If the number of cross-sections available for the same country is large enough, and their time span covers a sufficient number of years, one could interpret them as a pseudo-panel, in order to get as close as possible to model (3). In such a case the relevant model becomes where Y��� is the income of individual i born in year τ and sampled in survey t. In such a case, EOp can be repeatedly measured along three dimensions: in a specific year of survey t, repeated observations refer to different birth cohorts τ’s; for a specific birth cohort τ, repeated observations refer to different dates of survey t’s; for a specific age cohort �t�τ�, repeated observations refer to different life cycles. Section 2.2 initially adopts the approach described by model (5). It uses repeated cross-section surveys of the population of a specific country and estimates, for each year, the relevant parameters of the model. An extension which uses the cohort structure of model (6) is also considered. Both these _dynamic_ approaches provide interesting and distinct insights on the evolution of EOp.

# **2.2 Our empirical model**

This section presents a decomposition of measured inequality of opportunity into its constituting components in the same vein as what Solon (2004) did for intergenerational mobility of incomes. In the empirical literature (Ferreira and Peragine 2015), circumstances have included gender, age, ethnicity, region of birth, parental background (in terms of educational attainment and occupational status). For simplicity of exposition, let us consider circumstances as consisting of a single variable, parental education, indicated with E��� where θ denote generations.<sup>4</sup> We assume that parental background affects the income opportunity of the child through two main channels: _educational investment_ and _family networking_ .<sup>5</sup> The first channel can be simply described by the intergenerational persistence of educational attainment (Black and Devereux 2011) where E�� is the education of the child, E���� is the education of the parents, η is a measure of intergenerational persistence and ε captures any unobservable component (like ability as well as effort). This intergenerational correlation can be justified on various grounds: _cultural dependency_ (more educated parents value education more and press their children to follow in their footsteps), _financial resources_ (more educated parents hold better jobs and earn higher salaries which allow larger resources to be invested in education); _teaching practices_ (more educated parents are capable to support their children during their schooling career).

Education is valued in the labor market. Following the _Mincerian_ approach, we assume that individuals choose optimally the amount of schooling by balancing costs (foregone incomes) and benefits (higher wages expected in the future – see Heckman et al 2005). As a consequence, the earnings of people with different educational attainments will differ by an amount that will be proportional to the years of schooling, as in the following equation (where we abstract from the usual demographic information):

> 4 One could easily add additional circumstances (like gender, age and foreign citizenship, as we do in the empirical section) but the line of argument would remain unaffected.

> 5 Since parental background includes many other dimensions beyond education (like parental income, access to educational resources, family wealth, neighborhood), our model is observationally equivalent to many other models of intertemporal transmission of social status. See for example DeFraja (2002),

4