The development of international surveys on children’s learning like PISA, PIRLS and TIMSS—delivering comparable achievement measures across educational systems—has revealed large cross-country variability in average performance and in the degree of inequality across social groups. A key question is whether and how institutional differences affect the level and distribution of educational outcomes. In this contribution, we discuss the difference-in-differences strategies employed in the existing literature to evaluate the effect of early tracking on learning inequalities exploiting international assessments administered at different age/grades. In their seminal paper, Hanushek and Woessmann (Econ J 116:C63–C76, 2006) analyze with two-step estimation the effect of early tracking on overall inequalities, measured by test scores’ variability indexes. Later work of other scholars in the economics and sociology of education focuses instead on inequalities among children of different family background, using individual-level models on pooled data from different countries and assessments. In this contribution, we show that individual pooled difference-in-differences models are quite restrictive and that in essence they estimate the effect of tracking by double differentiating the estimated cross-sectional family background regression coefficients between tracking regimes and learning assessments. Starting from a simple learning growth model, we show that if test scores at different surveys are not measured on the same scale, as occurs for international learning assessments, pooled individual models may deliver severely biased results. Instead, the scaling problem does not affect the two-step approach. For this reason, we suggest using two-step estimation also to analyze family-background achievement inequalities. Against this background, using PIRLS-2006 and PISA-2012 we conduct two-step analyses, finding new evidence that early tracking fosters both overall inequalities and family background differentials in reading literacy.

国际上对儿童学习的调查（如PISA，PIRSS和TIMSS）的发展（在整个教育系统中提供可比较的成绩衡量标准）表明，跨国公司在平均成绩和社会群体之间的不平等程度存在很大的差异。一个关键问题是制度差异是否以及如何影响教育成果的水平和分布。在这项贡献中，我们讨论了现有文献中采用的差异差异策略，以利用在不同年龄/等级进行的国际评估来评估早期追踪对学习不平等的影响。Hanushek和Woessmann（Econ J 116：C63-C76，2006）在开创性的论文中，通过两步估算来分析早期跟踪对总体的影响。不平等，由考试分数的变异性指标衡量。其他学者在教育经济学和社会学方面的后来工作则侧重于不同家庭背景的儿童之间的不平等，对来自不同国家和评估的汇总数据使用个人级别的模型。在此贡献中，我们表明，个体合并的差异模型具有很大的局限性，并且从本质上讲，它们通过在跟踪方式和学习评估之间对估计的横截面家庭背景回归系数进行两次区分来估计跟踪的效果。从简单的学习增长模型开始，我们表明，如果像国际学习评估那样，在不同调查中测得的考试分数没有按相同的比例来衡量，则汇总的单个模型可能会产生严重偏差的结果。相反，缩放问题不会影响两步法。因此，我们建议也使用两步估算来分析家庭背景成就不平等。在这种背景下，我们使用PIRLS-2006和PISA-2012进行了两步分析，发现了新的证据，即早期追踪会在阅读素养上加剧总体不平等和家庭背景差异。