 ) are real numbers, either I (F1 ) > I (F2 ) or I (F1 ) = I (F2 ) or I (F1 ) < I (F2 ). In other words, an inequality measure can always decide whether two distributions have the same degree of inequality, or the one is more unequal than the other.

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101

In his classic On Economic Inequality, Amartya Sen warns the reader against assuming that the concept of inequality necessarily may be represented as a complete ordering: There are reasons to believe that our idea of inequality as a ranking relation may indeed be inherently incomplete. If so, to find a measure of inequality that involves a complete ordering may produce artificial problems, because a measure can hardly be more precise than the concept it represents. . . . this might well account for some of the difficulties with standard measures of inequality. (Sen 1997: 6) Moreover, the concept of inequality is not value free. Most of us have strong opinions about equality and inequality, and the word ‘unequal’ often has the connotation ‘unjust’. Amartya Sen comments: In a trivial sense it is, of course, the case that one can define ‘inequality’ precisely as one likes, and as long as one is explicit and consistent one may think one is above criticism. But the force of the expression ‘inequality’, and indeed our interest in the concept, derive from the meaning that is associated with the term, and we are not really free to define it purely arbitrarily. (Sen 1997: 47, 48) The theoretical approach to measuring inequality found in economic literature, consists of postulating a list of properties, or axioms, that define an inequality measure; axioms that are generally accepted as reasonable. The most commonly accepted axioms are: 1

2

3 4 5

Axiom of transfers: An equalising transfer of, say, 1 euro from one person to another person with smaller resources reduces inequality. (Provided, of course, that the original difference in resources is larger than 1 euro.) Axiom of anonymity: The inequality measure is not influenced by the identity of the persons disposing of resources. More formally: if a transfer is made from person A to person B such that they exactly change places in the distribution, A disposing of B’s former resources and vice versa, inequality is unchanged. This axiom is also called the axiom of impartiality or symmetry. Axiom of invariance to scale: Inequality is not changed by a proportional change in all resources. Axiom of invariance to population size: Inequality is not changed by changes in the size of the population, the distribution being otherwise unchanged. Axiom of normalisation: The inequality measure should equal zero if all resources are equal, and be greater than zero if at least two resources are unequal.

102 Measuring inequality The axiom of transfers is basic whatever our intuitive sense of inequality may be. It is the property which ensures that the inequality measure actually measures inequality. The property of anonymity is perhaps less obvious. It ensures that the only characteristic of a person relevant to the measure of inequality is the resources possessed by that person. Her merits do not count, nor do her needs. Impartiality implies that the variable we study must indeed be the one that is relevant for justice. Invariance to scale seems at first glance to be a purely practical property. It ensures that the inequality measure is not affected by the unit the resource is measured in: inequality in a distribution is the same whether the money measure is in euros, pounds, dollars or cents. But inequality is also unaffected by a proportional change in the real level of resources. Therefore, invariance to scale implies that inequality is unaffected by the total amount of resources available for distribution: we can compare inequality in a rich society with inequality in a poor society using the same measure. Invariance to scale also implies that the inequality measure is unchanged if the resources of every person increase (or diminish) proportionately, but the inequality measure decreases if the resources of every person change by the same absolute amount. The French economist Serge-Christophe Kolm has proposed an inequality measure that is invariant to equal absolute, but not to equal proportional changes in resources. His inequality measure will be discussed in Chapter 13. Invariance to the size of the population is a practical property, ensuring that the inequality measure can compare the distribution of resources in China, say, with the distribution in Norway, or indeed can compare the distributions within any groups of unequal size. The normalisation property is also a purely practical one. Observe that there is no axiom further defining the scale of the measure. An inequality measure satisfying the axioms on p. 101 gives a complete ordering of distributions, in the sense of always being able to decide whether one distribution is more unequal than another. But the algebraic value of the measure is arbitrary. Inequality measures are ordinal measures. Some implications of ordinality will be discussed further in the section ‘Ordinality of equality measures’. It can be shown that there are infinitely many inequality measures that satisfy the five axioms on p. 101. Some of them give the same ordering of distributions, but give different numerical values to the inequality measured. But there are also infinitely many inequality measures that give different orderings, like the Gini coefficient and the coefficient of variation in the case of Norwegian women and men shown in Table 12.2. There is not, however, complete anarchy. It can be shown that all inequality measures give the same ordering in one particular case, namely when there is Lorenz dominance. Formally: Let I (F ) be an inequality measure, and let F1 and F2 be two distributions. If F1 Lorenz dominates F2 , I (F1 ) < I (F2 ) for all inequality measures I (F ) satisfying

Lorenz curves and inequality measures

103

axioms 1 to 5. If on the other hand the two Lorenz curves cross, it is always possible to find two inequality measures, I (F ) and I ∗ (F ), both satisfying axioms 1 to 5, and such that I (F1 ) < I (F2 ) while I ∗ (F1 ) > I ∗ (F2 ). Figure 12.7 shows that women’s income distribution in 1990 Lorenz dominates that of 1982. Therefore, the Gini coefficient and the coefficient of variation should show the same inequality ranking of the two distributions, as indeed they do in Table 12.2. In the same table, the two measures give different rankings for women and men in 1982, so we know that the corresponding Lorenz curves must cross. To the question: does there exist a value free inequality measure, the answer is both yes and no. The criterion of Lorenz dominance gives an ordering that is acceptable to almost everyone, and it is an ordering that every inequality measure respects. When there is Lorenz dominance, the choice of inequality measure does not matter. On the other hand, when we compare distributions whose Lorenz curves cross, the ordering depends on our choice of inequality measure.

Ordinality of inequality measures Among the five axioms defining inequality measures, none fixes a numerical scale for them, except for the demand that they equal zero for equal distributions. Inequality measures as defined by axioms one to five are ordinal. They serve to rank or order distributions by degree of inequality; apart from this ranking, their numerical values have no meaning in themselves. In particular, the numerical value of the difference in inequality between two distributions makes no sense, neither does the difference measured as a percentage. Different inequality measures may be ordinally equivalent, that is, they give the same ordering of all distributions. Take the Gini coefficient as an example. It is defined by G = 2A, where A is the area between the Lorenz curve and the equality line (see Figure 12.5). Both G = 2A and G/2 = A are inequality measures, and it is easy to see that they will always give the same ordering of distributions as G does. If A1 < A2 , then obviously G1 < G2 . Indeed there are infinitely many measures that will give the same ordering of distributions as the Gini coefficient: another instance is G√2 since G21 < G22 if and only if G1 < G2 . Similarly, v 2 and v are both ordinally equivalent to v. However, ordinally equivalent measures may give different values of both absolute and percentage differences between distributions. Table 12.3 shows percentage changes in inequality calculated from Table 12.2. We see from the table that the Gini coefficient and the coefficient of variation give different absolute and percentage changes even when they show changes in the same direction. A and G are proportional (G = 2A), and so give the same rankings and the same percentage changes. But v and v 2 give different percentage changes although they are ordinally equivalent. Neither the numerical value of the inequality measure nor the numerical value of changes has meaning in themselves. This important point is often ignored in empirical analyses of income distributions.

104 Measuring inequality Table 12.3 Changes in inequality 1982–90; in per cent

G A v v2

Women

Men

All adults

−14 −14 −15 −28

+9 +9 −9 −17

−7 −7 −10 −19

Source: Table 12.2.

L1

C

B

L2 u*

U

Figure 12.9 Crossing Lorenz curves.

Some properties of different inequality measures One way of classifying inequality measures is according to their sensitivity to different parts of the distribution. When Lorenz curves cross, each of them will be nearer to the equality line in some part. Crossing Lorenz curves are shown in Figure 12.9. In Figure 12.9, L1 shows the greater inequality in the lower part of the distribution, for u < u∗ , while L2 shows the greater inequality for u > u∗ , in the upper part of the distribution. The Gini coefficient measures the difference in inequality as the difference between the two areas, G1 − G2 = B − C. Other inequality measures assign other values to these areas. In Table 12.2, we saw that the Gini coefficient and the coefficient of variation gave different rankings of the internal inequality of women and men in 1982. Therefore, we know that the corresponding Lorenz curves must cross. The crossing Lorenz curves are shown in Figure 12.10. It is possible, with a great deal of good will, to see that the curves cross somewhere after u = 0.90. The area corresponding to C in Figure 12.9 is minuscule. The coefficient of variation gives this tiny part of the curve greater weight than the preceding nine-tenths. It is to an extreme degree more sensitive to the upper part of the distribution than to the lower part.

Lorenz curves and inequality measures

105

1.0 0.8 0.6 Men 0.4 Women 0.2 0 0

0.2

0.4

0.6

0.8

U 1.0

Figure 12.10 Lorenz curves of women and men (1982).

To see how the Gini and the coefficient of variation value different parts of the distribution we can study the effect transfers have on their values. For ease of calculation, I shall use v 2 instead of v, since they are ordinally equivalent. There are several formulas for arithmetic calculation of the Gini coefficient. One of them is:  2 j j Yj n+1 − (12.4) G= 2 n m n Here, the observed resources Y are ranked according to size, and j is the ranking number. The square of the coefficient of variation is calculated by:  (1/n) j (Yj − m)2 2 v = m2 Now, let us study the effect on v 2 and G of 1 euro transferred from person number k to person number i, where k > i, so that the transfer is an equalising one. The transfer does not change the mean of the distribution. Let
v 2 and
G denote changes in the values of v 2 and G respectively. We find that: 2(Yi − Yk + 1) nm2 2(i − k)
G = n2 m 2
v 2 =

For v 2 , we see that
v 2 < 0 if Yk > Yi + 1. An equalising transfer decreases inequality as measured by the coefficient of variation and v 2 fulfills the axiom of transfers. The numerical value of the decrease in inequality depends on the numerical value of the difference between the two resources, Yi − Yk , in relation to the mean. For a given mean, a transfer of 1 euro from a person with resources of 1 million euros to a person with 0.5 million euros will therefore diminish inequality equally

106 Measuring inequality with the same transfer made from a person with 0.5 million euros to a person with 0. The effect of a given transfer does not depend on where in the distribution the transfer occurs. The effect on G of the transfer depends on i − k, the difference in ranking number between the giver and the receiver, not on the difference between their resources. For a given difference in resources between giver and receiver, the Gini coefficient will decrease more, the more persons there are in the interval between them. Roughly, the Gini coefficient weights transfers the more strongly, the closer the giver and taker are to the mode of the distribution. Now, resource distributions tend to be asymmetric and skewed towards the left (see Figure 12.4). But the mode and its relation to mean and median tends to change from group to group. It is therefore not always easy to interpret the Gini ordering when comparing distributions with different shapes. Let us now compare the effect of a series of transfers as measured by G and v 2 , starting from a distribution F1 with Lorenz curve L1 , Gini value G1 and coefficient of variation v12 . A transfer of 1 euro is made from a person with resources of 1 million euros to a person with zero resources; certainly an equalising transfer. The new distribution is F2 , with corresponding L2 and v22 . It follows from the axiom of transfers that F2 Lorenz dominates F1 , and therefore G2 < G1 and v22 < v12 . Now make the opposite kind of transfer, an unequalising one, from a person with resources worth 1 million to one with 2.5 million euros, and let the resulting distribution be number 3. Again, both inequality measures will agree that inequality has increased from distribution 2 to distribution 3. But when comparing distributions 1 and 3, the Gini coefficient and the coefficient of variation will disagree. The first transfer will affect the Gini more than the second one, since there are certainly more persons in the interval from 0 to 1 million than in the interval from 1 to 2.5 million. Therefore, G3 < G1 . For the coefficient of variation, on the other hand, a transfer across an interval of 1.5 million will always have a greater impact than one across an interval of 1 million. Therefore, v13 > v12 . From Table 12.2 and Figure 12.10 we saw that the coefficient of variation weights the upper end of the distribution more heavily than the Gini. Studying the effect of transfers showed the same result: transfers among the rich result in greater changes in v than in G. This difference between G and v is due to the shape of the distribution function, with its concentration of units at the lower end, as shown in the frequency functions in Figure 12.4. It is not, however, obvious what the criteria should be for choosing one inequality measure rather than another. Intuitively, it might seem as if a concern for equality would lead to a corresponding concern for the people with smaller resources, and hence to the choice of inequality measures weighting the lower part of the distribution. This can be shown to be so. Some inequality measures can be derived from social evaluation functions. For these, called ethical inequality measures, it is possible to state explicitly which value judgements they imply: they are those of the evaluation function. Ethical inequality measures will be considered in the next chapter.

13 Social evaluation of inequality

Lorenz dominance and inequality aversion A social evaluation function, as introduced in Chapter 4, is an instrument for analysing the trade-off between equality and affluence. The social evaluation functions in Chapter 4 were defined on individual welfares. It is not, however, generally agreed that individual welfare is what ought to be equally distributed in a just society. At the same time, the proper balance between equality and affluence is a question of general concern in theories of distributional justice. A social evaluation function can have as its arguments individual endowments of whichever resource or other variables that are relevant for justice. Let us assume that there is just one such variable. The social evaluation function could then be written: W (Y1 , . . . , Yj , . . . , Yn )

(13.1)

Here Yj is the amount of the resource accruing to person number j . More compactly, the social evaluation function can be written W (F ), where F is the distribution function of the resources, as in Chapter 12. The function in equation (13.1) is a Sen function if it is symmetric and inequality averse. There is an affinity between Sen functions and inequality measures. They are both symmetric. They are also both sensitive to equalising transfers, but in opposite ways. An equalising transfer increases the value of a Sen function but decreases the value of an inequality measure. In fact, when comparing two distributions with the same mean and where one distribution Lorenz dominates the other, a Sen function will always rank the Lorenz-dominating distribution above the dominated one. More formally: Let W (F ) be the value of a Sen function when the resource distribution is F (·). Then, W (F1 ) > W (F2 ) for all Sen functions if and only if F1 general Lorenz dominates F2 . If F1 and F2 have the same mean, W (F1 ) > W (F2 ) for all Sen functions if and only if F1 Lorenz dominates F2 . In the absence of dominance, the social ordering of distributions will depend on the shape of the Sen function; more precisely, on its degree of inequality aversion.

108 Measuring inequality

Ethical inequality measures An ethical inequality measure is an inequality measure derived from a Sen function. The advantage of an ethical inequality measure is that the value judgements implicit in all inequality measures are made explicit by specifying the Sen function it is based on. An ethical inequality measure measures inequality as the social cost of an unequal distribution. The corresponding Sen function decides what the size of the cost is. Let F0 be a distribution with mean m0 , and let W (F0 ) = W0 where W (·) is a Sen function. If resources are unequally distributed, an equalising transfer will increase the value of W (·). On the other hand, a proportional reduction of all resources will decrease the value of W (·), and, of course, decrease the mean of the distribution. Since a transfer does not change the mean, it must be possible to make an equalising transfer and at the same time decrease all resources proportionately so as to keep W (·) constant while decreasing the mean. In other words, there exists a distribution F1 with m1 < m0 such that W (F1 ) = W (F0 ), and F1 is a more equal distribution than F0 . Such operations are possible until all possibilities of equalising transfers are exhausted, in other words until resources are perfectly equally distributed. The corresponding mean will be written mE .

Y2

Y1 = Y2

Y 20

W0

Y 10

mE m0

Figure 13.1 The social cost of inequality.

Y1

Social evaluation of inequality

109

The situation is illustrated in Figure 13.1. There are two persons, they have resources Y10 and Y20 with mean m0 . The corresponding social indifference curve is W 0 . We see that this same social indifference curve is achievable when Y1 = Y2 = mE . It is clear that mE < m0 . For every Sen function W , given an unequal distribution F with mean m, there exists an equal distribution FE with mean mE < m and such that W (FE ) = W (F ). Both m and mE are measured in the same units as the resource, say euros. The difference m − mE equals the value of resources per capita wasted on unequal distribution, the average social cost of inequality. Note that m − mE depends on the shape of W as well as the distribution at the point of departure. For a given distribution F with mean m, differently shaped Sen functions will give different values of mE . In the case of just two persons, the reader can verify for herself with a suitable graph similar to Figure 13.1 that the size of mE will depend on the degree of curvature of the social indifference curve passing through the distribution Y10 , Y20 . The fraction RC =

m − mE mE =1− m m

equals the cost of inequality relative to the mean, and has no denomination. If the starting point is a perfectly equal distribution, m = mE and the relative cost will be 0. The smaller mE relative to m, the greater the social cost of inequality. As mE approaches 0, RC will approach 1. RC is almost an inequality measure. It is easily verified that RC satisfies three of the axioms of inequality measures. It satisfies the axiom of transfers and the axiom of anonymity, and RC = 0 when resources are equally distributed. Its upper limit is 1. But RC does not necessarily satisfy the axiom of invariance to scale. If all Y s increase proportionately, say by a factor p, m is also multiplied by p and the inequality of the distribution is unchanged. The increase in mE , however, may be equal to, smaller than or greater than p. This happens because the inequality aversion of the Sen function may change as total resources increase. The Sen function may evaluate inequality as being of greater importance when society is rich than when it is poor: in this case, mE will increase proportionately more than m. Conversely, if W evaluates inequality as of greater importance in a poor society than in a rich one, mE will increase proportionately less than m.

Atkinson’s inequality measure The inequality aversion of W may also be independent of the level of resources. A class of Sen functions with constant inequality aversion is the following,

110 Measuring inequality introduced by A. B. Atkinson (1970), and called the Atkinson function:
1 (1/n) Yj1−ε for ε > 0 and ε = 1 1−ε j  (1/n) Yj for ε = 1 WA (Yj , . . . , Yn ) = WA (Y1 , . . . , Yn ) =

(13.2)

j

The parameter ε measures the degree of inequality aversion of WA (·). For ε = 0, we get: WA (Y1 , . . . , Yn ) =

1
Yj = m n j

In this case, welfare equals the mean of resources and is not affected by their distribution. The Atkinson function is inequality neutral. For ε > 0 the function is inequality averse: an equalising transfer increases social welfare. The larger ε is, the greater is the degree of inequality aversion of the welfare function. At the same time, increasing ε means increasing the weight of the lower incomes. At the limit, as ε approaches infinity, the value of WA (·) will become wholly determined by the very lowest income, and the social evaluation function in equation (13.2) becomes equivalent to Rawls’s maximin criterion. From the formulas in equation (13.2), we can compute the value of the equally distributed mean, mE , and the social cost of inequality. For a given distribution, these magnitudes will depend on ε. Consider for example the distribution [1, 1, 6, 7, 10], with mean 5. For ε = 0.5, mE = 2.1, for ε = 2, mE = 1.4. The fraction RC = (m − mE )/m is 0.59 for ε = 0.5 and 0.90 for ε = 2. The larger ε, the larger is the proportion of resources considered as wasted on inequality. It is easy to verify that if all resources were doubled, the corresponding equally distributed mean would also double. Therefore, m and mE vary proportionately, and the fraction RC is independent of scale. Therefore, it defines an acceptable inequality measure. The corresponding inequality measure, called Atkinson’s inequality measure is: ⎤1/(1−ε) ⎡
 Yj 1−ε 1 ⎦ for ε > 0 and ε = 1 IA = 1 − ⎣ n m j (13.3)   Yj 1/n for ε = 1 IA = 1 − m j

For ε = 0, IA = 0 whatever the distribution, corresponding to the case when WA (·) is inequality neutral. As ε approaches infinity, the value of IA , like the corresponding social evaluation function, tends to be dominated by the very lowest resources. We see then that the parameter ε determines both the degree of inequality

Social evaluation of inequality

111

aversion in equation (13.2) and the weight IA gives to different parts of the distribution. Strong inequality aversion corresponds to strong weighting of the lower incomes. The numerical value of Atkinson’s inequality measure has a precise interpretation, namely the social cost of inequality. Therefore, it is a cardinal measure: a monotonic increasing transformation will be an inequality measure that is ordinally equivalent, but whose numerical value does not measure the social cost of inequality. There exists a family of inequality measures that are, in fact, ordinally equivalent to the family of Atkinson measures; it will be considered in the next chapter.

14 Some inequality measures

The Generalised Entropy class of inequality measures The coefficient of variation belongs to a class of inequality measures, the Generalised Entropy measures, or simply Entropy measures for short. The formula for computing them is: ⎤ ⎡
 Y j α 1 1 ⎣ − 1⎦ (14.1) I (α) = α(α − 1) n m j

Here, Yj stands for the resource of person j . The equation (14.1) is not defined for α = 0 and α = 1. Instead, the following are used:   Yj 1
Yj ln I (1) = T1 = n m m j   Yj 1
ln I (0) = T0 = − n m j

Thus, the whole class comprises measures where the parameter α may be any real number, positive, negative or zero. In practice, however, the choice of parameter is restricted if negative or zero resources occur in the data. If resources equalling 0 occur, the parameter α must be strictly positive. In the presence of negative resources, α must be an even integer, positive or negative. While the measure I (0) is defined for strictly positive variables only, I (1) may be used on data including zero observations by defining (Yj /m) ln(Yj /m) = 0 whenever Yj = 0.1 These demands limit the usefulness of the Entropy measures. To the class of Generalised Entropy measures belong measures constructed by several authors independently of one another. The measures I (0) and I (1) are called the Theil inequality measures, and were first presented in Theil (1967). They are closely related to the Entropy measure used in information theory, hence the name of the whole class: Generalised Entropy measures. The choice of α determines how the Entropy measure weights different parts of the distribution. The greater the numerical value of strictly positive α, the greater

Some inequality measures

113

the weight of large resources in I (α). Conversely, for negative α the small resources will have the greatest influence. At the limit, as α approaches minus infinity, only the smallest resource will count. A simple transformation of the coefficient of variation gives the Entropy measure with α = 2: ⎤ ⎡   1 ⎣ 1
Yj 2 v2 I (2) = − 1⎦ = m 2 2 n j

We see that I (2) is a strictly increasing transformation of v; therefore the two measures are ordinally equivalent. A more complicated transformation leads to the Atkinson inequality measures. The Atkinson parameter ε corresponds to the parameter α: α = 1 − ε. Since the Atkinson measures are defined for ε > 0 only, the ordinally equivalent Entropy measures have α < 1. Negative values of α give Entropy measures that are ordinally equivalent to Atkinson measures derived from strongly inequality averse social evaluation functions. The coefficient of variation, then, is not associated with any inequality averse social evaluation function. The Entropy measures have the useful property of being additively group decomposable: the inequality of a population can be expressed as the sum of inequality between and within groups of that population. In fact, the Entropy measures can be shown to be the only class of inequality measures that are additively decomposable. Decomposition of inequality measures will be discussed in Chapter 16.

The M-curve and the A-measure The Lorenz curve is an example of a concentration curve or inequality curve. Another is the M-curve, defined as M(u) =

L(u) m(u) = m u

(14.2)

The M-curve measures the average of resources accruing to the poorest 100u per cent of the population, m(u), in proportion to the average in the whole population. If the distribution is perfectly equal, M(u) = 1 for all u. Extreme inequality implies M(u) = 0 for all u except u = 1. From equation (14.2), we see that the M-curve contains exactly the same information as the Lorenz curve. But it gives a slightly different visual representation of a distribution by showing the lower parts of the distribution in more detail than does the Lorenz curve. Figure 14.1 shows the M-curve corresponding to the Lorenz curve in Figure 12.5. The M-curve defines a corresponding inequality measure similarly to the way the Gini coefficient is derived from the Lorenz curve. The measure, written IAa , is defined as the area between the M-curve and the corresponding line of equality, as

114 Measuring inequality 1.00 0.80 M (u) 0.60 0.40

L (u)

0.20 0.00 0.00

0.20

0.40

0.60

0.80

1.00

Figure 14.1 An M-curve.

shown in Figure 14.1. For a distribution of perfect equality, IAa = 0, for extreme inequality, IAa = 1. A formula for computing IAa is IAa = 1 −

n

n

j =1

j =1

1
1
mj = 1 − hj Y j nm nm

(14.3)

Here, mj is the mean of all resources equal to or lower than Yj , while hj = 1/j +1/(j +1)+· · ·+1/n; j is the ranking number when resources are numbered according to size. A transfer of 1 euro from person number i to person number k when i > k, changes IAa as follows:
IAa = −1/k − 1/(k + 1) − · · · − 1/(i − 1) The greater the distance in rank from the giver i to the receiver k, the greater the number of terms in the sum above. Like the Gini coefficient, IAa values equalising transfers according to the difference in the ranking numbers of giver and receiver, not the difference in their resources. For a given difference in ranking numbers, IAa will diminish the more, the smaller are the absolute values of i and k. Therefore, IAa is an inequality measure that gives more weight to the lower part of the distribution than does the Gini.

Kolm’s inequality measure Serge Christophe Kolm (1976a) has proposed a class of inequality measures that are not independent of scale. The Kolm measures, like Atkinson’s, are derived from

Some inequality measures

115

a social evaluation function, and depend on a parameter indicating the degree of aversion to inequality. ⎛ ⎞
1 1 Il = log ⎝ eα(m−Yj ) ⎠ (14.4) n α j

Here, α > 0. Il = 0 when all resources are equal. Like Atkinson’s measure, Il approaches 0 as α approaches zero, while the lower values of the resource variable are weighted more strongly as α increases. The inequality measure Il is unchanged if all resources increase by the same absolute amount, but increases if all resources change proportionately. It is therefore not scale invariant, and will depend on the way resources are measured. Kolm writes: But these problems are exactly the same ones which are traditionally encountered in the comparisons of national or per capita incomes . . . , and they can be given the same traditional solutions. Anyway, convenience could not be an alibi for endorsing injustice. (Kolm 1976a: 419, 420) The subscript l stands for leftist, which is the term Kolm himself uses. Kolm’s reason for not accepting scale invariance is the following: in May 1968, radical French students claimed that wage inequality was increased by an agreement raising all wage rates by the same proportion. Kolm therefore terms Atkinson’s measure as rightist. A general inequality measure, termed centrist, and including Atkinson’s and Kolm’s measures as special cases, are described in Kolm (1976a).

Choosing an inequality measure When choosing inequality measures for an analysis, there are both theoretical and practical considerations. First of all, several measures should be computed for each distribution. When there is no Lorenz dominance, we have seen that different inequality measures give different rankings of distributions. Since the question of interest very often is comparison of distributions over time, say, or between countries or regions, you can never trust one single inequality measure to tell the whole truth. The measures chosen should cover different parts of the distribution. The Atkinson or General Entropy families are both convenient in this respect; the same computational programme can be used for all measures with just one parameter to vary. The General Entropy family is easily computed with standard statistical programmes; essentially, it consists of computing the means of various transformations of the income or other resource variable to be analysed. Moreover, the measures in the Entropy family are additively group decomposable, which is an advantage for studying inequality within and between groups; age groups or regional groups for instance. (The technique will be explained in Chapter 16.)

116 Measuring inequality If the interpretation of inequality as a social cost is not important, the Entropy family is to be preferred to the Atkinson family, being easier to compute. But as noted above, the Entropy family also has a disadvantage: for many values of α, it cannot handle zero or negative observations. Some analysts try to avoid the problem by removing offending observations, and justify this by claiming that such observations represent errors. But there is no logical impossibility in zero or negative incomes. Government transfers and earnings cannot be negative, but capital income can. It is also perfectly possible for a person or a household to survive even though income is negative, since consumption can be paid for out of wealth. Pareto was wrong when he claimed that income must always be positive. Negative and zero incomes present no problems for calculating the Gini coefficient. The computation process is less straightforward than for the Entropy measures. The observations need to be sorted by size in order to compute the ranking number j in the equation (12.4). Also, standard statistical programmes normally have no ready-made procedure for computing the Gini. The Gini has the great advantage of being well known and easy to explain and interpret in a non-technical way. It is very widely used, which in itself is an advantage when we want to compare results from different analyses. The Gini coefficient alone, however, cannot tell the whole truth about distributions; it must be supplemented by other measures weighting other parts of the distribution. It is often claimed that it tends to give greatest weight to the middle part of distributions, but this claim is inaccurate. The Gini coefficient stresses that part of the distribution where the density is greatest. Often, but not invariably, this will be the lowest part. The Gini coefficient belongs to a family of inequality measures computed according to the same principles, but weighting different parts of the distribution. One such relation of the Gini is the IAa measure presented in the section ‘The M-curve and the A-measure’. Another related measure weighting the upper parts of the distribution is presented in Aaberge (1986). These measures are not, however, well known internationally. A disadvantage of the Gini and its cousins is that they are not group decomposable (see Chapter 16).

Inequality in some OECD countries Table 14.1 is taken from the web pages of the Luxembourg Income Study (LIS 2002). The income measured is household disposable cash income per equivalent adult, with equivalent adult scale n0.5 . All inequality measures used in this table give the same ranking of countries, with one exception. As is commonly the case, sampling errors are not given, so it is not possible to know which differences are statistically significant (see Appendix B).

Table 14.1 Inequality in selected OECD countries 1994/95 Country

Year

Gini coefficient

Atkinson ε = 0.5

Atkinson ε = 1.0

Australia Canada France Germany Norway Sweden UK US

1994 1994 1994 1994 1995 1995 1995 1994

0.311 0.285 0.288 0.261 0.238 0.221 0.344 0.355

0.084 0.067 0.069 0.058 0.052 0.047 0.100 0.105

0.184 0.136 0.132 0.116 0.104 0.104 0.204 0.214

Disposable income per equivalent adult. Source: Luxembourg Income Study.

15 Poverty

Defining poverty is deciding on a threshold value of economic resources; a threshold value below which we agree no person should be forced to live. This threshold value of resources is called the poverty line. But economic resources are distributed continuously. Finding a single value which distinguishes between poverty and sufficiency is essentially an arbitrary matter of convention. Nevertheless, if we want to study poverty, some poverty line must be determined. There are two main definitions of poverty: absolute poverty and relative poverty. One fairly usual procedure for fixing an absolute poverty line is to begin with a list of foodstuffs that secure adequate nourishment for a household in the cheapest possible way. Quantities will depend, of course, on the size of the household. The corresponding expenditure is computed, and an acceptable budget percentage for food is decided on. If minimum food expenditure is c and the acceptable ratio for food expenditure is a, the poverty line Z is computed so that c/Z = a, and Z = c/a. The food expenditure is regularly revised as prices change, but not the items included in it. The official poverty line in the United States was determined in this way, with a = 1/3. It was set in 1965 and has since remained unchanged except for adjustments for price changes. In 2001 the poverty line for a single person was an income of 9,214 dollars a year, for a family of four it was 17,960 dollars. Internationally, the World Bank uses poverty lines of 1 and 2 dollars a day per person, calculated in the local currency and adjusted for purchasing power. In 1998, it was estimated that 1.2 billion people had consumption levels below the lowest line, corresponding to 1 dollar a day, and 2.8 billion had less than 2 dollars a day.

Relative poverty Within the European Union, poverty is defined as relative. The official poverty line is half the median household income per equivalent adult. It is sometimes claimed that relative poverty is a meaningless concept because it implies that a certain fraction of the population will always be poor as long as there is economic inequality at all. This claim confuses the concept of a fraction of the median or mean income with a fraction of the population. It is logically possible to have an unequal distribution of resources with no person having less than a certain fraction of median income.

Poverty

119

F1

Income

F2

Z

Persons

Figure 15.1 Distributions with and without relative poverty.

Figure 15.1 shows two distributions of a given total, one with and one without relative poverty. The curves represent the inverse distribution function F −1 , as in Figure 12.2. The poverty line Z is fixed at half the mean. In distribution 1, 10 per cent of the population has an income below Z. To create distribution 2, the income of every person above the poverty line has been proportionately reduced exactly enough to lift every poor person just above the poverty line. The mean income is unchanged. Inequality is certainly reduced, but not eliminated. The rationale of defining poverty in relative rather than absolute terms lies in the idea of social exclusion. The locus classicus is Adam Smith discussing taxation: By necessaries, I understand, not only the commodities which are indispensably necessary for the support of life, but whatever the custom of the country renders it indecent for creditable people, even of the lowest order, to be without. A linen shirt, for example, is, strictly speaking, not a necessity of life. The Greeks and Romans, lived, I suppose, very comfortably though they had no linen. But in the present time, through the greater part of Europe, a creditable day–labourer would be ashamed to appear in public without a linen shirt, the want of which would be supposed to denote that disgraceful state of poverty, which, it is presumed, no body can well fall into without extreme bad conduct. Custom, in the same manner, has rendered leather shoes a necessary of life in England. The poorest creditable person of either sex would be ashamed to appear in public without them. (Smith 1961, vol II: 399, 400) This famous quotation can be interpreted to mean that a shirt and leather shoes was necessary at the time ‘to keep up with the Joneses’, as the saying goes. We may react, perhaps, by feeling that the effort should be directed towards making society

120 Measuring inequality more liberal and accepting of variations in dress. But all societies, without exception, have standards of minimum decency in dressing and personal presentation. Contemporary Western societies may accept ragged jeans and a tee shirt, but not body odour. What revolts us in the homeless is not their rags, but their dirt and their smell. Now, keeping oneself clean and odourless requires not merely a deodorant, but daily showers and frequent laundering of clothes, all of which requires a certain stock of clothes and a minimum access to privacy and running water. The point Smith makes, is the same as Rawls when the latter describes ‘the social basis for self-respect’ as a primary good. The concept of poverty as social exclusion means that you are poor if your lack of economic resources prevents you from participating in society. We participate in society in many ways: ‘as citizens, workers, parents, householders, neighbours and members of the local community’ (Cripps et al. 1981: 1841 ). In order to participate in society in one or more of these respects, we need more than bare subsistence. For example, to obtain and keep work in modern Western society, we need an address, a telephone, (Don’t call us, we’ll call you), perhaps a car if public transport is scarce and unreliable. A widely used example of another kind is television in homes with children. If the teacher assumes everyone to have television at home, and uses references to programmes in class, the child without television is handicapped in her learning. The commodities needed to participate in society change, of course, over time. When I grew up in Norway in the fifties, a middle-class family did not normally possess a car and might well not be on the telephone. Television was unknown, and so unmissed. On the other hand, as Sen (1984b) points out, a relative definition of poverty may also lead to absurd results. If everybody starves, no one, by the relative definition, is poor. Sen therefore suggests a definition of poverty which is absolute in capabilities, not income and wealth. The temptation to think of poverty as being altogether relative arises partly from the fact that the absolute satisfaction of some of the needs might depend on a person’s relative position vis-a-vis others. (Sen 1984b: 333) Sen cites the quotation from Adam Smith about shame on page 119 to illustrate the point he is making. Avoiding shame is a capability, and an absolute. There is no question of suffering relatively less shame than others. The commodities needed to avoid shame, linen shirts and leather shoes, are determined by what the normal wear in society is, and so relative. In our days, the commodity of importance would be trainers, not leather shoes.

Measuring poverty Having defined a poverty line, we then have to measure the extent of poverty. There are two obvious measures. One is simply the number of persons living below the

Poverty

121

poverty line, the head count, so called. The other measure answers the questions: how far below the poverty line are the poor? How much would it cost to eliminate poverty? This is the poverty gap, computed as N
(Z − Yj )

(15.1)

j =1

where Yj is the income of the poor person number j , N is the number of poor persons and Z is the poverty line. A more general class of poverty measures, which includes both the head count and a normalised version of the poverty gap as special cases, is: Pα =

 N 
Z − Yj α

(15.2)

Z

j =1

For α = 0, the measure becomes the headcount, Pα = N . For α = 1, we obtain the normalised poverty gap: N
(Z − Yj ) j =1

(15.3)

Z

The importance of equivalence scales The choice of equivalence scales makes a considerable difference to the number of poor as well as to the composition of the poor population, as illustrated in Table 15.1 and Figure 15.2. Both the table and the figure show the results of computing household size as ne for various values of e. As e increases from 0, income per equivalent adult decreases in the larger households. This effect changes the whole distribution, including the median. As the Table 15.1 Poverty rates in selected countries by equivalent adult scale Country

e=0

e = 0.25

e = 0.36

e = 0.55

e = 0.72

Australia Canada Germany Norway Sweden UK US

18.0 17.1 10.5 14.3 13.9 17.0 19.7

16.0 15.0 7.6 10.3 7.9 15.2 17.9

14.8 14.4 6.6 8.9 6.5 14.0 17.8

12.3 13.2 5.2 5.1 5.4 11.4 17.2

11.7 12.3 5.4 5.2 5.3 8.1 17.2

Poverty line 50% of median income. Source: Buhmann et al. 1988.

122 Measuring inequality

4+ persons

14

Poverty rate

3 persons 12

2 persons

10

1 person

8 6 4 2 0 e =0

e = 0.1

e = 0.3

e = 0.5

e = 0.8

e=1

Figure 15.2 Composition of the Norwegian poor in 1996 by equivalent adult scale.

median changes, the poverty line changes when poverty is defined as relative. A single person with a low income for e = 0 may become relatively well to do for e = 1. Table 15.1 is taken from Buhmann et al. (1988). Figure 15.2 is based on my own computations from the Norwegian 1996 income survey. It shows the percentage of poor persons (adults and children) and their distribution among households with one, two, three and four or more members. The pattern shown in Figure 15.2 is similar to the one for France in Atkinson 1998, figure 1.7 and the one for Finland shown in Jäntti and Danziger 2000, figure 4. The majority of elderly live in single or two person households, while the larger households are mainly families with children. Therefore, Figure 15.2 also shows how the poor are divided between the elderly and families with children according to choice of equivalence scale.

16 Decomposition of inequality measures

Inequality measures and concentration curves describe the distribution of resources. Often we would also like to explain the distribution. Decomposing inequality measures may represent a step towards such analysis. Since inequality measures are purely descriptive statistics, the technique of decomposition never in itself gives explanations, only more detailed descriptions. But decomposition is sometimes a useful way of exploring the data in order to find the best analysis. There are two ways of decomposing inequality measures: by groups and by component.

Decomposition by group When decomposing by groups, we divide the population into mutually exclusive groups, for instance into men and women, into age groups or by economic activity. We then study the inequality within and between groups separately. The Entropy measures The Generalised Entropy measures are decomposable into terms expressing between-group inequality and within-group inequality. Divide the population into groups in such a way that each person belongs to one and only one group. Let subscript  g denote group g and let pg denote the group’s proportion of the population: g pg = 1. Between-group inequality, IB (α), is computed as if the resources of all persons within a group were equal.  
 mg  α 1 IB (α) = pg −1 α(α − 1) g m

(16.1)

Let the inequality within group g be Ig (α), and let µg = mg /m be the mean income in each group relative to the overall mean. The Generalised Entropy measure can then be written as
I (α) = pg µαg Ig (α) + IB (α) (16.2) g

124 Measuring inequality Here, the first part is the weighted sum of within-group inequalities, while the second part is the between-group inequality. The above decomposition is useful for several purposes. One obvious application is to correct inequality for the age composition of the population. As explained in the section ‘Lifetime income’ in Chapter 9, large inequalities between age-groups can be consistent with low inequality in lifetime incomes. A group decomposition of inequality is not, however, unique. Every term in the decomposition formula (16.2) is sensitive to the choice of α. As we know, withingroup inequality depends on the choice of α. The weights of the within-group inequalities, pg µαg also depend on α. For α = 0 the weights reduce to pg , but for α  = 0 the weights will also depend on the mean income of the groups. As seen from equation (16.1), the choice of α also influences between-group inequality. Note that between-group inequality automatically increases with the number of groups. At the limits, IB (α) = I (α) if every person is a group, while of course IB = 0 when the whole population is seen as one group. From equation (16.2) it is seen that total inequality always decreases if inequality within one group, Ig (α), decreases while the within-group inequalities, group means and group shares are constant. This is the property that is meant by the entropy measures being additively decomposable. It is a property not possessed by any other type of inequality measure, for example the Gini coefficient. The Gini coefficient To see why, consider the computation formula for the Gini coefficient:  n+1 j j Yj G=2 2 − n m n where j is the number of the ranking in the total distribution as before. Now, if the population is split into groups, each person will have a ranking number within the group that is different from her ranking in the population as a whole. Therefore, there is no simple correspondence between the group Gini coefficients and the population Gini coefficient. It is even possible to have transfers that decrease Gini inequality within one group but increase total inequality, as is seen from the example in Table 16.1. In Table 16.1, distribution 2 is created from distribution 1 by means of one equalising and one unequalising transfer within group A. The result is decreased inequality within group A, unchanged (of course) inequality within group B, and increased inequality in the total population. Table 16.1 Population and group Ginis Group

A

A

B

B

B

A

Gini

Gini A

Gini B

Distribution 1 Distribution 2

0 2

5 2

10 10

15 15

20 20

25 26

0.39 0.40

0.56 0.53

0.15 0.15

Decomposition of inequality measures

125

This kind of effect can only occur after a combination of equalising and unequalising transfers.

Decomposition by group: an example Table 12.2 shows that the total inequality in Norway as well as the internal inequality of Norwegian women decreased from 1982 to 1990 according to both the Gini coefficient and the coefficient of variation. We shall see how decomposition by group can bring out a pattern lying behind the decrease. It indicates that the decrease in inequality can be explained by changes in the occupational status of women, in particular by the rise in women’s labour force participation. Table 16.2 shows internal group inequalities for Norwegian women grouped by occupational status. The inequality measure used is the entropy measure with parameter α = 0.5, which gives approximately the same ordering as the Gini. Inequality is given for every second year in the period 1982 to 1990 and for 1996.1 We see that while inequality for women as a whole decreased steadily from year to year, there was no systematic change within each occupational group. Indeed, internal inequality of employees and pensioners was as good as constant, while internal inequality of the two other groups fluctuated. The decrease in population inequality must therefore be due to one of two changes. Either inequality between the groups has decreased, or women have moved to the two groups with low internal inequality, employees and pensioners. In fact, the relative incomes of occupational groups did not change during this period. What did change was the proportion of women who were employees (from 41 per cent in 1982 to 49 per cent in 1990) and pensioners (from 24 to 32 per cent). These changes in occupational status also caused women’s average income to increase from 48 to 57 per cent of that of men.∗

Table 16.2 Inequality by occupational group Group

1982

1984

1986

1988

1990

1996

Self-employed Employees Pensioners Others All women

0.17 0.07 0.10 0.54 0.36

0.13 0.07 0.10 0.61 0.35

0.17 0.08 0.11 0.46 0.29

0.15 0.07 0.11 0.46 0.27

0.14 0.07 0.11 0.52 0.27

0.33 0.07 0.17 0.60 0.28

Total gross income. Women 18 years and over.

* For not a few women, individual income increases when they become pensioners, as they are entitled to a minimum old age pension from the government whatever the size of their previous individual incomes.

126 Measuring inequality Table 16.3 Group decomposition of inequality Group

All

Men

Women

Year

1982 1990 1996 1982 1990 1996 1982 1990 1996

Total inequality

0.35 0.31 0.32 0.25 0.27 0.30 0.36 0.27 0.28

Between-group inequality Sex

Age

Status

0.07 0.04 0.03 — — — — — —

0.06 0.08 0.07 0.08 0.09 0.08 0.03 0.05 0.05

0.20 0.16 0.15 0.12 0.14 0.12 0.19 0.15 0.14

Total gross income. Persons 18 years and over.

Table 16.3 shows the contribution of between-group inequalities to total inequality in the years 1982, 1990 and 1996. The table shows inequality decomposed by three different groupings: by sex, by age and by occupational status. Looking first at total inequality, we see that the contributions to total inequality from inequality between women and men has decreased. So has the contribution from inequality between occupational groups, while the contribution from age groups has increased. Looking at the inequality of men and women separately, we see that all changes in the structure of total inequality from 1982 to 1990 can be traced to changes in the structure of women’s inequality. The contributions to women’s inequality from age differences is smaller than for men, but increasing. The contribution from occupational status is greater than for men, but decreasing. Altogether, the structure of women’s internal inequality seems to be approaching that of men. Table 16.3 also shows that total inequality of men increased from 1990 to 1996, and that the increase was not due to increases in between-group inequality. Neither was there any change in the distribution of men between occupational groups. The change from 1990 to 1996 must therefore be due to changes in within-group distribution. Analyses have indicated that the tendency to increased inequality in Norway during the 1990s was due to changes in the size and distribution of capital income. In order to study this question, we need to analyse the influence of the various income components on inequality.

Decomposition by income component Total income is, as we saw in Chapter 9, a sum of four components: wage income, entrepreneurial income, capital income and transfers. We would expect

Decomposition of inequality measures

127

these income components to be differently distributed among the population. There is a long history of analysis of factor shares, which is sometimes interpreted as the distribution of income between workers and capitalists. However, in practice it is not possible to find many persons that receive one kind of income only, at least in modern, industrialised economies. Capital income does, however, tend to accrue chiefly to persons with large total incomes. There exists no agreed method for analysing the influence of the various income components on total income inequality. There are two methods for decomposing inequality by income components. Each method has its advantages and disadvantages; none of them gives unambiguous answers. In order to analyse the effect of an income component on the overall distribution of income, we need to know how the components interact with one another and with total income. One way of analysing this interaction is by studying where in the distribution of total income the various components accrue. This approach leads to a decomposition of the Lorenz curve.

Decomposing the Lorenz curve For every u, the Lorenz curve measures the share of total resources accruing to the poorest 100u per cent of the population. Assume that there are two kinds of resources: Y = Y 1 + Y 2 . For each component, we can then define a new curve: l 1 (u) and l 2 (u). The curve l 1 (u) shows the share of component 1 accruing to the poorest 100u per cent of the population, and similarly for l 2 (u). These new curves are called interaction curves. Interaction curves for transfers and capital income are shown in Figures 16.1 and 16.2. Note that the interaction curve for capital income, l C (u), in Figure 16.1 takes negative values in its lowest range. This is because the lowest values of capital income are negative. For an income component which is equally distributed, l i (u) = u for all u and the interaction curve will coincide with the main diagonal, marked 0–1 in Figures 16.1 and 16.2. This main diagonal represents the equality line, as for the Lorenz curve. If the whole of component i, say, accrues the poorest person, l i (u) = 1 for all u. A component accruing entirely to the richest person will have l i (u) = 0 for all u except u = 1, where l i (u) = 1. Therefore, we have 0
l i (u)
1 for every u. When the interaction curve lies entirely above the equality line, the corresponding income component accrues mainly to persons in the lower part of the distribution of total income. When it lies entirely below the equality line, the income component accrues chiefly to persons in the higher part of the distribution. In Figure 16.1, we see that the interaction curve for transfers lies slightly above the equality line, while the interaction curve for capital income lies well below it, and rises steeply when u > 0.8.

128 Measuring inequality 1.0 T 0.8

0.6

0.4 C 0.2

0 0

0.2

0.4

0.6

0.8

1.0

–0.2

Figure 16.1 Interaction curves: capital income and transfers, employees. 1.00 0.90 0.80 T

0.70 0.60 0.50 0.40 0.30

C

0.20 0.10 0.00 0

0.2

0.4

0.6

0.8

1.0

Figure 16.2 Interaction curves: capital income and transfers, pensioners.

The Lorenz curve is a weighted sum of interaction curves:

L(u) =

m1 1 m2 2 l (u) + l (u) m m

(16.3)

Here mi is the mean of component i. Equation (16.3) can be generalised to any number of components.

Decomposition of inequality measures

129

Interaction coefficients A Gini interaction coefficient is defined analogously to the Gini coefficient, being based on the area of the surface between the interaction curve and the line u = 1. The area will be denoted  i . The corresponding interaction coefficient is γ i = 2 i − 1 The area  i equals 0 for a component accruing entirely to the poorest person, 1/2 for an equally distributed component and 1 for a component accruing entirely to the richest person. Therefore, −1
γ i
1, and γ i = −1 for a component accruing wholly to the poorest person, γ i = 0 for an equally distributed component and γ i = 1 for a component accruing wholly the richest person. Note that the richest and the poorest persons are the richest and poorest in terms of the distribution of total income. The interaction coefficients do not measure the inequality in the distribution of the corresponding income component, except in the special case of complete equality when γ i = 0. In fact, the income component taken by itself will have a perfectly unequal distribution both when γ i = −1 and γ i = 1, although its place in the total distribution will be completely different in these two cases. Since the Lorenz curve is a weighted sum of the interaction curves, the Gini coefficient is a weighted sum of the interaction coefficients: G=

m 1 1 m2 2 γ + γ m m

(16.4)

Equation (16.4) can be generalised to any number of income components. It makes a certain sense to interpret an interaction coefficient as a measure of the effect on total inequality of the corresponding income component. The term γ i mi /m we may interpret as the contribution to total inequality (as measured by G) of income component number i. The term ‘contribution to inequality’ should, however, be interpreted with some caution. If component i is equally distributed, γ i = 0, and the component contributes nothing to total inequality. On the other hand, it follows from the properties of inequality measures in the section ‘Inequality measures’ of Chapter 12, that if income component i increases proportionately, inequality of total income decreases. The interaction coefficients therefore do not predict the effect of increases or decreases in the corresponding income components. A computation formula for the interaction coefficients can be derived from equation (12.4) on page 105: γi =

2 covar(j, Yji ) nmi

(16.5)

The inequality measure A is similarly decomposable into A=

m1 1 m2 2 α + α m m

(16.6)

130 Measuring inequality where the interaction coefficients α k may be computed by: αi = −

1 covar(hj Yji ) mi

(16.7)

The constants hj are defined as in equation (14.3) on page 114. Decomposing the coefficient of variation The squared coefficient of variation is the only inequality measure that can be additively decomposed into terms containing the inequality of each separate component. Decomposing v 2 is straightforward, and can be carried out with any standard statistical computer programme. The disadvantage of the method is that v 2 is not in itself an attractive inequality measure. Since  v=

1/n



(Yj − m)2

m2

we also have v = 2

1/n



(Yj − m)2 var(Y ) = 2 m m2

As before, assume there are just two kinds of income. Total income is then Y = Y 1 + Y 2. Applying a well-known property of the variance of a sum, we obtain: var(Y ) = var(Y 1 ) + var(Y 2 ) + 2 covar(Y 1 , Y 2 )

(16.8)

Dividing both terms in equation (16.8) by m2 gives a natural decomposition of the squared coefficient of variation:

v 2 (Y ) =

m21 2 m22 2 2 covar(Y 1 , Y 2 ) v + v + m 2 1 m2 2 m2

(16.9)

We see that the inequality in total income is determined by the inequality in either component weighted by their income shares, and by their covariance. A natural way of defining the contribution to total inequality of each component would be to ascribe exactly half of the covariance term to each, making the contribution to

Decomposition of inequality measures

131

total inequality of component i: wi =

m2i 2 covar(Y 1 , Y 2 ) var(Y i ) + covar(Y 1 , Y 2 ) + = v m2 i m2 m2

The relative contribution to inequality of component i is: var(Y i ) + covar(Y 1 , Y 2 ) wi = si = 2 var(Y ) v

(16.10)

Both equation (16.9) and the above expressions can be rewritten in various ways according to taste, in particular to include the coefficient of correlation, which may be more familiar to some readers than the covariance.2 The covariance term covar(Y 1 , Y 2 ) measures the interaction between the two kinds of income. The covariance between wage income and capital income, say, will be negative if persons with low wage income have high capital income, positive if persons with low wage income also tend to have low capital income. The equation (16.8) can be generalised to any number of income components, but quickly becomes unwieldy, since the number of covariance terms increases faster than the number of components. A simpler formula when more than two components are involved, is based on the variance of a sum written as a sum of covariances. Let Y = Y W + Y T + Y C + Y E . Then, var(Y ) = covar(Y, Y ) = covar(Y, Y W ) + covar(Y, Y T ) + covar(Y, Y C ) + covar(Y, Y E ) Dividing the above by m2 , we obtain: v2 =

1
covar(Y, Y i ) m2

(16.11)

i

Decomposition by component: an example We saw in Table 16.3 that there seemed to be a slight increase in income inequality for adults from 1990 to 1996. Table 16.4 shows inequality in 1990 and 1996 Table 16.4 Inequality by occupational group Year

1990 1996

All adults

Employees

Pensioners

v

G

v

G

v

G

0.92 1.71

0.40 0.41

0.65 1.03

0.26 0.27

0.63 3.60

0.28 0.35

Total income. Persons 18 years and over.

132 Measuring inequality measured by the Gini coefficient and the coefficient of variation, and for all adults as well as for the two largest occupational groups: employees and pensioners. To facilitate decomposition, Table 16.4 is based on a definition of income that is slightly different from that in Table 12.2. Note that in both tables, the rise in inequality seems more striking when measured by the coefficient of variation than by the Gini. As we know, the coefficient of variation is strongly influenced by changes in the upper part of the distribution. Tables 16.5 and 16.6 show decompositions of the Gini coefficient and the coefficient of variation by income component in 1996. The rows of Table 16.5 show the elements in equation (16.4) determining the Gini: the interaction coefficient γ i in column 1, and γ i weighted by the income share (γ i mi /m), in column 2. These ‘contributions to inequality’ add up to the Gini coefficient of total income. They are shown as per cent of the Gini in column 3, to be compared with the corresponding income component as per cent of total income in column 4. In Table 16.6, the first column shows the elements of the sum in equation (16.11), that is, for each income component covar(Y, Y i )/m2 is shown. The two tables show that the relative contribution of each income component to total inequality depends on the inequality measure. For all adults, capital income contributes 14 per cent to total inequality measured by the Gini coefficient, and 71 per cent measured by v 2 . Since the coefficient of variation strongly reflects the top end of the distribution, this large percentage indicates that capital income is

Table 16.5 Decomposition of the Gini coefficient Income component Wage income Entrepreneurial income Capital income Transfers Total income

γi

Contribution to G

Per cent of G

Per cent of income

0.43 0.64

0.26 0.10

64 25

61 14

0.82 −0.10 —

0.06 −0.02 0.41

14 −3 100

7 16 100

Total income. Persons 18 years and over.

Table 16.6 Decomposition of the coefficient of variation Income component

Contribution to v 2

Per cent of v 2

Per cent of income

Wage income Entrepreneurial income Capital income Transfers Total income

0.43 0.39 2.09 −0.07 2.91

15 16 71 −2 100

61 14 7 16 100

Total income. Persons 18 years and over.

Decomposition of inequality measures

133

Table 16.7 Capital income, transfers and inequality

Employees

Pensioners

Per cent of G Per cent of v 2 Per cent of income Per cent of G Per cent of v 2 Per cent of income

Capital income

Transfers

19 65 5 19 97 18

−4 −1 6 54 2 87

Total income. Persons 18 years and over.

strongly concentrated among the top incomes. See also the interaction curves for capital in the Figures 16.1 and 16.2. Table 16.7 shows, in a more summary way, the contributions of capital income and transfers to the inequality of the two groups, employees and pensioners. It shows that the effect of an income component depends on which subgroup of the population we analyse. Note in particular that transfers contribute negatively to inequality for employees, while they contribute positively to inequality for pensioners for both inequality measures. The reason is, of course, that transfers constitute by far the greatest component of income for pensioners, and so must contribute positively to inequality as long as pensions are not the same for all.

Appendix A: uncertainty and expected utility

Consider a person who has a sum of money to invest and who has the choice between three different projects. Each project may have one of four different results. The possible incomes from the investments are listed in Table A.1. For each project, there is a given probability for achieving each of the four incomes. For simplicity, all four results in the columns of Table A.1 are assumed to be equally probable, with probability 41 . The expected income from a project is defined as the weighted mean of the incomes with the probabilities as weights. It is denoted by E(Y ), where Y denotes income. In Table A.1, the expected income of project 2 is calculated as 41 (25 + 50 + 125 + 200) = 100. More generally, with n different incomes, all with the same probability 1/n, we have: E(Y ) =


1 Yj n

(A.1)

j

It can be shown that under reasonable assumptions, the preferences of a rational investor can be characterised by associating a number with each possible outcome. The rule associating numbers with outcomes is called a utility function, and the numbers can be interpreted as measures of the utility associated with a given outcome. The expected utility of a project is the weighted sum of the utilities with Table A.1 Expected income and expected utility Project 1

E(Y ) E(U )

Project 2

Project 3

Income

Utility

Income

Utility

Income

Utility

0 45 150 205

0 7 12 14

25 50 125 200

5 7 11 14

50 75 160 215

7 9 13 15

100

100 8.25

125 9.25

11

Appendix A

135

the probabilities as weights, and is denoted E(U ). Assuming n different incomes, all with probability 1/n, we have: E(U ) =


1 U (Yj ) n

(A.2)

j

From the same assumptions that imply the existence of a utility function, it follows that the investor will always choose the project that gives the greatest expected utility. The choice of project will not only depend on expected incomes, but also on the preferences of the investor; that is, on the shape of his utility function. The theory distinguishes between three types of preferences and hence three types of investors: risk averse, risk neutral and risk loving. When choosing between a project with a certain income and an uncertain project with the same expected income, the risk averse investor will always prefer the certainty. A risk neutral investor will be indifferent between them, and the risk loving investor will prefer the uncertain project. Figure A.1 shows the utility functions of a risk averse investor. It has the same shape as the utility function in Figure 4.1, Chapter 4. Decreasing marginal utility of income implies risk aversion. In general, investors with different preferences will choose differently. But in certain cases, all investors will agree on preferring one project to another. The preferred project is then said to dominate the other. There are two types of dominance of particular interest, called first order and second order (stochastic) dominance. In Table A.1, project 3 dominates the two others. Every single outcome (income) is better than the corresponding case for the two other projects. This is called stochastic first order dominance.

U U(Y )

Y

Figure A.1 Utility and risk aversion.

136 Appendix A

F –1(u)

F2–1 F1–1

0

1

u

Figure A.2 Second order stochastic dominance.

Project 1 and 2 have the same value for expected incomes, but project 2 is less risky: the lowest values are higher and the highest value lower than in project 2. We say that project 2 second order dominates project 1. Figure A.2 shows second order dominance in a more general situation with many different incomes. First order dominance is illustrated in Figure 12.2. In both figures, the incomes are ordered from the lowest to the highest, their numbers in the ranking are shown along the horizontal axis, the corresponding income is shown along the vertical axis. Now it can be shown that if project 1 first order dominates another, the dominating project will be preferred by all investors that maximise expected utility. If project 1 second order dominates another, the dominating project will be preferred by all risk averse investors.

Appendix B: sampling errors

Inequality measures and other observators of income distributions are in practice computed by means of data from sample surveys. Therefore, they are statistical estimators of the underlying parameters in the population and subject to sampling errors. In principle, these sampling errors should themselves be estimated, and the estimates of, for example, inequality measures given as statistical confidence intervals. In particular, differences in inequality should be subjected to tests of statistical significance. In practice, standard errors of the estimates are hardly ever computed. The reason is that the formulas for standard errors look forbidding, and standard programs for computing them are not available. A formula for estimating the variance of the Gini coefficient is ˆ n) = v (G 2

   ij 2i − 1 i j ˆ , − − 1 − Gn min n n nn n i=1 j =1   2j − 1 ˆ n (Yi+1 − Yi )(Yj +1 − Yj ) × −1−G n i=n−1
j =n−1




(B.1)

ˆ n is the Gini coefficient estimated by equation (12.4) in a sample of n Here, G units, and Yi , Yj are resources number i and j when ranked. The variance of the entropy measures is estimated by   A2 αz α 2 z2 2 2 s s (B.2) − 2 + s var(Iα ) = 12 nm2α 2 m m2 1 Here, A = 1/(α(α −1)); m is the mean of Y and z is the mean of Y α ; s12 = var(Y ); 2 = var(Y α , Y ). s22 = var(Y α ); s12 Statistics Norway has a program for computing the standard errors of Gini coefficients. Some results are given in Table B.1. The standard errors depend on the size of the (estimated) Gini coefficient as well as on the size of the sample. In addition, they depend on the shape of the underlying distribution function. Note that the standard errors do not seem to decrease with sample size in Table B.1, perhaps because the smallest sample is already fairly large.

138 Appendix B Table B.1 Gini coefficients and their standard deviations Year

1985

1988

1990

1992

1994

Gini coefficient×100 Standard error

23.6 0.61

23.0 0.40

24.2 0.43

24.4 0.49

26.5 0.49

Sample size

2,652

3,423

6,046

8,104

12,799

Disposable household income per equivalent adult. Source: Aaberge (2001).

A 95 per cent confidence interval for the Gini coefficient of 1985 is [22.4, 24.8], for the 1994 coefficient [25.5, 27.5]. In the light of these confidence intervals, it does not seem useful to give the values of Gini coefficients with an accuracy of more than two digits. It also seems a reasonable rule of thumb that differences must be larger than one percentage point (or larger than 0.01 at the scale used in Table 12.2). Note that all the differences between Gini coefficients in Table 12.2 are significant by this rule of thumb except the difference between women (0.36) and men (0.37) in 1990.

Notes

1 Introduction 1 Human Development Report 1995: 88. 2 The Guardian, 12 November 2002. 3 The Guardian, 15 January 2003 (Polly Toynbee: Who Cares?). 2 About distributional justice 1 See Aristotle, Nichomachean Ethics viii, 1976: 177. 2 See, for example, Rubery et al. 1999. 3 Deserts and the fruits of our labour 1 See David Hume, Essays of Commerce, 1987: 265. 2 Quoted from Bowles and Gintis 2000. 4 Welfarism: utilitarianism and welfare economics 1 Quoted from Rawls 1999a: 22. 8 Children and their mothers 1 Personal communication from Øystein Kravdahl, Professor of demographics. 9 Income and wealth 1 See Adam Smith, 1961, Vol. II: 179. 2 There are also reasons of efficiency: see Barr 1992 or 1999. 11 What should we measure? 1 See, for example, Jenkins et al. 1998. 14 Some inequality measures 1 Since xlnx → 0 when x → 0. 15 Poverty 1 Quoted from Atkinson 1983: 229. 16 Decomposition of inequality measures 1 Computations for the missing years between 1982 and 1990 show the same pattern. 1 2 2 Denoting √ the coefficient of correlation as r12 , we have: covar(Y , Y ) = r12 s1 s2 . Here, si = var(Yi ).

Suggested further reading

Part I A good place to start reading philosophers in the original is a collection of extracts. I recommend Solomon and Murphy (2000). They also have extracts from two schools of thought not considered in this book: communitarianism and bargaining theories. An introduction to communitarian thought is Sandel (1982). Gauthier (1986) is an introduction to bargaining theories of justice. Sen (1997) is a new edition of a classic covering many of the same subjects as this book, and it is a slim volume. For a more comprehensive treatment of several theories, I found Barry (1989) both readable and enlightening. There are two collections of papers that I have found particularly useful: Sen and Williams (1982) and Nussbaum and Sen (1993). Roemer (1994, 1996) are mathematically demanding, but much referred to. Okun (1975) considers equality and efficiency from the point of view of an economist. Phelps (1973) is an old but interesting collection of papers, including an early article by Rawls. LeGrand (1991) is interesting on choice. On utilitarianism, there are several papers in Sen and Williams (1982). Social welfare functions and their properties are presented in most textbooks of microeconomics, for instance Varian (1999). For non-economists, Barr (1998) Chapter 4 is a reasonably untechnical presentation of welfare economics. Hausman and Mcpherson (1993, 1996) are critical discussions of inter alia welfare economics, the 1993 paper is the shorter and, in my view, better. There is an enormous, and growing, literature on Rawls. Daniels (1975) was the first of many, the most recent is Freeman (2003). Rawls (2001) is his own presentation of his theory in textbook format. I prefer the original A Theory of Justice. The first 100 pages or so cover the basics. Nearly all books and articles on justice in distribution have some comments on his theory. Two other modern contractarian theories are found in Scanlon (1982, 1998) and in Barry (1995). Among the numerous articles and books Sen has written on the capability approach, I would recommend Sen (1992, 1993). Nussbaum’s view on capabilities is presented in Nussbaum (2000) Chapter 1. Libertarians write well. Nozick (1974) is the most readable of philosophers; Friedman and Friedman (1980) is written for the general reader. Marxists do not

Suggested further reading

141

write well. The first few chapters of Capital volume I is after all the least worst on Marxist theory of value and exploitation. Marx (1875) contains what little Marx wrote on distributive justice, and is a typical example of the prophet grumbling. For mathematically schooled economists, Morishima (1979) gives a precise and clear formalisation of Marx. Okin (1989) and Pateman (1988) are classic feminist critiques of theories of justice; there is also Nussbaum (1999), Chapter 2. About children, there are Folbre (1994a,b) and Gutman (1982). Chapter 8 is to a large extent based on Bojer (1996, 2000).

Part II Atkinson and Bourgignon (2000a) is a collection of articles on many of the topics covered in Part II. In particular, Cowell (2000) is a more precise and formal presentation of the theory of inequality measures, with references to original articles with proofs. Similarly, Jäntti and Danziger (2000) give a comprehensive survey, with detailed references, of the definition and measurement of poverty. There are also several empirical papers on income inequality in various parts of the world, while the editors’ introduction ‘Income Distribution and Economics’ (2000b) is a survey of the quality to be expected from these distinguished authors. The theoretical articles are written by and for economists. Cowell (1995) is a less technical presentation of inequality measures. On the various definitions of income and wealth there is no substitute for a careful reading of the chapter on definitions in statistical publications. Smeeding and Weinberg (2001) is a recent review of concepts. Jenkins et al. (1998) is a collection of articles on extended income. On equivalence scales, there is no up-to-date survey article. Myles (1995) is a brief technical presentation with further references. Blackorby and Donaldson (1991) give a theoretical basis similar to that in Chapter 10, while the subjective definition is explained in Praag and Sar (1988). On the econometrics of equivalence scales there is Blundell and Lewbel (1991). Nelson (1993) comments on the shifting welfare interpretations of equivalence scales through the years. Danziger and Taussig (1979) is the standard reference on units of analysis. The problems of measuring income, equivalence scales etc. are also considered in Atkinson (1983) and (1998).

Appendix A The theory of choice under uncertainty can be found in any textbook of microeconomics, for example, Gravelle and Rees (1992), Chapter 19 or Varian (1999), Chapter 12. An alternative source is a textbook of financial economics, for example, Huang and Litzenberger (1988), Chapter 1. Chapter 2 is an introduction to stochastic dominance.

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Index

Aaberge, Rolf 116 affluence 107 altruism 15, 34 ambition 47 Aristotle 7, 11, 12 Arrow, Kenneth 27 Arrow’s possibility theorem 27 assets 76 Atkinson, A. B. 122 Atkinson inequality measure 109–11, 113, 115; arithmetic formula 110 bargaining theory 9 Barry, Brian 9, 38, 42 Becker, Gary 73 Bengal 34 Bentham, Jeremy 21 Bergson, Abram 27 between-group inequality 123 Blanc, Louis 16 capabilities 46–50, 56, 62, 86, 87, 120 capital 18 capitalism 14 capitalists 127 child care 3, 8, 56, 57, 59, 73, 82, 87, 89 children 3, 11, 12, 17, 18, 43, 45, 56–62, 87, 88; as least advantaged group 61; conditional cost of 82; cost of 58, 79, 81–4, 86, 87; distributional rights of 56; property of parents 59; the good of 58–9, 62; time cost of 82–3 choice 87 citizen 13, 23, 43, 44, 60 class struggle 55 coefficient of correlation 131

coefficient of variation 100, 103, 113, 130, 132; decomposition of 130–1; sensitivity to transfers 105–6 coercion 13 complete ordering 100 concentration curve 92, 113 confidence interval 138 consequentialism 32 consequential justice 11 consumer durables 70–1 consumer sovereignty 31 consumer units 78 consumption 67–8; government paid 71–2; rights in 67 consumption capital 76 contribution to inequality 129, 131 cost of living function 80 covariance 130 Danziger, S. 122 decency 120 decile 95 decile group 95 deserts 15–17, 56, 57 Dickens, Charles 34 difference principle 39–42, 44, 61 discrimination 2, 11, 56 distributional justice: definition of 7; a virtue of society 7 distribution function 92–6 Dworkin, Ronald 2, 11, 19, 32, 47–8, 50, 62, 86 earnings 87 economic capability 62, 88

148 Index economic goods 2, 7–9, 20, 23, 36, 42, 48, 60, 65–6, 92; access to 3, 12, 66, 77; definition of 8, 65; lifetime access to 76 economic resources 118 education 18 efficiency 72 effort 16, 18, 19 egalitarianism 12–13, 24, 39 egoism 34 Elster, Jon 9 empathy 21 endorphins 34 endowment 47 Engel method 83–5 Engel’s law 84 Enlightenment 10, 55 entitlement theory 52 entropy measure 112–13, 115, 125, 137; decomposition of 123, 124 envy 32 envy-free distribution 47 equalising transfer 29, 97, 101, 107, 125 equality 12, 41, 107; of capabilities 12; of consumption 12; economic 12, 46, 50, 61; of income 12, 13, 24; of marginal utilities 25; moral 12; of opportunity 12, 13; of outcome 12, 13; of primary goods 12, 46; of resources 12, 47; of rights 14; social and political 12; utilitarian 24; of wages 13; of welfare 12, 13, 24, 46 equally distributed mean 110 equivalent adult scales 78–86, 88, 121; estimating 83 ethical individualism 10, 31, 60, 87 expected income 134 expected utility 42, 134–6 exploitation 14, 54 extended income 68, 70–3, 89–90

Friedman, Milton 11, 51 Friedman, Milton and Rose 60 full consumption 73 full income 45, 68, 73, 82, 88–9 functionings 48–9

factor shares 127 family 43, 60, 61; head of 11; and the public sphere 60; a voluntary association 60 family budgets 83 feudalism 54 Folbre, Nancy 58 food, budget share of 118 fractile 94 free choice 13, 17, 19, 45, 47, 87 freedom 7, 11, 59 free goods 65 frequency curve 95

impartial justice 9, 38 income 21, 23, 39, 41, 44, 46, 48, 66–76, 86, 92; annual income 74–6, 90; as measure of welfare 86; as primary good 44–5; capital income 69; cash income 68; components of 69–70, 126; disposable income 70; entrepreneurial income 69; equivalent income 78, 80, 81, 84, 86; factor income 70; Hicks definition of 66, 87, 88; Hicksian income 67; household income 45, 78, 88, 118; household income per equivalent adult 79; individual income

gambling 19 generalised Lorenz curve 98 genital mutilation 49, 50 Gini coefficient 99, 103, 104, 116, 125, 129, 132, 137; arithmetic formula 105; group decomposition of 124–5; sensitivity to transfers 105–6 global justice 8 government consumption 71 Habermas, Jürgen 37 Hammond, Peter 20 handicaps 18, 26, 48, 49 happiness 2, 8, 20 Harsanyi, John 22, 23, 33 Hayek, Friedrich von 11, 14, 51 health 44 health service 50 Hicks, John 20, 66 Hobbes, Thomas 10, 11, 13 home production 68, 70, 72–3 Homer 18 household 13, 45, 78, 90 household economies of scale 12, 78 housewife 73 housework 8, 72 human capital 18, 47, 62, 86 humanism 31 human nature 43 Hume, David 10, 14 Hutcheson, Francis 21 Huxley, Aldous 35

Index 88; market income 68; monetary income 8, 65; non-work income 73; Pareto on 67; primary income 70; Simons definition of 67, 87, 88; standard income, definition of 69; taxable income 69; total income 70; transfer income 69; wage income 69; and wealth 43, 44, 62, 66, 67 income sharing in households 79 index problem 44, 47 individual goods 65, 80 inequality 39, 92, 101; contribution to 132, 133; social cost of 108–9 inequality aversion 29–31, 107, 109, 111 inequality measures 92, 99–107, 137; axioms defining 101–2; decomposition by component 126–33; decomposition by group 123–6; decomposition of 123–33; definition of 100; ethical 106, 108–11; ordinality of 103 inequality neutrality 28 informal sector 8 inheritance 18, 47, 60, 70 interaction coefficients 129–30 interaction curves 127 inverse distribution function 94 invisible hand 52 Jäntti, M. 122 justice in holdings 52 Kant, Immanuel 10, 40 Kolm inequality measure 114 Kolm, Serge 9, 11, 12, 23, 42, 114 Korsgaard, Christine 46 labour 17; division of 16; fruits of 14, 16–19, 54, 56 labour market 2 labour theory of value 54 leisure 44, 68, 73 liberal society 36, 39 libertarianism 11, 14, 51–3, 59–60 liberty 14, 39, 44 life plan 11, 37, 39 life-span 56 lifetime earnings 12 lifetime income 42, 74–6, 90–1 lifetime prospects 42–4 local justice 9 Locke, John 10, 16, 57

149

Lorenz curve 92, 96–9, 127, 129; decomposition of 127–8 Lorenz dominance 96, 98, 99, 102, 103, 107–8, 115 love 62 luck 18, 19, 48; brute 19; option 19 Luxembourg Income Study 116 marginal utility 135 market 8 Marxism 14, 54 maximin principle 39–41, 110 M-curve 113 median income 93 men 11, 12, 38, 56, 74, 87 Mill, John Stuart 22, 56 money 8 moral philosophy 38 mothers 56, 59, 89 Napoleon 18 natural good 44, 50 natural resources 17 needs 13, 44 Ng, Y.-K. 34 Nozick, Robert 11, 14, 51–3, 59 Nussbaum, Martha 2, 48–50, 56, 60, 62, 87 Okin, Susan Moller 56 old-age pensions 15 opportunity 38, 43 options 87 ordinality 102 original position 37–9, 42, 60, 61 outcome 13 parade of dwarfs 92 parenthood 58 parents 45, 57–9, 62, 88 Pareto improvement 27 Pareto principle 27, 29 Pareto, Vilfred 67 partial ordering 99 part-time work 12 paternalism 35 Pen, Jan 92 Pinker, S. 15 Plato 7, 11 Pollak, Robert A. 82

150 Index poverty 8, 18, 118–22; absolute 118; head count 121; measures 120–1; poverty gap 121; relative 118–20 poverty line 118, 121 preferences 11, 21, 23, 24, 26, 27, 34, 37, 45, 48, 58, 66, 80, 87, 135; adaptive 34; antisocial 33; expensive 26, 32–4; and interpersonal comparability 21; moral 23; repulsive 32; true 33 primary goods 39, 42–5, 47, 50, 62, 87, 88, 120 private sphere 61 probability distribution 94 procedural justice 11, 14 procreation 58, 61 profit 69 public goods 65, 71, 80 public sphere 60 quality of life 46 Rakowski, Eric 58, 62 rational choice 9, 42 Rawls, John 1, 2, 7, 10, 11, 14, 18, 24, 28, 34, 36–46, 48, 50, 51, 56, 60, 62, 86, 110, 120 reciprocity 15 reflective equilibrium 10 rent 69 resources 46–8, 87, 88; internal 50 results 16 rewards according to contribution 17–19 rewards according to effort 10 rights 7, 11, 14, 16, 32, 34, 38, 39, 43, 44; of children 59; of parents 58, 59; of women 56; of women and children 60; to consumption 67 risk aversion 42, 48, 61, 135 risks 19 Roemer, John 19, 38, 42, 62 Rothbart method 85 Rousseau, Jean Jacques 10, 11, 13 rule of law 11 sadism 32 sampling error 137–8 Scanlon, Thomas 14 scarce goods 65 self-interest 9, 23, 37, 38 self-respect 43, 44, 50, 62, 120 Sen, Amartya 1, 2, 11, 12, 20, 25, 28, 34, 48–50, 62, 101

Sen function 29–30, 107, 108; definition 29 shame 49, 120 Shaw, George Bernard 17 significance 137 Simons, George 67 single mothers 16, 19 Slesnick, D. T. 21 Smith, Adam 16, 49, 119 smoking 32 social contract 13–14, 37, 39, 42, 56; and children 60–2 social cooperation 36 social evaluation 34 social evaluation function 26–32, 41, 107, 113; definition 26; Sen function 31; utilitarian 31; welfarist 27 social exclusion 119, 120 social indifference curve 27, 29; utilitarian 28 social insurance 72 social welfare function 26; Bergson-Samuelson 29; utilitarian 26, 27, 42 souls 38 standard error 100, 137 standard of living 81 stochastic dominance 135, 136 subsistence 120 talents 18, 47 third-person criterion 73 Tiny Tim 34 trade-off between wealth and equality 30–1, 39, 41 uncertainty 13, 18, 19, 23, 37, 41–2, 47, 61, 134–6 unemployment 89 unit of analysis 85 unpaid work 3, 72 utilitarianism 10, 11, 20–4, 28, 31, 40; act utilitarianism 22, 34; preference utilitarianism 22; rule utilitarianism 22, 34 utility 20, 24; marginal 24, 25, 32, 46 utility function 24, 25, 32, 81, 134 utility machine 25 Utopia 51 value 16 veil of ignorance 9, 23, 37, 48

Index wage rate 69, 73 Wales, T. 82 Walzer, M., 9 wealth 41, 67, 68, 76–7 welfare 2, 20–2, 27, 28, 31, 32, 34, 42, 46, 48, 80, 86, 88, 107; average 23; measuring 21; social 26, 27 welfare economics 11, 20, 28 welfarism 11, 20, 35, 42, 56–9, 62, 86, 87; definition of 20; ethical criticism of 32,

151

35; ethical properties of 31–2; paternalistic 58; respectful 58 well-being 20 within-group inequality 124, 125 women 8, 11, 12, 38, 43, 49, 56, 60, 74, 87; economic independence of 45, 62; just economic position of 61; justice to 3; labour force participation 125; rights of 56 workers 127 working class 14, 54