Despite the increasing spread of standardized assessments of student learning, longitudinal data on achievement data are still lacking in many countries. This article raises the following question: Can we exploit cross-sectional assessments held at different schooling stages to evaluate how achievement inequalities related to individual-ascribed characteristics develop over time? This is a highly policy relevant issue, as achievement inequalities may develop in substantially different ways across educational systems. We discuss the issues involved in estimating dynamic models from repeated cross-sectional surveys in this context; consistently with a simple learning accumulation model, we propose an imputed regression strategy that allows to "link" two surveys and deliver consistent estimates of the parameters of interest. We then apply the method to Italian achievement data of fifth and sixth graders and investigate how inequalities develop between primary and lower secondary school.