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In this book we are concerned with income profile based ethical social index numbers. An ethical index is designed from an explicit social evaluation function with a specific purpose in mind. For example, an ethical relative inequality index determines the fraction of total income that could be saved without any welfare loss if society distri­ buted incomes equally. Ethical indices contrast with descriptive indices which are de­ rived without using any concept of social welfare. Needless to say, ethical indices are not meant to supplant descriptive indices, rather they are constructed with different aims. We begin Chapter 1 with a formal discussion on the concept of a social evaluation function. In the main body of this chapter we consider the problem of ranking income profiles using a social evaluation function. In Chapter 2 we set about analyzing alter­ native approaches to the measurement of inequality. In Chapter 3 we focus our attention on the Gini index, the most frequently used index of inequality, and its extensions. In Chapter 4 we formulate the notion of an ethical distance function that measures welfare of one population relative to another. Chapter 5 is devoted to quantifications and discussions of alternative definitions of relative deprivation put forward by Runci­ man(1966).

Inhaltsverzeichnis

Frontmatter

Chapter 1. On Quasi-Orderings of Income Profiles

Abstract
In income distributions theory quite often we become interested in developing a criterion that can rank alternative profiles of income. Income profiles cannot be socially ordered if we do not make some prior value judgements. Value judgements, which are generally regarded as ethical statements, cannot be ascertained to be true or false on the basis of factual evidence. In the context of income profile ranking it is a convention to make the following value judgements: social preference for a more ’equitable’ profile and higher incomes, ceteris paribus. These value judgements are referred to as ’equity preference’ and ’efficiency preference’ respectively.
Satya R. Chakravarty

Chapter 2. Ethical Indices of Inequality

Abstract
While the Lorenz criterion provides only a quasi-ordering of income profiles, an alternative statistic that completely orders the set of all income profiles is an inequality index. An inequality index is a scalar representation of interpersonal income differences within a given population. Quite often indices of inequality are used in the public finance and development studies to evaluate a paricular profile of income or to examine the distributional effects of a particular economic policy. The standard questions that arise in these studies are: (i) Is the income profile in region A more equal now than it was in the past? (ii) Is income inequality in region B less than that in region C? (iii) Is post-tax income profile more equal than the pre-tax income profile? (iv) What are the contributions of different income sources to the aggregate inequality in region A?
Satya R. Chakravarty

Chapter 3. The Gini Indices of Inequality

Abstract
The most frequently used index of inequality is perhaps the Gini coefficient attributed to Gini(1912) and analysed, among others, by Dalton(1920), Atkinson(1970), Newbery (1970), Kats(1972), Sheshinski(1972), Dasgupta, Sen and Starrett(1973), Rothschild and Stiglitz(1973), Sen(1973, 1974, 1976, 1976a, 1978), Chipman(1974), Pyatt(1976), Graaff (1977), Hagerbaumer(1977), Blackorby and Donaldson(1978, 1980), Michal(1978), Dorfman(1979), Schwartz and Winship(1979), Takayama(1979), Yitzhaki(1979, 1980, 1982, 1982a, 1983), Donaldson and Weymark(1980, 1983), Hey and Lambert(1980), Kakwani (1980, 1980b, 1981, 1984, 1985, 1988), Amiel(1981), Berrebi and Silber(1981, 1985, 1987, 1987a, 1987b), Weymark(1981), Nygård and Sandstrom(1982), Thon(1982), Zagier (1983), Chakravarty and Chakraborty(1984), Lerman and Yitzhaki(1984, 1985), Shalit and Yitzhaki(1984), Foster(1985), Lambert(1985), Trannoy(1986), Basu(1987), Chakravarty(1988), Ebert(1988, 1988a) and Bossert(1989a).
Satya R. Chakravarty

Chapter 4. Ethical Indices Of Distance Between Income Profiles

Abstract
In the growing literature on the welfare comparisons of income profiles, a concept which has recently received some attention is that of economic distance between income profiles. The economic distance (or distance for short) between two income profiles is supposed to reflect the degree of affluence or well-being of one population relative to another. Hence this rules out a simple comparison of the inequality of incomes (according to some inequality index) within the respective populations, since this approach neglects differences in mean incomes and so ignores an important factor which influences the relative well-being of two populations.
Satya R. Chakravarty

Chapter 5. The Measurement of Relative Deprivation

Abstract
Deprivation can roughly be defined as the utility foregone because of not possessing the economic variable under consideration, here income. Deprivation is relative because people feel deprived by comparing themselves with persons who have higher incomes. In this chapter we are mainly concerned with interpretations and quantifications of alternative definitions of relative deprivation put forward by Runciman(1966).
Satya R. Chakravarty

Chapter 6. Ethically Flexible Indices of Poverty

Abstract
In the decades since the World War II, lot of attention has been paid by economists to the problem of development of the Third World countries and the associated problems of poverty. Even in the developed countries poverty remains one of the major issues of current economic and social policy. To understand the threat that the problem of poverty poses, it is necessary to know its dimensions and the process through which it seems to be aggravated. In this chapter and in the next chapter of this book we are interested in the quantification of poverty.
Satya R. Chakravarty

Chapter 7. Additively Decomposable Indices of Poverty

Abstract
Ranking income profiles by summary indices is just a first step in the analysis of poverty. For deeper analysis we should inquire into the factors contributing to poverty using time series or cross-section income data. For carrying out such analysis we need a poverty index that exhibits additive decomposability: for any partitioning of the population, defined along ethnic or geographical or other lines, the total poverty is a weighted average of the subgroup poverty levels. Clearly, this will enable us to calculate a particular subgroup’s contribution to total poverty. Hence this type of poverty breakdown becomes suitable for identifying causal factors of poverty and in choosing and implementing poverty alleviation policies.
Satya R. Chakravarty

Chapter 8. Measurement of Tax Progressivity and Horizontal Inequity

Abstract
Various economic decisions taken by the government affect us in several ways. The taxation principle adopted by the government is an appropriate example of this. An important job is, therefore, to look at the degree of progression of the tax structure. Traditionally, a fiscal system is qualified as progressive if the average rate of taxation increases with income before tax. Equivalently, we say that the elasticity of income after tax with respect to income before tax is less than unity at all income levels. But these indices are local indices of progression. Such indices measure the deviation from proportionality of the tax function at a particular income level. On the other hand, ’… effective progression measures the extent to which a given tax structure results in a shift in the distribution of income toward equality’ (Musgrave and Thin(1948)). In Section 3 of this chapter we propose an ethical index of global tax progressivity that measures shifts in the income profile toward equality caused by the tax system taken as a whole. This index is constructed by comparing the welfare value (as measured by the sum of identical individual utility functions) of the actual post-tax income profile with the welfare value of the hypothetical income profile that would arise if the same aggregate amount of tax were realised through a proportional tax rule. Consequently, a tax system will be regarded as progressive by this index if the actual post-tax income profile strictly Lorenz dominates the hypothetical post-tax income profile. In a limiting situation the index equals the proportionate gap between the Theil(1967) entropy index of inequality of the pre-tax income profile and that of the post-tax income profile. For completeness and also for preparing the background for constructing the ethical index in Section 3, we discuss the Musgrave — Thin(1948) indices of local tax progressivity and their consistency in terms of the Lorenz quasi-ordering in Section 2.
Satya R. Chakravarty

Chapter 9. Ethical Indices of Income Mobility

Abstract
Indices of inequality are typically summary statistics of the dispersion of incomes at a particular point of time. Even if such indices are computed for a number of successive periods, by their very nature they will ignore many features of time path of incomes which are of interest. As time progresses we observe changes in relative incomes as well as changes in the absolute income differences found in any given time period. Indices of income mobility are meant to measure the magnitude of these changes. Indices of relative mobility measure changes in relative incomes while indices of absolute mobility measure changes in income differences.
Satya R. Chakravarty

Backmatter

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