On estimating achievement dynamic models from repeated cross-sections

Despite the increasing spread of standardized assessments of student learning, longitudinal 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? We discuss the issues involved in estimating dynamic models from repeated cross-sectional surveys and, 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 it to Italian achievement data of 5th and 6th graders and investigate how inequalities develop between primary and lower secondary school.