Gaston Yalonetzky

Stochastic Dominance with Ordinal Variables: Conditions and a Test

A re-emerging literature on robustness in multidimensional welfare and poverty comparisons has revived interest in multidimensional stochastic dominance. Considering the widespread use of ordinal variables in wellbeing measurement, and particularly in composite indices, I derive multivariate stochastic dominance conditions for ordinal variables. These are the analogues of the conditions for continuous variables (e.g., Bawa, 1975, and Atkinson and Bourguignon, 1982). The article also derives mixed-order-of-dominance conditions for any type of variable. Then I propose an extension of Andersons nonparametric test in order to test these conditions for ordinal variables. In addition, I propose the use of vectors and matrices of positions in order to handle multivariate, multinomial distributions. An empirical application to multidimensional wellbeing in Peru illustrates these tests.

Conditions for the most robust multidimensional poverty comparisons using counting measures and ordinal variables

A natural concern with multivariate poverty measures, as well as with other composite indices, is the robustness of their ordinal comparisons to changes in the indices’ parameter values. Applying multivariate stochastic dominance techniques, this paper derives the distributional conditions under which a multidimensional poverty comparison based on the popular counting measures, and ordinal variables, is fully robust to any values of the indices’ parameters. As the paper shows, the conditions are relevant to most of the multidimensional poverty indices in the literature, including the Alkire–Foster family, upon which the UNDP’s “Multidimensional Poverty Index” (MPI) is based. The conditions are illustrated with an example from the EU-SILC data set.

Introduction to Robustness in Multidimensional Wellbeing Analysis

The multidimensional nature of wellbeing is now the widely accepted approach in frontier research on poverty, inequality and policy analysis. However, significant challenges and disagreement remain over whether multiple dimensions of wellbeing should be monitored and assessed separately, as in a dashboard approach, or whether these should be evaluated jointly, e.g., by resorting to composite indices. At least two reasons can be used to justify the latter approach in some applications. Firstly, it is not always easy to keep track of trends in each dimension of wellbeing separately when there are too many indicators. Secondly, even when just a few dimensions are involved, we may be interested in computing measures of multidimensional wellbeing that take into account the joint distribution of indicators in the population. Multiple indicators are related, substitutes, and complements. Examples of multidimensional poverty indices include those of Alkire and Foster (2010). This multidimensional approach to wellbeing is not new.1 Yet it

On Bi‐Polarization and the Middle Class in Latin America: A Look at the First Decade of the Twenty‐First Century

This paper proposes new measures and graphical representations of the change in bi-polarization and in the relative importance of the middle class that took place in a given country during a given period. These tools extend, in fact, the concepts of inter-distribution income inequality and Lorenz curves by making, first, a distinction between overall, “pure growth based” and “shape related” distributional changes; and then between a “first-order” and a “second-order” change in “shape related” distributional change. The empirical illustration is based on data covering 17 Latin American countries in 2000 and 2009, obtained from the Latinobarometro surveys for these years. The standard of living of individuals was derived on the basis of correspondence analysis. These new tools help us to understand the changes that took place in the distribution of standards of living during the period analyzed.

Chapter 4 Measuring Inequality in Life Chances with Ordinal Variables

Purpose – We propose applying Reardons approach to the measurement of ordinal segregation to the study of inequality in life chances in the case of ordinal variables. We also propose additional measures of inequality in life chances in such a case. Methodology – We state the desirable properties of measures of inequality in life chances when the variable under study is ordinal and check which properties are fulfilled by the various indices examined in this chapter. Findings – All the indices defined in this chapter seem suitable for the analysis of inequality in life chances with ordinal variables but we found some trade-off between indices fulfilling the population composition invariance and those fulfilling the group replication invariance. Originality – Besides extending the indices suggested by Reardon to the study of inequality of life chances, we propose, to analyze this issue, two additional sets of indices based on the notion of distributional dissimilarity.

Measuring Group Disadvantage with Inter-Distributional Inequality Indices: A Critical Review and Some Amendments to Existing Indices

A long literature on inter-distributional inequality (IDI) has developed statistical tools for measuring the extent of inequality between two groups (e.g. men versus women). Firstly, I introduce the property of group-specific disadvantage focus (GDF). Indices satisfying this property are only sensitive to inequalities that are disadvantageous to one specific group. Then the paper reviews some of the most prominents IDI indices proposed in the last four decades. The assessment focuses on whether these indices satisfy GDF and, if not, how they react to inequalities that are disadvantageous to different groups. I also discuss whether these indices are informative, or not, regarding other interesting features related to IDI comparisons, e.g. distributional equality, absence of distributional overlap and presence of first-order stochastic dominance. Finally, I propose amendments to several of these indices in order to render them in fulfillment of GDF and more informative on the mentioned distributional features.

The state of female autonomy in India: A stochastic dominance approach

Abstract The promotion of female autonomy is both intrinsically and instrumentally desirable. We document differences in the distribution of female autonomy in India (using the National Family Health Survey 2005–2006) addressing two methodological challenges: the multidimensional nature of the concept and its frequent measurement with ordinal variables (which are not amenable to direct comparisons of social averages). We tackle these challenges with three methods based on stochastic dominance techniques suited for ordinal and dichotomous variables. Whenever these dominance conditions hold for a pairwise comparison, we can conclude that the multidimensional autonomy distribution in one state is more desirable than in another one across a broad range of criteria for the individual and social welfare evaluation of autonomy. Consistently across the three methods, we find that most of the states with better autonomy distributions (in pairwise comparisons) come from the north east and the south, whereas most of the states with worse autonomy distributions come from the north.

Fuzzy Chronic Poverty: A Proposed Response to Measurement Error for Intertemporal Poverty Measurement

A number of chronic poverty measures are now empirically applied to quantify the prevalence and intensity of chronic poverty, vis-a-vis transient experiences, using panel data. Welfare trajectories over time are assessed in order to identify the chronically poor and distinguish them from the non-poor, or the transiently poor, and assess the extent and intensity of intertemporal poverty. We examine the implications of measurement error in the welfare outcome for some popular discontinuous chronic poverty measures, and propose corrections to these measures that seeks to minimize the consequences of measurement error. The approach is based on a novel criterion for the identification of chronic poverty that draws on fuzzy set theory. We illustrate the empirical relevance of the approach with a panel dataset from rural Ethiopia and some simulations.

The Necessary Requirement of Median Independence for Relative Bipolarisation Measurement

The relative bipolarisation literature features examples of indices which depend on the median of the distribution, including the renowned Foster-Wolfson index. This note shows that the use of the median in the design and computation of relative bipolarisation indices is both unnecessary and problematic. It is unnecessary because we can rely on existing well-behaved, median-independent indices. It is problematic because, as the note shows, median-dependent indices violate the basic transfer axioms of bipolarisation (defining spread and clustering properties), except when the median is unaffected by the transfers. The convenience of discarding the median from index computations is further illustrated with the proposal of a corrected, median-independent version of the Foster-Wolfson index which always fulfills the basic transfer axioms.

Introduction to Special Section: Quantitative Approaches to the Measurement and Analysis of Female Empowerment and Agency

Abstract This special issue presents four novel applications of quantitative methods to address measurement and analytical issues in the appraisal of female empowerment and agency. The methods presented comprise mixed methods, dominance analysis and structural equation models. The use of these methods is illustrated with empirical applications in Cambodia, India, Mali, and Turkey.