# **1. Introduction**

The recent empirical literature on equality of opportunity (EOp) has provided a significant body of evidence on the extent of inequality of opportunity in different countries. See Brunori et al. (2015) for a first assessment of the existing evidence and Ferreira and Peragine (2016), Ramos and Van de Gaer (2016) and Roemer and Trannoy (2015) for methodological and conceptual issues related to the measurement of EOp.

A common feature of the existing literature is the static approach. Almost all empirical analyses use income distribution at a given point in time as the relevant distribution of individual advantages and are limited to computation of inequality of opportunity as a snapshot for a given country or set of countries.<sup>1</sup> This paper instead is concerned with the evolution of inequality of opportunity, i.e. with a dynamic approach. In addition, the time variation of EOp allows to study its main determinants. By so doing, we move the research on EOp a step forward and propose and test a (simple) empirical model that can explain the generation of inequality of opportunity in a given economy.

There are three different ways to analyze the evolution of inequality of opportunity, which correspond to three different concepts of inequality dynamics: (i) inequality measured across repeated snapshots of the population (repeated cross-sectional analysis); (ii) inequality measured along life courses (longitudinal analysis); (iii) inequality measured across generations (cohort analysis).

While analysis (ii) requires the availability of a rich longitudinal data set containing information of individual incomes and circumstances over the entire life cycle of the individuals, the analyses (i) and (iii) can be potentially carried out by using repeated cross-section surveys, hence are much less data intensive. This is the reason why in the present paper we focus on analyses (i) and (iii). See Aaberge et al. (2011) for an analysis of long-term inequality of opportunity along the lines of concept (ii).

# **2. The model**

# **2.1 Canonical models of inequality of opportunity**

The conceptual basis for the definition of inequality of opportunity is provided by the distinction, among the factors influencing the individual achievements, between individual efforts and predetermined circumstances – defined as those which lie outside the realm of individual responsibility. The EOp approach considers that inequality due to the former is not ethically offensive, whereas it suggests that differences in individual outcomes due to the latter represent a violation of the principle of equality of opportunity and should be removed. In what follows we will follow the simple framework introduced by Checchi and Peragine (2010) to measure inequality of opportunity.

Consider a distribution of income Y in a given population. Suppose that all determinants of Y, including the different forms of luck, can be classified into either a set of circumstances C that lie beyond individual responsibility, belonging to a finite set Ω, or as responsibility characteristics, summarized by a variable e, denoting effort,<sup>2</sup> belonging to the set Θ. The outcome of interest is generated by a function g: Ω �Θ →R such that:

> 1 Also the cross-country comparability is a relevant issue, given the potentially different definitions of outcome and circumstances involved in the analysis.

> 2 Effort could also be treated as a vector. However, we follow the literature and treat it as a scalar.

2