literacy skills to report poor health, to believe that they have little impact on political processes, and not to participate in associative or volunteer activities.” (OECD, 2013) Most studies on inequality of educational outcomes focus on assessing inequality in educational attainment by measuring the dispersion in years of schooling.<sup>1</sup> However, years of schooling is an imperfect measure for educational outcomes: what someone learns in any given country in grade 6, for example, is not comparable to what they would have learned at the same grade in another country. This is more problematic at higher levels of education, as enrollment into tertiary programs is highly endogenous to learning achievements.

To avoid the problems associated with using years of schooling, we use data from PISA to assess inequality of opportunity in educational achievement. PISA is an international student assessment that measures learning rather than mastery of specific school curricula for students roughly 15 years old. This allows us to compare students’ academic achievement with a common benchmark. PISA also provides information on several socio-demographic characteristics of students, many of which are socially-inherited factors: gender, parent’s education, economic, social and cultural status, etc.

Unlike others who have used the raw scores in the analysis for similar purposes (Ferreira and Gignoux, 2013), we construct a binary variable of proficiency using the cutoffs defined by the OECD. We choose _Level 2 proficiency_ as our cutoff, which, according to the OECD is a baseline proficiency level at which students are able to demonstrate the skills that will enable them to _participate effectively and productively in life_ (OECD, 2010a). Scoring at or above level 2 can be defined as an “opportunity”, not only because it is a socially desirable minimum standard, but also because it is low enough to be either affordable by most societies already or in the near future given the available technology.<sup>2</sup> How do we measure inequality of opportunity? We start from Roemer’s (1998) distinction between “circumstances” and “effort”. Circumstances are socially-inherited factors, thus exogenous to the individual. Effort is endogenous but may also depend on circumstances and other factors (parents who push their children to strive at school, for example). Hence, outcomes can be generally modeled in the following way: where denotes the outcome variable, yy= ff[XX, EE(XX, vv), uu], denotes a vector of circumstances, is a vector of effort where denotes a vector of circumstances, is a vector of effort variables that depends on circumstances and other unobservables (innate ability and motivation, for yy XX EE example), and is a vector of other purely random factors. To measure inequality of opportunity would imply measuring the extent to which uu Ferreira and Gignoux (2014) present a simple measure of inequality of opportunity, given by the FF(yy|XX) ≠FF(yy).

ratio of the conditional and unconditional variances of scores. They apply this methodology to the context of inequality of educational opportunities using data from PISA 2006.

> 1 For example: Thomas et al. (2001); Caestello y Domenech (2002), or Morrison and Murtin (2007).

> 2 In the Republic of Korea 91% of the students score at/above the level 2 of proficiency in math, while in countries like Colombia, Peru and Indonesia, less than 30% of students do so. Similar results emerge for reading and science.

3