Restricted and Unrestricted Dominance for Welfare, Inequality and Poverty Orderings (original) (raw)

Sequential Stochastic Dominance and the Robustness of Poverty Orderings

SSRN Electronic Journal, 1999

When comparing poverty across distributions, an analyst must select a poverty line to identify the poor, an equivalence scale to compare individuals from households of di erent compositions and sizes, and a poverty index to aggregate individual deprivation into an index of total poverty. A di erent c hoice of poverty line, poverty index or equivalence scale can of course reverse an initial poverty ordering. This paper develops sequential stochastic dominance conditions that throw light on the robustness of poverty comparisons to these important measurement issues. These general conditions extend well-known results to any order of dominance, to the choice of individual versus family based aggregation, and to the estimation of critical sets of measurement assumptions. Our theoretical results are brie y illustrated using data for four countries drawn from the Luxembourg Income Study data bases.

Poverty measures and poverty orderings

SORT (Statistics and …, 2007

We examine the conditions under which unanimous poverty rankings of income distributions can be obtained for a general class of poverty indices. The "per-capita income gap" and the Shorrocks and Thon poverty measures are particular members of this class. The conditions of dominance are stated in terms of comparisons of the corresponding TIP curves and areas.

Statistical Inference for Stochastic Dominance and for the Measurement of Poverty and Inequality

Econometrica, 2000

We derive the asymptotic sampling distribution of various estimators frequently used to order distributions in terms of poverty, welfare, and inequality. This includes estimators of most of the poverty indices currently in use, as well as estimators of the curves used to infer stochastic dominance of any order. These curves can be used to determine whether poverty, inequality, or social welfare is greater in one distribution than in another for general classes of indices and for ranges of possible poverty lines. We also derive the sampling distribution of the maximal poverty lines up to which we may confidently assert that poverty is greater in one distribution than in another. The sampling distribution of convenient dual estimators for the measurement of poverty is also established. The statistical results are established for deterministic or stochastic poverty lines as well as for paired or independent samples of incomes. Our results are briefly illustrated using data for four countries drawn from the Luxembourg Income Study data bases.

A Simple Axiomatization of the Foster, Greer and Thorbecke Poverty Orderings

Journal of Public Economic Theory, 2002

The paper presents a simple characterization of the poverty orderings which are represented by a poverty measure belonging to the Foster, Greer, and Thorbecke class. All properties introduced are formulated within an ordinal framework. Furthermore, a new concept is proposed: the equivalent societal income which-if given to each individual in society-yields the same level of poverty as the actual income distribution. It is a specific indicator of the underlying poverty ordering, has attractive properties and allows us to prove the main result in a direct way.

Multidimensional Poverty Orderings

This paper generalizes the poverty ordering criteria available for one-dimensional income poverty to the case of multi-dimensional welfare attributes. A set of properties to be satisfied by multidimensional poverty measures is first discussed. Then general classes of poverty measures based on these properties are defined. Finally, dominance criteria are derived such that a distribution of multi-dimensional attributes exhibits less poverty than another for all multi-dimensional poverty indices belonging to a given class . These criteria may be seen as a generalization of the single dimension poverty-line criterion. However, it turns out that the way this generalization is made depends on whether attributes are complements or substitutes.

On the robustness of multidimensional counting poverty orderings

The Journal of Economic Inequality

Counting poverty measures have gained prominence in the analysis of multidimensional poverty in recent decades. Poverty orderings based on these measures typically depend on methodological choices regarding individual poverty functions, poverty cut-offs, and dimensional weights whose impact on poverty rankings is often not well understood. In this paper we propose new dominance conditions that allow the analyst to evaluate the robustness of poverty comparisons to those choices. These conditions provide an approach to evaluating the sensitivity of poverty orderings superior to the common approach of considering a restricted and arbitrary set of indices, cut-offs, and weights. The new criteria apply to a broad class of counting poverty measures widely used in empirical analysis of poverty in developed and developing countries including the multidimensional headcount and the adjusted headcount ratios. We illustrate these methods with an application to time-trends in poverty in Australia and cross-regional poverty in Peru. Our results highlight the potentially large sensitivity of poverty orderings based on counting measures and the importance of evaluating the robustness of results when performing poverty comparisons across time and regions.

ORIGINAL PAPER Deprivation, welfare and inequality

We provide a characterization of the generalised satisfaction-in our terminology non-deprivation-quasi-ordering introduced by S.R. Chakravarty (Keio Econ Stud 34:17-32, (1997)) for making welfare comparisons. The non-deprivation quasi-ordering obeys a weaker version of the principle of transfers: welfare improves only for specific combinations of progressive transfers, which impose that the same amount be taken from richer individuals and allocated to one arbitrary poorer individual. We identify the 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 quasiordering. We extend the approach to the measurement of inequality by considering the corresponding relative and absolute ethical inequality indices.

Counting poverty orderings and deprivation curves

2009

Most of the data available for measuring capabilities or dimensions of poverty is either ordinal or categorical. However, the majority of the indices introduced for the assessment of multidimensional poverty behave well only with cardinal variables. The counting approach introduced by Atkinson (2003) concentrates on the number of dimensions in which each person is deprived, and is an appropriate procedure that deals well with ordinal and categorical variables. A method to identify the poor and a number of poverty indices has been proposed taking this framework into account. However, the implementation of this methodology involves the choice of a minimum number of deprivations required in order to be identified as poor. This cutoff adds arbitrariness to poverty comparisons. The aim of this paper is twofold. Firstly, we explore properties which allow us to characterize the identification method as the most appropriate procedure to identify the poor in a multidimensional setting. Then the paper examines dominance conditions in order to guarantee unanimous poverty rankings in a counting framework. Our conditions are based on simple graphical devices that provide a tool for checking the robustness of poverty rankings to changes in the identification cutoff , and also for checking unanimous orderings in a wide set of multidimensional poverty indices that suit ordinal and categorical data.

Ranking Income Distributions by Deprivation Orderings

1999

This paper has examined the problem of ranking income distributions using absolute deprivation ordering. It appears that the ranking of distributions by this ordering may be more unambiguous than that generated by the relative deprivation ordering. The class of average deprivation indices consistent with the absolute deprivation criterion is also identified.