Equality of Opportunity with Categorical data/Igualdad De Oportunidades Con Datos categoricos/L'egalite Des Chances Avec Des Donnees Categoriques

By Herrero, Carmen; Villar, Antonio | Lecturas de Economia, July-December 2014 | Go to article overview

Equality of Opportunity with Categorical data/Igualdad De Oportunidades Con Datos categoricos/L'egalite Des Chances Avec Des Donnees Categoriques


Herrero, Carmen, Villar, Antonio, Lecturas de Economia


--Introduction. --I. The model. --II. An empirical illustration. --III. Final remarks. --References. --Appendix.

Introduction

The need to introduce distributive considerations in the analysis of social outcomes is already well established. Income distribution, health, education, or human development are instances in which this concern has been systematically incorporated from different perspectives (e.g. Roemer, 1996; Bleichrodt & van Doorslaer, 2006; Fleurbaey, 2008; Stiglitz, Sen & Fitoussi, 2009; OECD, 2010; United Nations, 2010). Equality of opportunity is one of the most relevant approaches to address distributive justice. There is a wide spectrum of views with respect to what is required for equality of opportunity, from the non-discrimination viewpoint to the consideration that social provision should compensate for all forms of disadvantage. Common to those views is that individuals are accountable, to some extent, for the achievement of the advantage in question, whether this refers to health, education, income, utility or welfare. Indeed, the issue of responsibility has become prominent in some of the recent developments within the areas of political philosophy and welfare economics (see Arnesson, 1989; Cohen, 1989; Fleurbaey, 1995; Bossert, 1995; Bossert & Fleurbaey, 1996; Roemer, 1998; Fleurbaey, 2008; and the literature cited therein).

The bottom line behind the equality of opportunity principle is that people who are relatively disadvantaged due to external circumstances deserve some kind of compensation. And, complementarily, that we should not be concerned for those outcome differences that derive from other people's characteristics that could be deemed irrelevant for the problem under consideration.

We propose in this paper a way of applying the equality of opportunity approach to the evaluation of societies when individual outcomes are categorical (e.g. when the data that describe their achievements correspond to ordinal perceptions, positions in a ranking, or quality levels). To do so we start by grouping people according to their circumstances so that society is partitioned into a finite number of types, each of which gathers individuals with similar circumstances. In that way all people of the same type share the same opportunity and therefore, outcome differences within types will be deemed irrelevant from an ethical viewpoint. The differences in the distribution of individual achievements across types, on the contrary, can be regarded as differences in people's opportunities. This is the kind of inequality we are interested in.

The novelty of our contribution is that we provide a complete cardinal measure of equality of opportunity that is not based on decomposability principles (additive decomposability of inequality indices, as in Ruiz-Castillo, 2003; Villar, 2005; Lefranc, Pistolesi & Trannoy, 2008 and 2009 or Checchi & Peragine, 2010, or the decomposition of outcomes between characteristics and returns, as in Bourguignon, Ferreira & Menendez, 2007 or Calo-Blanco & Garcia-Perez, 2012). (1) Moreover, it is applicable to categorical data, a case in which only ordinal incomplete rankings are found, mostly based on the application of Lorenz dominance criteria (e.g. Allison & Foster, 2004; Abul-Naga & Yalcin, 2008; Zheng, 2011).

The paper is structured as follows. Section 1 presents the reference model. Section 2 presents an empirical application out of the last PISA data on fifteen-year old students' performance regarding mathematics in the Spanish regions. A few final words in Section 3 close the paper.

I. The model

Consider the problem of providing an assessment of the equality of opportunity for a society with m agents, M = {1, 2, ..., m}, when individual outcomes are categorical. That is, there is a partition of all possible individual outcomes into a set C = {1, 2, ..., [gamma]} of categories so that each individual outcome belongs to one of those categories. …

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