Assessing the marginal effect under partial observability in a selection context

Eduardo Alarcón-Bustamante, Pablo Espinoza, David Torres Irribarra, María Inés Godoy

DOI: 10.64028/xotj795639

Keywords: missing at random, predictive validity, ignorability, academic performance, informative assumptions

Abstract: The predictive capacity of admission tests depends on their ability to anticipate academic performance, which is directly related to the marginal effect of test scores. However, in selection contexts, this effect is not identifiable since academic performance is only observed for admitted students. In this paper, we first propose a decomposition of the marginal effect based on the law of total probability, distinguishing a within-group effect, which measures how academic performance varies with test scores within each program, and a between-group effect, which captures how test scores explain differences in average predictions across programs and influence admission probabilities. We then propose identification bounds for the marginal effect based on contextual assumptions about the admission system.

Submission Number: 18