The article analyses the effect of gender in professors' career advancement using data on the entire population of professors in the Italian university system, data on the National Scientific Qualification (NSQ) accreditation scheme, and data on scientific productivity (SciVal) for bibliometric scientific sectors. As NSQ accreditation is a prerequisite for career advancement in Italian universities, using this data makes it possible to rule out women's reluctance to apply for promotions -candidate professors must apply for accreditation- as a mechanism for explaining the gender gap in academia. Our results show a relevant gender gap in career advancement that is not explained by gender differences in productivity (above the minimum level needed to obtain the accreditation). A structural gender bias also remains after controlling for available resources and for the percentage of female full professors in the academic scientific sector. The results contribute to the debate on the introduction of gender quotas.