Analysis of group performance with categorical data when agents are heterogeneous: The evaluation of scholastic performance in the OECD through PISA

This paper analyzes the evaluation of the relative performance of a set of groups when their outcomes are defined in terms of categorical data and the groups’ members are heterogeneous. This type of problem has been dealt with in Herrero and Villar (2013) for the case of a homogeneous population. Here we expand their model controlling for heterogeneity by means of inverse probability weighting techniques. We apply this extended model to the analysis of the scholastic performance of fifteen-year-old students in the OECD countries, using the data in the PISA. We evaluate the relative performance of the different countries out of the distribution of the students’ achievements across the different levels of competence, controlling by the students’ characteristics (explanatory variables regarding schooling and family environment). We find that differences in mathematical and reading abilities across OECD countries would lower by between 40% and 50% if the students’ characteristics would be those for the OECD average.