Is Inequality of Opportunity Robust to the Measurement Approach?

• Published date: 01 March 2021
• Author: Xavier Ramos,Dirk Van de gaer
• Date: 01 March 2021
• DOI: http://doi.org/10.1111/roiw.12448

© 2020 International Association for Research in Income and Wealth

18

IS INEQUALITY OF OPPORTUNITY ROBUST TO THE MEASUREMENT

APPROACH?

by Xavier ramos

Universitat Autònoma de Barcelona, IZA, and EQUALITAS

AND

Dirk van De gaer

Ghent University and CORE, Université Catholique de Louvain

Recent literature has suggested many ways of measuring equality of opportunity. We analyze in a sys-

tematic manner the various approaches put forth in the literature to show whether and to what extent

different choices matter empirically. Drawing on data for most European countries for 2005 and 2011,

we find that the choice between ex-ante and ex-post approaches is crucial and has a substantial influ-

ence on inequality of opportunity country orderings. Growth regressions also illustrate the potential

relevance of conceptual choices.

JEL Codes: D3, D63

Keywords: direct approach, effort, equality of opportunity, EU-SILC, ex-ante, ex-post, income, indirect

approach, measurement, responsibility

1. introDuction

Responsibility-sensitive egalitarianism shifts the focus from outcomes to their

determinants, when assessing economic inequalities, and advocates offsetting the

effect of circumstances, for which individuals are not deemed responsible, while

respecting the effects of effort. Since the first contributions by Dworkin (1981),

Arneson (1989), and Cohen (1990), the economics literature has laid out the basic

principles that ought to guide measurement, following seminal contributions by

Roemer (1993, 1998), Fleurbaey (1995) and Bossert (1995) on allocation rules and

policy. In a recent paper (Ramos and Van de Gaer, 2016), we bring together the

theoretical and the empirical literature and draw attention to the conceptual differ-

ences of the empirical measures. This paper takes those lessons as starting point

with the intention to investigate whether those important conceptual differences

have any bearing in ordering distributions when taken to the data, and bring about

systematic differences in orderings. To this end, we estimate a wide range of

inequality of opportunity measures to the same set of data, the European

*Correspondence to: Xavier Ramos, Departament d’Economia Aplicada, Campus UAB, 08193

Bellaterra, Spain (Xavi.Ramos@uab.cat).

Review of Income and Wealth

Series 67, Number 1, March 2021

DOI: 10.1111/roiw.12448

bs_bs_banner

Review of Income and Wealth, Series 67, Number 1, March 2021

19

© 2020 International Association for Research in Income and Wealth

Union–Statistics on Income and Living Conditions (EU-SILC), an empirical exer-

cise which has not been done so far.1

Conceptually, the most frequently used measures of inequality of opportu-

nity can be classified on the basis of three criteria. The first criterion distinguishes

between ex-ante and ex-post measures. Ex-ante measures compute the inequality

in the values of individuals’ opportunity sets while ex-post measures compute the

inequality in the incomes of those that have the same efforts. Initially, the theoreti-

cal literature treated ex-ante and ex-post approaches as being very similar (Roemer,

2002; Roemer etal., 2003). Recent theoretical contributions stress they are differ-

ent and often conflict (Ooghe etal., 2007; Roemer, 2012; Fleurbaey and Peragine,

2013). Most of the empirical literature continues to treat them as interchangeable,

by motivating their concern with inequality of opportunity from ex-post intuitions

and using ex-ante measures of inequality of opportunity. We find that the distinc-

tion between ex-ante versus ex-post matters a lot for country orderings. The second

criterion, due to Pistolesi (2009), distinguishes between direct and indirect mea-

sures. Direct measures calculate the inequality in a counterfactual income distribu-

tion where all income inequalities are exclusively due to individuals’ circumstances.

Indirect measures calculate the difference between the inequality in the actual

income distribution and the inequality in a counterfactual income distribution in

which there is no inequality of opportunity. Our results suggest that the distinction

between direct and indirect measures is of secondary importance. The third crite-

rion focuses on whether a parametric or non-parametric method is used to con-

struct the counterfactual. This choice is relevant when the often-used parsimonious

linear specification does not yield a reasonable fit, and it is thus data-dependent.

In the next Section we provide a more detailed description of these criteria,

present and formally define the most frequently used measures of inequality of

opportunity and classify them. Section 3 describes the EU-SILC data and the cir-

cumstances and effort variables used in the empirical analysis, Section 4 presents

our empirical strategy, while Section 5 reports our main results. We first exam-

ine the incidence of choices on country orderings, and then show estimates from

growth regressions to illustrate further their empirical relevance. The concluding

section wraps up.

2. measurement approaches

As responsibility-sensitive egalitarianism distinguishes between efforts and

circumstances, the empirical model assumes that for each individual k in the pop-

ulation N={1,⋯,n}, his income,

yk

, depends on his circumstances, given by a

dC

-dimensional vector

aC

k

, his efforts, given by a

dR

-dimensional vector

aR

k

, and a

random term

ek

, such that2

1Previous papers provide partial (not systematic) comparisons, which do not allow drawing robust

conclusions about the importance of conceptual choices. For instance, drawing on the same EU-SILC

data, Checchi etal. (2016) compare non-parametric ex-ante

Ic1

and ex-post

Ic4

measures, defined in Table

1, using the same two inequality indices we employ, the Gini coefficient and the Mean Log Deviation.

2We discussed the consequences of unobserved random variation in Ramos and Van de Gaer

(2016), and abstract from that complication here.