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E-raamat: Lectures on Inequality, Poverty and Welfare

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These lectures aim to help readers understand the logics and nature of the main indicators of inequality and poverty, with special attention to their social welfare underpinnings. The key approach consists in linking inequality and poverty measurement with welfare evaluation. As concern for inequality and poverty stems from ethical considerations, the measurement of those aspects necessarily involves some value judgments. Those value judgments can be linked, directly or indirectly, to welfare assessments on the distribution of personal and social opportunities. Inequality and poverty are thus considered to be partial aspects of the welfare evaluation of the opportunities in a given society. The volume includes two applications that illustrate how the models can be implemented. They refer to inequality of opportunity and poverty in education, using PISA data.

1 Introduction
1(18)
1.1 Equality and Welfare
1(5)
1.1.1 We Have a Problem
1(3)
1.1.2 Measuring Inequality and Poverty
4(1)
1.1.3 Purpose
5(1)
1.2 Equality of What?
6(5)
1.2.1 Income Distributions
6(1)
1.2.2 Wealth, Income and Expenditures
7(2)
1.2.3 The Units of Reference: Equality Among Whom?
9(1)
1.2.4 Needs and Deserts
10(1)
1.2.5 Multidimensionality
11(1)
1.3 Plan of the Book
11(8)
References
13(6)
Part I Inequality
2 Inequality Indices
19(12)
2.1 Introduction
19(1)
2.2 Properties of Inequality Indices
20(4)
2.3 Inequality and Dispersion
24(7)
2.3.1 The Variance (σ2)
25(4)
2.3.2 The Coefficient of Variation (CV)
29(1)
References
29(2)
3 Positive Inequality Indices
31(26)
3.1 The Lorenz Curve
31(3)
3.2 The Gini Index
34(5)
3.2.1 From Lorenz to Gini
34(3)
3.2.2 The Generalised Gini Index
37(2)
3.3 Theil's Inequality Indices
39(9)
3.3.1 The First Index of Theil: From Information Theory to Inequality Measurement
39(3)
3.3.2 The Second Index of Theil (Mean Logarithmic Deviation)
42(2)
3.3.3 The Generalised Indices of Theil (Tθ)
44(4)
3.4 Quantile Measures: The Palma Ratio
48(9)
Appendix: Decomposability of the Generalised Indices of Theil
53(2)
References
55(2)
4 Normative Inequality Indices
57(16)
4.1 Introduction
57(3)
4.1.1 The Arrowian Approach to Normative Inequality Indices
57(3)
4.1.2 The Social Evaluation Function Approach
60(1)
4.2 Dalton's Approach to Inequality Measurement
60(2)
4.3 Atkinson Inequality Measures
62(11)
4.3.1 Preliminaries
62(2)
4.3.2 The Atkinson Family of Inequality Indices
64(4)
4.3.3 The Atkinson and the Entropy Families of Inequality Indices
68(2)
References
70(3)
5 Inequality of Opportunity
73(20)
5.1 Introduction
73(3)
5.2 Measuring Inequality of Opportunity by Theil's Inequality Index
76(5)
5.2.1 Motivation
76(1)
5.2.2 The Model
77(3)
5.2.3 The Second Index of Theil
80(1)
5.3 Equality of Opportunity With Categorical Data
81(12)
5.3.1 Motivation
81(1)
5.3.2 The Model
82(2)
5.3.3 Empirical Illustration: Inequality of Opportunity in Compulsory Education in the OECD, According to PISA (2012)
84(3)
Appendix
87(4)
References
91(2)
6 Inequality and Welfare
93(22)
6.1 Introduction
93(1)
6.2 Social Evaluation Functions
94(7)
6.3 Multidimensional Inequality and Welfare
101(8)
6.3.1 Multidimensional Welfare Indicators
103(2)
6.3.2 Multidimensional Inequality
105(2)
6.3.3 Weights and Units
107(2)
6.4 The Human Development Index
109(6)
References
110(5)
Part II Poverty
7 Poverty Measurement
115(20)
7.1 Introduction
115(2)
7.2 Poverty Indices
117(5)
7.2.1 Head Count Ratio
118(1)
7.2.2 Poverty Gap Measures
119(1)
7.2.3 The Sen's Family of Poverty Measures
120(1)
7.2.4 Decomposable Poverty Measures
121(1)
7.3 Multidimensional Poverty Indices
122(3)
7.4 Deprivation and Non-monetary Poverty Measures
125(10)
7.4.1 At Risk of Poverty or Social Exclusion (AROPE)
125(2)
7.4.2 The United Nations Multidimensional Poverty Index
127(6)
References
133(2)
8 Multidimensional Poverty and Welfare
135(20)
8.1 Introduction
135(1)
8.2 The Setting
136(3)
8.3 Adding Structure
139(3)
8.3.1 Quasi-concavity, Scale and Factor Decomposability
139(2)
8.3.2 Multiplicative Factor Decomposability
141(1)
8.4 Closing the Formula
142(3)
8.4.1 Anonymity, Inequality and Welfare
142(1)
8.4.2 Subgroup Decomposability
143(2)
8.5 Measuring Educational Poverty from PISA
145(10)
8.5.1 The Model
145(2)
8.5.2 The Results
147(4)
8.5.3 Final Comments
151(1)
References
151(4)
9 The Evaluation of Relative Achievements
155(16)
9.1 Introduction
155(1)
9.2 The Basic Model
156(6)
9.2.1 Measuring the Achievements
157(4)
9.2.2 Application to the Example of the Hypothetical University
161(1)
9.3 Extensions
162(4)
9.3.1 Weighted Symmetry and Weighted Neutrality
162(2)
9.3.2 Generalised Means
164(1)
9.3.3 A Graphical Illustration
165(1)
9.4 An Application: The Green Economy Progress Index
166(5)
9.4.1 The Setting
166(2)
9.4.2 The Index
168(3)
9.4.3 Results
171(1)
References 171
Antonio Villar is Professor of Economics at the Universidad Pablo de Olavide (Seville), where he arrived in 2005 from the University of Alicante. He is also Senior Researcher at the Ivie (Valencian Institute for Economic Research).





He got a Ph.D. at the University of Oxford in 1990, after a B.A. in Economics (University of Valencia, 1978) and a previous Doctorate (University of Alicante, 1983).





He has been Visiting Professor at Stanford University, the European University Institute (Florence, Italy), the Institute for Advanced Studies (Vienna), Senior Associate at St. Antonys College, University of Oxford, and Visiting Researcher at the University of York, among others. During 2015/2016 he held a Thomas J. Alexander Fellowship at the OECD/EDU in Paris.





In 2010 he got the Andalusian Prize for distinguished research in Social Sciences and Humanities.





Hisresearch activity concentrates on Microeconomic Theory and its applications. In particular: (a) Welfare economics and social choice, including aspects of efficiency with externalities, public goods and non-convexities, distributive problems, inequality and welfare measurement, multidimensional indicators, Human Development and Economics of Education; and (b) General equilibrium, with special interest on the effects of increasing returns to scale in market economies. His latest research deals with the welfare analysis of some economic aspects that involve both private and public decisions, such as health, education and income distribution. A common theme of some of those topics is the design of multidimensional indicators and evaluation formulas capable of dealing with qualitative data.





He has published 14 books and some 80 research papers.
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