Income Distributions and Decomposable Divergence Measures

Inequality indices (i) evaluate the divergence between the income distribution and the hypothetical situation where all individuals have the mean income and (ii) are unambiguously reduced by a Pigou-Dalton progressive transfer. This paper proposes a new approach to evaluate the divergence between any two income distributions, where the second one can be a reference distribution for the first. In the case where the reference distribution is perfectly egalitarian, and uniquely in this case, we assume (i) that any progressive transfer reduces the divergence and (ii) that the divergence can be additively separated between inequality and efficiency loss. We characterize the unique class of decomposable divergence measures consistent with these views, and we derive the associated relative (resp. absolute) subclasses, which express constant relative (resp. absolute) inequality aversion. This approach extends the generalized entropy studied in inequality measurement.Inequality measures, progressive transfers, generalized entropy, information theory, Bregman divergences

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

Risk and Inequality Aversion in Social Dilemmas

We experimentally investigate cooperative behavior in a social dilemma situation, where the socially efficient outcome may be encouraged by risk aversion and/or inequality aversion. The first part of our experiment is devoted to the elicitation of subjects' aversion profile, taking care to not confuse the two dimensions. Subjects are then grouped by three according to their aversion profiles, and interact in a repeated social dilemma game. In this game, agents are characterised by a social status so that higher the agent's status, higher will be her earnings. Cooperation is costly for a majority of agents at each period, but statuses can be reversed in future periods. We show that cooperation is strongly in°uenced by the group's aversion profile. Groups averse in both dimensions cooperate more than groups averse in only one dimension. Moreover cooperation seems to be more affected by risk aversion, whereas one might interpret cooperative behavior as an inequality averse or altruistic attitude.

Social Welfare, Inequality and Deprivation

We provide a characterization of the generalised satisfaction -- in our terminology non-deprivation -- 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.Export diversification, FDI, Growth, MENA, GMM system

Ranking Distributions of an Ordinal Attribute

This paper establishes foundational equivalences between alternative criteria for comparing distributions of an ordinally measurable attribute. A first criterion is associated with the possibility of going from distribution to the other by a finite sequence of two elementary operations: increments of the attribute and Hammond transfers. The later transfers are like the famous Pigou-Dalton ones, but without the requirement - that would be senseless in an ordinal setting - that the "amount" transferred from the "rich" to the "poor" is fixed. A second criterion is a new easy-to-use statistical criterion associated to a specifically weighted recursion on the cumulative density of the distribution function. A third criterion is that resulting from the comparison of numerical values assigned to distributions by a large class of additively separable social evaluation functions. Dual versions of these criteria are also considered and alternative equivalence results are established. Illustrations of the criteria are also provided

Comparing Distributions of Body Mass Index Categories

This paper compares distributions of Body Mass Index (BMI) among men and women in France, the US and the UK on the basis of a new normative criterion. Comparing distributions of BMI from a normative standpoint is conceptually challenging because of the ordinal nature of the variable. Our normative criterion is well-suited to handle this issue. It coincides with the possibility of moving from the dominated distribution to the dominating one by a finite sequence of Hammond transfers and/or elementary efficiency gains. An additional difficulty with BMI is that it is not monotonically increasing (or decreasing) with health or well-being. We therefore perform our analysis by considering all health-consistent rankings of BMI values. Our empirical results are striking. For a large class of these rankings of BMI values, it is shown that the distribution of BMI in France has worsened on the period 2008-2010 for both men and women according to first order dominance. It is also shown that for most welfare rankings of BMI values, the distribution of BMI is worse in every period in the female population than in the male one in all three countries

Ranking distributions of an ordinal variable

La Mesure des Inégalités Ordinales et MultidimensionnellesCHALLENGING INEQUALITIES: A INDO-EUROPEAN PERSPECTIVELes préférences pour la redistribution: fondements, représentation et implications pour les décisions sociale

Can transparency of information reduce embezzlement? Experimental Evidence from Tanzania

Embezzlement is a major concern. By means of a sequential dictator game, we investigate theoretically and experimentally whether making information more transparent and reducing the number of intermediaries in transfer chains can reduce embezzlement. Consistent with reference-dependent preferences in terms of moral ideal, we show that the impact of transparency is conditional on the length of the transfer chain and on the position of the intermediary in the chain. Its direct effect on image encourages honesty. Its indirect effect via expectations plays in the opposite direction, motivating intermediaries to embezzle more when expecting that the following intermediary will embezzle less

The Absence of Deprivation as a Measure of Social Well-Being. An Empirical Investigation

The generalised Lorenz criterion is widely used for making welfare comparisons within and across countries on the basis of their income distributions. Experimental studies have challenged this way of proceeding by showing that the principle of transfers, which underlies the generalised Lorenz criterion, does not meet with widespread agreement among the public that theorists would have expected. We propose to substitute the non-deprivation quasi-ordering introduced by S.R. Chakravarty (Keio Economic Studies 34 (1997), 17–32) for the generalised Lorenz criterion. This criterion is less demanding than the generalised Lorenz criterion as it builds on a weaker version of the principle of transfers and it is therefore more likely to be accepted by the public. We use income data from the Luxembourg Income Study for 17 countries in order to contrast the generalised Lorenz and the non-deprivation criteria. Although the non-deprivation quasi-ordering is less decisive than the generalised Lorenz criterion, it is shown that the former approximates the latter surprisingly well.Progressive Transfers, Social Welfare, Inequality, Deprivation