Upper and Lower Bound Estimates of Inequality of Opportunity: A Cross‐National Comparison for Europe

• Published date: 01 December 2023
• Author: Rafael Carranza
• Date: 01 December 2023
• DOI: http://doi.org/10.1111/roiw.12622

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Review of Income and Wealth

Series 69, Number 4, December 2023

DOI: 10.1111/roiw.12622

UPPER AND LOWER BOUND ESTIMATES OF INEQUALITY OF

OPPORTUNITY: A CROSS-NATIONAL COMPARISON FOR EUROPE

BY RAFAEL CARRANZA∗

Institute for New Economic Thinking at the OxfordMartin School, Department of Social Policy and

Intervention, and Nufeld College,University of Oxford

I provide lower and upper bound estimates of inequality of opportunity (IOp) for 32 European coun-

tries,between 2005 and 2019. Lower bound estimates use machine learning methods to address sampling

variability. Upper bound estimates use longitudinal data to captureall-time invariant factors. Across all

years and countries, lowerbound estimates of IOp account from 6 percent to 60 percent of total income

inequality, while upper bound estimates account from 20 percent to almost all income inequality. On

average, upper bound IOp saw a slight decrease in the aftermath of the GreatRecession, recovering and

stabilizingat around 80 percent of total inequality in the second half of the 2010s. Lowerbound estimates

for 2005, 2011, and 2019 show a similar pattern. My ndings suggest thatlower and upper bound esti-

mates complement each other, corroborating information and compensating each other’s weaknesses,

highlighting the relevance of a bounded estimate of IOp.

JEL Codes: D31, D63, J62

Keywords:equality of opportunity, inequality, longitudinal data, machine learning

1. INTRODUCTION

Promoting equal opportunities lies at the core of several national and

cross-national policy agendas. Many governments and international institutions

haveincorporated the challenge of achieving equal opportunities in their long-term

strategies. Indeed, the rst of thethree European Pillars of Social Rights of 2017 is

to promote equal opportunities (European Comission, 2021). The same holds for

other institutions as well as many national governments. To be able to pursue the

goal of equal opportunity,we rst need to know the potential extent of inequality of

opportunity (IOp), both across countries and overtime. With that in mind and using

the EU-SILC, I provide“upper bound” estimates of IOp for 32 European countries

between 2005 and 2019 and “lower bound” estimates for 2005, 2011, and 2019.

Note: I am grateful to Chico Ferreira, Stephen Jenkins, Berkay Özcan, Xavi Ramos, two anony-

mous reviewers, and the editor for their useful comments. I would also like to acknowledge the com-

ments offered by the participants of the “Equal Chances” workshop in Bari, ECINEQ 2019 and the

“Opportunities, Mobility and Well-Being”workshop in Warsaw. This research has been supported by

the Centre for Social Conict and Cohesion Studies (ANID/FONDAP/15130009), the Becas Chile

programme fromANID (ANID/PFCHA/DOCTORADO BECAS CHILE/2016-72170193), and Euro-

pean Research Council Synergy Grant 75446 for project DINA—Towards a System of Distributional

National Accounts.

*Correspondence to:Rafael Carranza,Institute for New Economic Thinking, Manor Road Build-

ing, Manor Rd, Oxford OX13UQ, UK (rafael.carranzanavarrete@spi.ox.ac.uk).

© 2022 The Authors.Review of Income and Wealth published by John Wiley & Sons Ltd on behalf of

International Association forResearch in Income and Wealth.

This is an open access article under the terms of the Creative Commons Attribution License,which

permits use, distribution and reproductionin any medium, provided the original work is properly cited.

838

Review of Income and Wealth, Series 69, Number 4, December 2023

The key precept behind IOp is that the source of inequality matters from an

ethical point of view. In particular, what matters is the distinction between morally

legitimate sources, commonly called “effort,” “preferences,” or “responsibility,”

and morally illegitimate sources, called “circumstances” (Roemer, 1998), with IOp

quantifying the importance of the latter. The growing interest in measuring IOp

can be seen in varied theoretical developments, applications for several countries,

and multiple review articles on the subject (Bourguignon, 2018; Ferreira and

Peragine, 2016; Ramos and Van de gaer, 2016; Roemer and Trannoy, 2015).

Most approaches to measuring IOp follow what is typically called the “lower

bound” approach to estimating IOp (Ferreira and Gignoux, 2011; Luongo, 2011).

This approach relies on a vector of circumstances, typically obtained from retro-

spective modules in socioeconomic surveys and aims to quantify the extent to which

these variables can explain total income inequality. Many methods are available to

do so, such as cell-based or regression-based analysis, or focusing on before or after

effort has been exerted (referred to as “ex-ante” and “ex-post” approaches, respec-

tively) as well as using different measures of inequality (see Ramos and Van de

gaer,2021, for an overview of the different methods). Among the multiple methods,

a common characteristic of this approach is that the set of available circumstances

is never exhaustive, and thus these methods are grouped under the general term

“lower bound” approach.

Recent literaturehas pointed out that these estimates also suffer from upwards

bias, due to sampling variance (Brunori et al.,2019b). This is especially true when

the sample size is small and there are a large number of potential circumstances. To

avoidsuch an issue, a number of articles have suggested the use of machine learning

methods when estimating IOp (Brunori et al.,2021). These methods treat the esti-

mation of IOp as a prediction problem and are aimed at improving both in-sample

and out-of-sample predictions, thus providing a good benchmark to choose an “op-

timal” set of circumstances.In this article I use conditional inference random forests

to estimate the lowerbounds of IOp. While I acknowledge and address this upwards

bias, for consistency with the existing literature I still refer to this approach as the

“lower bound” approach.

Niehues and Peichl (2014) proposed an alternative to the lower bound

approach, providingupper bound estimates of IOp through the use of longitudinal

data. The intuition behind this approach is that most circumstances are already

given when one reaches adulthood and are therefore xed at the point of obser-

vation. Using longitudinal data, they predict a xed effect for each individual in

a given sample, which they then use as their measure of circumstances. This is a

“black box” approach as it does not tell us what those circumstances are, only

that they are accounted for. Because the xed effect is assumed to capture all (or

at least, most) circumstances but also time invariant efforts, this approach results

in “upper bound” estimates of IOp. While not as widespread as the lower bound

approach, a few articles have provided upper bound estimatesfor the UK and some

middle-income countries (Flatscher, 2020; Hufe et al.,2022).

Because lower and upper bound estimates differ from the “real” level of IOp,

reporting them on their own can create some issues. First, from a measurement

point of view,we do not know how far these estimates depart from the actual levelof

IOp, a point discussed in Ferreiraand Peragine (2016) for the lower bound estimate.

© 2022 The Authors.Review of Income and Wealth published by John Wiley & Sons Ltd on behalf of

International Association forResearch in Income and Wealth.

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