In 2017 the Italian government established the Fund to Finance Basic Research Activities – FFABR – with the purpose of assigning a 3,000-euro research grant to the most productive applicants among eligible assistant and associate professors. We show that many low-productivity researchers applied to the program while many high-productivity ones did not. Our evidence from both a simple structural model of program participation estimated on registry data, and a survey of the eligible population suggests that high-productivity researchers under-estimate their own position in the productivity distribution relative to the assignment threshold, while the opposite holds for low-productivity ones.