Assessing causal effects of extra compulsory learning on college students’ academic performances

Summary In Italian state universities candidate freshmen must take an entrance examination. Candidates who obtain a test score less than or equal to a pre‐fixed threshold may enrol at the university but must comply with an additional compulsory educational obligation, called obblighi formativi aggiuntivi (OFA).  The OFA assignment rule appeals to a (sharp) regression discontinuity design with the entrance examination score acting as the forcing variable.  We assess causal effects of OFA status by using data from a school of engineering of a specific Italian state university. For subpopulations of units for which our regression discontinuity design can be described as a local randomized experiment, we draw inference on the causal effects of OFA on students’ academic performances measured by using two variables: the number of university credits awarded at the end of the first academic year and the corresponding average grade. These outcome variables suffer from the problem of truncation by ‘death’, because neither is defined for students who decide not to enrol. Moreover, nor is the average grade defined for students who enrol but do not either take or pass any examination in the first academic year.  We deal with these issues by using the framework of principal stratification and adopting a Bayesian approach to inference. We find some evidence that the receipt of OFA may negatively affect students’ academic performances, although the posterior distributions of the causal estimands have high variability.