We use unique administrative data from a leading Italian university to estimate whether the use of admission tests and conditional progression schemes are effective strategies to select high-performing students. Previous work, which has been predominantly correlational, has focused on the effect of selectivity policies on widening university access for individuals from ethnic minorities and disadvantaged backgrounds. Our evaluation method applies a difference-indifference (DD) design, which, under the assumption that the trends of the outcome variables would be the same across all departments within the same university in the absence of treatment, identifies the causal impact of selectivity policies. The estimates indicate that selectivity schemes may not lead university students to achieve better outcomes, in terms of greater likelihoods of completing their degrees, obtaining top marks and finishing their studies within the required minimum period. The study concludes with a discussion of the main findings and their implications.