On Estimating Achievement Dynamic Models from Repeated Cross Sections

Abstract

Summary.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 the model to Italian achievement data of 5 th and 6 th graders and investigate how inequalities develop between primary and lower secondary school.

The gender gap in mathematics achievement: Evidence from Italian data

“…Further, coefficients based on standardized test scores also depend on the achievement variability at each assessment. 9 Hence, if this variability increases between two surveys for reasons not related to gender (for example, due to increasing differences across socioeconomic levels), we might observe a diminishing gender gap even if there are no forces at work making girls catching up the previous disadvantage (Contini and Grand, 2015).…”

“…In the absence of longitudinal data, we use pseudo-panel techniques proposed by De Simone (2013) and Contini and Grand (2015), allowing to estimate simple dynamic models with repeated cross-9 Ignoring other control variables, the standardized gender gap at age/year j is: ( ̅ ̅ ) ⁄ . Clearly, the score variability may vary over time as a result of multiple driving forces, including increasing differences across social backgrounds or ethnic status.…”

“…In this paper, we apply the method adopted in Contini and Grand (2015). To illustrate its rationale, consider two cross sectional assessments using a single scale to measure achievement (i.e.…”

“…Following Contini and Grand (2015), as an instrumental variable we use the month of birth, since there is widespread evidence that younger children generally underperform their older peers, in particular at early school stages (see for example Crawford et al, 2007;Robertson, 2011;Crawford et al, 2014 among many others). Further, younger children are also more likely to have negative emotional and social experiences, such as, for example, being bullied on the playground (Ballatore et al, 2015), that might also affect their schooling outcomes.…”

The Evolution of Educational Inequalities in Spain: Dynamic Evidence from Repeated Cross-Sections

“…RCS are more abundant than panel data and, under certain conditions (formalized by Moffitt 1993, andVerbeek andVella 2005), they are useful for providing consistent achievement estimations in dynamic models. To the best of our knowledge, only De Simone (2013) and Contini and Grand (2015) have applied this methodology to dynamic achievement models, focusing on the evolution of the socioeconomic gap between primary and secondary school in Italy. There are nevertheless some discrepancies in their results, probably due to a combination of factors related to the use of different datasets and identification strategies.…”