Measuring Inequality Without the Pigou-Dalton Condition

income differentials, deprivation, satifaction, Lorenz dominance, progressive transfers, expected utility, generalized Gini social

The Difficulty of Income Redistribution with Labour Supply

Two common principles in distributional analysis are that (i) a progressive transfer moves the Lorenz curve upwards, and (ii) progressive [neutral] taxation reduces [leaves unchanged] inequality. In order to establish these results it is currently assumed that the distribution of income is exogenously given. The relevance of these results is therefore limited in practice where incomes are determined by the working decisions of the agents in the economy. Considering a simple economy with two goods and two agents we indicate sufficient conditions for inequality in net income to decrease as a result of rich to poor transfers or progressive taxation. By means of simple examples we show that, when one incorporates labour supply responses, the fulfillment of these conditions is highly hypothetical and that everything can happen.Endogenous labour supply

Elitism and Stochastic Dominance

Stochastic dominance has typically been used with a special emphasis on risk and inequality reduction something captured by the concavity of the utility function in the expected utility model. We claim that the applicability of the stochastic dominance approach goes far beyond risk and inequality measurement provided suitable adpations be made. We apply in the paper the stochastic dominance approach to the measurment of elitism which may be considered the opposite of egalitarianism. While the usual stochastic dominance quasi-orderings attach more value to more equal and more efficient distributions, our criteria ensure that the more unequal and the more the efficient the distribution, the higher it is ranked. two instances are provided by (i) comparisons of scientific performance across institutions like universities or departments and (ii) comparisons of affluence as opposed to poverty across countries.Decumulative distribution functions; Stochastic dominance; Regressive transfers; Elitism; Scientific Performance; Affluence

Utilitarianism or Welfarism: Does it Make a Difference?

We show that it is possible to reconcile the utilitarian and welfarist principles under the requirement of unanimity provided that the set of profiles over which the consensus is attained is rich enough. More precisely, we identify a closedness condition which, if satisfied by a class of n-tuples of utility functions, guarantees that the rankings of social states induced by utilitarian and welfarist unanimities over that class are identical. We illustrate the importance of the result for the measurement of unidimensional as well as multidimensional inequalities from a dominance point of view.Unanimity; Utilitarianism; Welfarism; Stochastic Dominance; Inequality

Rearrangements and Sequential Rank Order Dominance. A Result with Economic Applications

Distributive analysis typically involves comparisons of heterogeneous distributions where\r\nindividuals differ in more than just one attribute. In the particular case where there are two\r\nattributes and where the distribution of one of these two attributes is fixed, one can appeal\r\nto sequential rank order dominance for comparing distributions. We consider the degenerate\r\ncase where all individuals differ with respect to the attribute whose distribution is fixed and we show that sequential rank order domination of one distribution over another implies that the dominating distribution can be obtained from the dominated one by means of a finite sequence of favourable permutations, and conversely. We provide three examples where favourable permutations prove to have interesting implications from a normative point of view.Rearrangements, Favourable Permutations, Sequential Rank Order Dominance, Matching, Mobility, Impatience

Comparisons of Heterogeneous Distributions and Dominance Criteria

We are interested in the comparisons of standard-of-living across societies when observations of both income and household structure are available. We generalise the approach of Atkinson and Bourguignon (1987) to the case where the marginal distributions of needs can vary across the household populations under comparison. We assume that a sympathetic observer uses a utilitarian social welfare function in order to rank heterogeneous income distributions. Insofar as any individual can play the role of the observer, we take the unanimity point of view according to which the planner’s judgements have to comply with a certain number of basic normative principles. We impose increasingly restrictive conditions on the household’s utility function and we investigate their effects on the resulting rankings of the distributions. This leads us to propose four dominance criteria that can be used for providing an unambiguous ranking of income distributions for heterogeneous populations.Normative Analysis, Utilitarianism, Welfarism, Multidimensional Inequality and Welfare, Bidimensional Stochastic Dominance, Inequality Reducing Transformations.

International comparisons of income distribution

When incorporating differences in household characteristics, the choice of equivalence scale can affect the ranking of income distributions. An alternative approach was pioneered by A.B. Atkinson and F. Bourguignon (G.R. Feiwel (Ed.), Arrow and the Foundation of the Theory of Economic Policy, Macmillan, New York, 1987), who derive a sequential Lorenz dominance criterion for com-paring distributions with an identical population structure. In order to make their approach applicable to international comparisons, we extend their criterion to the case of different marginal distributions of household types, and derive a sequential stochastic dominance criterion that highlights the importance of first order dominance of the marginal distribution of household characteristics for obtaining consistent rankings of income distributions. Comparisons of distributions are made using the Luxembourg Income Study database for a number of countries

Social welfare, inequality and deprivation

We provide a characterization of the generalised satisfaction - in our terminology nondeprivation - quasi-ordering introduced by S.R. Chakravarty (Keio Economic Studies 34 (1997), 17-32) for making welfare comparisons based on the absence of deprivation. We show that the non-deprivation quasi-ordering obeys a weaker version of the principle of transfers: welfare improves only for specific combinations of progressive transfers which require that the same amount be taken from richer individuals and allocated to one arbitrary poorer individual. We identify the subclass of extended Gini social welfare functions that are consistent with this principle and we show that the unanimity of value judgements among this class is identical to the ranking of distributions implied by the non-deprivation quasi-ordering. We extend the approach to the measurement of inequality by considering the corresponding relative and absolute ethical inequality indices

Poverty Measurement in Economics (In French)

This paper gives an overview of the way the issue of poverty measurement is typically addressed in economics. After having briefly defined what is meant by poverty in economics, I examine successively the unidimensional approach to poverty based on the income or expenses, and the multidimensional approach, which introduces non-monetary attributes in addition to income. Particular emphasis is placed on those properties of the poverty measures, that are deemed reasonable, and on their implications for the structure of the corresponding indices. I also insist on the dominance approach, which allows one to take into account a large range of points of views concerning the way poverty should be assessed.Poverty, Indices, Stochastic dominance

Bidimensional Inequalities with an Ordinal Variable

We investigate the normative foundations of two empirically implementable dominance criteria for comparing distributions of two attributes, where the first one is cardinal while the second is ordinal. The criteria we consider are Atkinson and Bourguignon\'s (1982) first quasi-ordering and a generalization of Bourguignon\'s (1989) ordered poverty gap criterion. In each case we specify the restrictions to be placed on the individual utility functions, which guarantee that all utility-inequality averse welfarist ethical observers will rank the distributions under comparison in the same way as the dominance criterion. We also identify the elementary inequality reducing transformations successive applications of which permit to derive the dominating distribution from the dominated one.Normative Analysis, Utilitarianism, Welfarism, Bidimensional Stochastic Dominance, Inequality Reducing Transformations