Estimating student learning value-added models from repeated cross-sections

In this paper we address the problem of estimating school achievement value-added models from repeated cross-sections. We use data of the INVALSI standardized assessment on primary and lower secondary school 2010. We address the problem of estimating school achievement value-added models from repeated cross-sections. Consistently with a simple learning accumulation model, we propose a strategy that allows to “link” two surveys, and we apply it to INVALSI data on 5th and 6th grades. By explicitly addressing the issue of measurement error (due to the substitution of true lagged values with proper estimates), we obtain consistent estimates of the parameters of the model of interest even with another source of measurement error (test scores imperfectly measuring achievement), also affecting genuine panel data. Results suggest that given 5th grade performance, socio-economic status affects 6th grade scores in Italian only mildly but does not affect math scores. Similar results hold for gender. On the other hand, territorial gaps increase substantially. Overall, these results support the thesis that learning is particularly important during the early stages of the schooling career. Yet, the finding that, given social background and ability in primary school, children in the first year of lower secondary school (only one year later) living in the South still perform substantially worse than their peers in the North, confirm the existence of a large territorial divide in the quality of schooling at both primary and lower secondary school levels.