This paper presents, a two-step analysis based on the new Piaac data (Programme for the International Assesment of Adult Population). Specifically: a) a study of the effects of ascriptive variables (as gender, parents’ education, etc.) on educational attainment in four age cohorts (born from 1946 to 1955, from 1956 to 1965, from 1966 to 1975 and from 1976 to 1985) aimed to produce an overview of the structure of educational inequalities over time; b) an analysis of the effect of the educational level when testing proficiency in reading skills (controlled by ascriptive variables and educational attainment). Thanks to the Piaac data features (which not only include background variables and the educational level, but also cognitive skills), this study aims to explore the advantage linked to the different educational levels on reading skills in the four age cohorts. Another goal of this essay is to analyse the influence of the ascriptive variables over the relationship between educational level and cognitive skills, in particular evaluating the effect of each of these independent variables and their dynamic over time.