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Probably the best capture of the general motivation for why economists study income inequality and its measurement, which is also used, referenced, or quoted by many researchers who measure inequality, may be found in the second paragraph of Hugh Dalton’s 1920 article . In it, Dalton criticizes a statement by an American writer who claimed that the research problem faced by an economist choosing a measure of inequality when analyzing the distribution of wealth is the same as that faced by a biologist choosing a measure of the distribution of any physical characteristic. Dalton develops a similar analogy describing the situation of a cultivator “measuring the inequality of rainfall in the various districts of a large agricultural area”. What is important is not rainfall as such, but the“objection to great inequality of rainfall is the resulting loss of potential crop. The objection to great inequality of the incomes is the resulting loss of potential economic welfare”. This idea can be expanded upon because, although accurate, it is still quite general. Researchers of income inequality are not only guided by the goal of examining inequality in the context of welfare in a given society or for a given income distribution at a given moment but also by comparing different income distributions over time, in different situations (e.g., before and after a change in income taxation) or between different countries or broader social groups – obviously with the aim of assessing differences in welfare levels. The researcher is therefore faced with the choice of an appropriate measure of dispersion that best reflects shifts in income distribution in terms of variations in inequality and the resulting impact on welfare. Applying different measures to the same comparison of given income distributions may lead to different assessments in terms of inequality and, thus, welfare, i.e., the degree of inequality, the size of the change of inequality and even the direction of this change and their consequences in terms of welfare. Thus, a researcher might choose a particular measure based on the hypotheses they want to prove right. We can imagine the following example, in which we compare two identical income distributions: in each of them, we have 10 people, the poorest of whom earns an income of 1, the second earns 2, the third earns 3, and so on. Most of us would probably assess both distributions as equally unequal. Many dispersion measures applied to this situation would assess both distributions as being characterized by the same dispersion, e.g., in the case of both distributions the Gini coefficient would yield a value of approximately 0.3, the coefficient of variation would be equal to 0.55, the decile dispersion ratio (90/10) would amount to 4.79, the Palma ratio would be 4.0, and the Theil index would yield a value of 0.15. However, if we apply some subjective elements to the analysis, as, for example, differentiating between the discomfort both populations suffer from their distribution of income not being equal, e.g., in one of the populations inequality aversion would be higher than inequality aversion in the other population, the assessment of the degree of inequality for these distributions of income would be different. One such measure which could give us distinct results is the Atkinson index, whose value, ceteris paribus (i.e., as in our example above), depends on the degree of aversion to inequality, i.e., the degree of dislike of income inequality in a given society, the feeling of aversion to a given income distribution. The assessment of the degree of inequality of the same income distribution will depend on the size of the inequality aversion parameter – the greater it is, the greater the aversion to inequality in a given society (let us assume this for illustrative purposes, without going into details about who expresses or determines this aversion to inequality), the more unequal the income distribution will be seen to be, i.e., the lower the level of welfare it will correspond to. Without any further explanation at this point – as the rest of the monograph is dedicated to the analysis of the Atkinson dispersion measure and the inequality aversion – if we assume that the inequality aversion parameter (thus, inequality discomfort) in one population equals 1.0 and 2.0 in the other (indicating a greater inequality aversion), then for the example above we would get two Atkinson index values – 0.1766 for the first and 0.3792 for the second distribution of income, which would indicate a difference in the degree of inequality existing in the distribution under analysis. Thus, there are some reasons for including inequality aversion in the measurement of income inequality. The simplest argument would be to say that with the same, let us say, two income distributions, different degrees of aversion to inequality will mean that income inequality will be perceived differently in the two societies, which will affect the level of welfare in these countries – after all, in one country the same situation is perceived as more painful, hence as lower welfare.1 Unfortunately, 1 In fact, in the case of the Atkinson measure, it would be better to say that with greater aversion to inequality, society would be willing to sacrifice a greater part of total income (loss of income) in order the problem may become more serious, because when comparing different income distributions, e.g., for many countries, the use of different values of aversion to inequality in each case may change the order of countries in the ranking of increasing income inequality, which will be shown later in this monograph. This means that, depending on the choice of the inequality aversion parameter, we could argue different things to support our thesis. For example, with low inequality aversion in two countries, one country would have a less unequal income distribution than the other, and with high inequality aversion, the opposite would be true. Finally, there is not only a dilemma as to what level to set the inequality parameter at, but also whether it should be the same for comparing different distributions or different for different income distributions (e.g., countries). This raises the question of what level of inequality aversion should be set – is it a universal value, can we set it arbitrarily or compare the same distribution by changing only the value of the inequality aversion parameter, or would it be necessary and possible to empirically examine, determine, and estimate this parameter, in other words, are inequality aversion and the Atkinson measure operationalizable? It turns out that numerous empirical studies, the most important of which will be discussed in this study, as well as survey research, show that individual aversion to inequality as well as social aversion to inequality, both of which are measured or estimated using various methods presented in this monograph, take on different values.
(excerpt from the introdution)
[[[separator]]]
INTRODUCTION
1 THEORETICAL FOUNDATIONS OF SOCIOECONOMIC INEQUALITY
1.1. Definitions and dimensions of inequality
1.1.1. Equality, equity, differences and inequality
1.1.2. Dimensions of inequality
1.2. Social justice – philosophical underpinnings
1.3. The role of inequality measurement in economic policy
1.4. Taxonomy of inequality measures
2 THE ATKINSON INDEX – CONCEPTUAL AND MATHEMATICAL ESSENCE
2.1. Mathematical formulation, key assumptions and interpretation of the Atkinson index
2.2. Axiomatic foundation of the index
2.3. Relationship with risk theory – similarities and differences
2.4. Historical background, comparison with other normative measures and the problematic goal of perfect equality
3 THE INEQUALITY AVERSION PARAMETER
3.1. Definition and theoretical justification
3.2. Mathematical sensitivity to epsilon and empirical behavior of Atkinson’s index
3.3. Determinants of inequality aversion, attitudes, and redistribution preferences – empirical insights
4 METHODS OF f ESTIMATION AND OPERATIONALIZATION IN EMPIRICAL RESEARCH
4.1. The leaky bucket
4.2. The natural rate of subjective inequality
4.3. The concept of equal sacrifice
4.4. Estimation of the utility function
4.5. Parametric income distributions
4.6. Discussion and conclusions
5 CRITICAL SYNTHESIS, METHODOLOGICAL CRITIQUE AND FUTURE PATHWAYS
5.1. Introduction – the role of a critical synthesis
5.2. Theoretical and ethical limitations of the Atkinson index
5.3. Empirical challenges in application
5.4. Methodological critique – estimation of the inequality aversion parameter – summary
5.5. Empirical extensions of the Atkinson index application
5.6. Recommendations for researchers and policymakers
5.7. Conclusion – reflections and final critique
REFERENCES
LIST OF FIGURES
LIST OF TABLES
Opis
Wstęp
Probably the best capture of the general motivation for why economists study income inequality and its measurement, which is also used, referenced, or quoted by many researchers who measure inequality, may be found in the second paragraph of Hugh Dalton’s 1920 article . In it, Dalton criticizes a statement by an American writer who claimed that the research problem faced by an economist choosing a measure of inequality when analyzing the distribution of wealth is the same as that faced by a biologist choosing a measure of the distribution of any physical characteristic. Dalton develops a similar analogy describing the situation of a cultivator “measuring the inequality of rainfall in the various districts of a large agricultural area”. What is important is not rainfall as such, but the“objection to great inequality of rainfall is the resulting loss of potential crop. The objection to great inequality of the incomes is the resulting loss of potential economic welfare”. This idea can be expanded upon because, although accurate, it is still quite general. Researchers of income inequality are not only guided by the goal of examining inequality in the context of welfare in a given society or for a given income distribution at a given moment but also by comparing different income distributions over time, in different situations (e.g., before and after a change in income taxation) or between different countries or broader social groups – obviously with the aim of assessing differences in welfare levels. The researcher is therefore faced with the choice of an appropriate measure of dispersion that best reflects shifts in income distribution in terms of variations in inequality and the resulting impact on welfare. Applying different measures to the same comparison of given income distributions may lead to different assessments in terms of inequality and, thus, welfare, i.e., the degree of inequality, the size of the change of inequality and even the direction of this change and their consequences in terms of welfare. Thus, a researcher might choose a particular measure based on the hypotheses they want to prove right. We can imagine the following example, in which we compare two identical income distributions: in each of them, we have 10 people, the poorest of whom earns an income of 1, the second earns 2, the third earns 3, and so on. Most of us would probably assess both distributions as equally unequal. Many dispersion measures applied to this situation would assess both distributions as being characterized by the same dispersion, e.g., in the case of both distributions the Gini coefficient would yield a value of approximately 0.3, the coefficient of variation would be equal to 0.55, the decile dispersion ratio (90/10) would amount to 4.79, the Palma ratio would be 4.0, and the Theil index would yield a value of 0.15. However, if we apply some subjective elements to the analysis, as, for example, differentiating between the discomfort both populations suffer from their distribution of income not being equal, e.g., in one of the populations inequality aversion would be higher than inequality aversion in the other population, the assessment of the degree of inequality for these distributions of income would be different. One such measure which could give us distinct results is the Atkinson index, whose value, ceteris paribus (i.e., as in our example above), depends on the degree of aversion to inequality, i.e., the degree of dislike of income inequality in a given society, the feeling of aversion to a given income distribution. The assessment of the degree of inequality of the same income distribution will depend on the size of the inequality aversion parameter – the greater it is, the greater the aversion to inequality in a given society (let us assume this for illustrative purposes, without going into details about who expresses or determines this aversion to inequality), the more unequal the income distribution will be seen to be, i.e., the lower the level of welfare it will correspond to. Without any further explanation at this point – as the rest of the monograph is dedicated to the analysis of the Atkinson dispersion measure and the inequality aversion – if we assume that the inequality aversion parameter (thus, inequality discomfort) in one population equals 1.0 and 2.0 in the other (indicating a greater inequality aversion), then for the example above we would get two Atkinson index values – 0.1766 for the first and 0.3792 for the second distribution of income, which would indicate a difference in the degree of inequality existing in the distribution under analysis. Thus, there are some reasons for including inequality aversion in the measurement of income inequality. The simplest argument would be to say that with the same, let us say, two income distributions, different degrees of aversion to inequality will mean that income inequality will be perceived differently in the two societies, which will affect the level of welfare in these countries – after all, in one country the same situation is perceived as more painful, hence as lower welfare.1 Unfortunately, 1 In fact, in the case of the Atkinson measure, it would be better to say that with greater aversion to inequality, society would be willing to sacrifice a greater part of total income (loss of income) in order the problem may become more serious, because when comparing different income distributions, e.g., for many countries, the use of different values of aversion to inequality in each case may change the order of countries in the ranking of increasing income inequality, which will be shown later in this monograph. This means that, depending on the choice of the inequality aversion parameter, we could argue different things to support our thesis. For example, with low inequality aversion in two countries, one country would have a less unequal income distribution than the other, and with high inequality aversion, the opposite would be true. Finally, there is not only a dilemma as to what level to set the inequality parameter at, but also whether it should be the same for comparing different distributions or different for different income distributions (e.g., countries). This raises the question of what level of inequality aversion should be set – is it a universal value, can we set it arbitrarily or compare the same distribution by changing only the value of the inequality aversion parameter, or would it be necessary and possible to empirically examine, determine, and estimate this parameter, in other words, are inequality aversion and the Atkinson measure operationalizable? It turns out that numerous empirical studies, the most important of which will be discussed in this study, as well as survey research, show that individual aversion to inequality as well as social aversion to inequality, both of which are measured or estimated using various methods presented in this monograph, take on different values.
(excerpt from the introdution)
Spis treści
INTRODUCTION
1 THEORETICAL FOUNDATIONS OF SOCIOECONOMIC INEQUALITY
1.1. Definitions and dimensions of inequality
1.1.1. Equality, equity, differences and inequality
1.1.2. Dimensions of inequality
1.2. Social justice – philosophical underpinnings
1.3. The role of inequality measurement in economic policy
1.4. Taxonomy of inequality measures
2 THE ATKINSON INDEX – CONCEPTUAL AND MATHEMATICAL ESSENCE
2.1. Mathematical formulation, key assumptions and interpretation of the Atkinson index
2.2. Axiomatic foundation of the index
2.3. Relationship with risk theory – similarities and differences
2.4. Historical background, comparison with other normative measures and the problematic goal of perfect equality
3 THE INEQUALITY AVERSION PARAMETER
3.1. Definition and theoretical justification
3.2. Mathematical sensitivity to epsilon and empirical behavior of Atkinson’s index
3.3. Determinants of inequality aversion, attitudes, and redistribution preferences – empirical insights
4 METHODS OF f ESTIMATION AND OPERATIONALIZATION IN EMPIRICAL RESEARCH
4.1. The leaky bucket
4.2. The natural rate of subjective inequality
4.3. The concept of equal sacrifice
4.4. Estimation of the utility function
4.5. Parametric income distributions
4.6. Discussion and conclusions
5 CRITICAL SYNTHESIS, METHODOLOGICAL CRITIQUE AND FUTURE PATHWAYS
5.1. Introduction – the role of a critical synthesis
5.2. Theoretical and ethical limitations of the Atkinson index
5.3. Empirical challenges in application
5.4. Methodological critique – estimation of the inequality aversion parameter – summary
5.5. Empirical extensions of the Atkinson index application
5.6. Recommendations for researchers and policymakers
5.7. Conclusion – reflections and final critique
REFERENCES
LIST OF FIGURES
LIST OF TABLES
Opinie
Probably the best capture of the general motivation for why economists study income inequality and its measurement, which is also used, referenced, or quoted by many researchers who measure inequality, may be found in the second paragraph of Hugh Dalton’s 1920 article . In it, Dalton criticizes a statement by an American writer who claimed that the research problem faced by an economist choosing a measure of inequality when analyzing the distribution of wealth is the same as that faced by a biologist choosing a measure of the distribution of any physical characteristic. Dalton develops a similar analogy describing the situation of a cultivator “measuring the inequality of rainfall in the various districts of a large agricultural area”. What is important is not rainfall as such, but the“objection to great inequality of rainfall is the resulting loss of potential crop. The objection to great inequality of the incomes is the resulting loss of potential economic welfare”. This idea can be expanded upon because, although accurate, it is still quite general. Researchers of income inequality are not only guided by the goal of examining inequality in the context of welfare in a given society or for a given income distribution at a given moment but also by comparing different income distributions over time, in different situations (e.g., before and after a change in income taxation) or between different countries or broader social groups – obviously with the aim of assessing differences in welfare levels. The researcher is therefore faced with the choice of an appropriate measure of dispersion that best reflects shifts in income distribution in terms of variations in inequality and the resulting impact on welfare. Applying different measures to the same comparison of given income distributions may lead to different assessments in terms of inequality and, thus, welfare, i.e., the degree of inequality, the size of the change of inequality and even the direction of this change and their consequences in terms of welfare. Thus, a researcher might choose a particular measure based on the hypotheses they want to prove right. We can imagine the following example, in which we compare two identical income distributions: in each of them, we have 10 people, the poorest of whom earns an income of 1, the second earns 2, the third earns 3, and so on. Most of us would probably assess both distributions as equally unequal. Many dispersion measures applied to this situation would assess both distributions as being characterized by the same dispersion, e.g., in the case of both distributions the Gini coefficient would yield a value of approximately 0.3, the coefficient of variation would be equal to 0.55, the decile dispersion ratio (90/10) would amount to 4.79, the Palma ratio would be 4.0, and the Theil index would yield a value of 0.15. However, if we apply some subjective elements to the analysis, as, for example, differentiating between the discomfort both populations suffer from their distribution of income not being equal, e.g., in one of the populations inequality aversion would be higher than inequality aversion in the other population, the assessment of the degree of inequality for these distributions of income would be different. One such measure which could give us distinct results is the Atkinson index, whose value, ceteris paribus (i.e., as in our example above), depends on the degree of aversion to inequality, i.e., the degree of dislike of income inequality in a given society, the feeling of aversion to a given income distribution. The assessment of the degree of inequality of the same income distribution will depend on the size of the inequality aversion parameter – the greater it is, the greater the aversion to inequality in a given society (let us assume this for illustrative purposes, without going into details about who expresses or determines this aversion to inequality), the more unequal the income distribution will be seen to be, i.e., the lower the level of welfare it will correspond to. Without any further explanation at this point – as the rest of the monograph is dedicated to the analysis of the Atkinson dispersion measure and the inequality aversion – if we assume that the inequality aversion parameter (thus, inequality discomfort) in one population equals 1.0 and 2.0 in the other (indicating a greater inequality aversion), then for the example above we would get two Atkinson index values – 0.1766 for the first and 0.3792 for the second distribution of income, which would indicate a difference in the degree of inequality existing in the distribution under analysis. Thus, there are some reasons for including inequality aversion in the measurement of income inequality. The simplest argument would be to say that with the same, let us say, two income distributions, different degrees of aversion to inequality will mean that income inequality will be perceived differently in the two societies, which will affect the level of welfare in these countries – after all, in one country the same situation is perceived as more painful, hence as lower welfare.1 Unfortunately, 1 In fact, in the case of the Atkinson measure, it would be better to say that with greater aversion to inequality, society would be willing to sacrifice a greater part of total income (loss of income) in order the problem may become more serious, because when comparing different income distributions, e.g., for many countries, the use of different values of aversion to inequality in each case may change the order of countries in the ranking of increasing income inequality, which will be shown later in this monograph. This means that, depending on the choice of the inequality aversion parameter, we could argue different things to support our thesis. For example, with low inequality aversion in two countries, one country would have a less unequal income distribution than the other, and with high inequality aversion, the opposite would be true. Finally, there is not only a dilemma as to what level to set the inequality parameter at, but also whether it should be the same for comparing different distributions or different for different income distributions (e.g., countries). This raises the question of what level of inequality aversion should be set – is it a universal value, can we set it arbitrarily or compare the same distribution by changing only the value of the inequality aversion parameter, or would it be necessary and possible to empirically examine, determine, and estimate this parameter, in other words, are inequality aversion and the Atkinson measure operationalizable? It turns out that numerous empirical studies, the most important of which will be discussed in this study, as well as survey research, show that individual aversion to inequality as well as social aversion to inequality, both of which are measured or estimated using various methods presented in this monograph, take on different values.
(excerpt from the introdution)
INTRODUCTION
1 THEORETICAL FOUNDATIONS OF SOCIOECONOMIC INEQUALITY
1.1. Definitions and dimensions of inequality
1.1.1. Equality, equity, differences and inequality
1.1.2. Dimensions of inequality
1.2. Social justice – philosophical underpinnings
1.3. The role of inequality measurement in economic policy
1.4. Taxonomy of inequality measures
2 THE ATKINSON INDEX – CONCEPTUAL AND MATHEMATICAL ESSENCE
2.1. Mathematical formulation, key assumptions and interpretation of the Atkinson index
2.2. Axiomatic foundation of the index
2.3. Relationship with risk theory – similarities and differences
2.4. Historical background, comparison with other normative measures and the problematic goal of perfect equality
3 THE INEQUALITY AVERSION PARAMETER
3.1. Definition and theoretical justification
3.2. Mathematical sensitivity to epsilon and empirical behavior of Atkinson’s index
3.3. Determinants of inequality aversion, attitudes, and redistribution preferences – empirical insights
4 METHODS OF f ESTIMATION AND OPERATIONALIZATION IN EMPIRICAL RESEARCH
4.1. The leaky bucket
4.2. The natural rate of subjective inequality
4.3. The concept of equal sacrifice
4.4. Estimation of the utility function
4.5. Parametric income distributions
4.6. Discussion and conclusions
5 CRITICAL SYNTHESIS, METHODOLOGICAL CRITIQUE AND FUTURE PATHWAYS
5.1. Introduction – the role of a critical synthesis
5.2. Theoretical and ethical limitations of the Atkinson index
5.3. Empirical challenges in application
5.4. Methodological critique – estimation of the inequality aversion parameter – summary
5.5. Empirical extensions of the Atkinson index application
5.6. Recommendations for researchers and policymakers
5.7. Conclusion – reflections and final critique
REFERENCES
LIST OF FIGURES
LIST OF TABLES
