We test the basic assumption underlying the job competition and crowding out hypothesis: that employers always prefer higher educated to lower educated individuals. To this end, we conduct a randomised field experiment in which duos of fictitious applications by bachelor and master graduates are sent to real vacancies requiring only a bachelor degree. Our design allows to look at whether employers' preferences for overqualified versus adequately qualified applicants depend on the demand and supply context, sectoral activity and type of organisation, and characteristics of the posted vacancy. For the overall sample, we find that master graduates are 19% more likely to be directly invited for a job interview. Nonetheless, we conclude that eventual crowding out of bachelor graduates as a consequence of this selection policy is unlikely to be large since the advantage for master graduates is particularly observed for jobs with high overall invitation rates.