In this paper we build a theoretical model to show the role of self-confidence in leading to inefficient job matching equilibria: underconfident highly-qualified workers do not apply for highly-skilled jobs, because mistakenly perceive themselves as having relatively lower abilities with respect to other candidates, and firms are no longer selecting their workers from a pool containing the best fitted ones. Policies to foster underconfident workers to apply for highly-skilled jobs cannot easily be implemented, because under-confidence is not an observable characteristic, and any attempt to elicit this information from workers can be easily manipulated. However, if gender is correlated with this psychological bias, and there more underconfident female workers than male workers, a second best policy based on gender affirmative action may enhance the efficiency of matching in the job market. We show that increasing the gender diversity of the qualified applicants by imposing an affirmative action may positively affect the selection of candidates because it increases the average quality of the pool of candidates for high-qualified jobs.