The selection of employees in the Italian central bank is conducted through a competitive exam. This analysis evaluates the various stages of the exam, assessing its effectiveness in identifying the most able candidates while also investigating the presence of gender discrimination. To accomplish this, a multi-equation model is employed, which combines the scores of different exam questions, the choices made by candidates regarding which questions to answer, and individual unobserved heterogeneity. The results indicate that the exam performs well in filtering out less able candidates, as those who progress to subsequent stages tend to exhibit higher levels of ability compared to the initial pool of applicants. Moreover, a measure of the unobserved ability of hired candidates tends to be positively correlated to work performance. Furthermore, there is no evidence to suggest that the decline in the proportion of women who pass the exam, relative to the number of female applicants, can be attributed to discrimination. Finally, certain modifications to the exam structure could potentially enhance the selection process, thereby increasing the average ability of the selected candidates.