We derive a theoretical model of effort in the presence of career concern based on the multi-unit all-pay auction, and closely inspired by the Italian academic market. In this model, the number of applicants, the number of new posts, and the relative importance of the determinants of promotion determine academics' effort. Because of the specific characteristics of Italian universities, where incentives operate only through promotion, and where all appointment panels are drawn from strictly separated and relatively narrow scientific sectors, the model fits well Italian academia, and we test it in a newly constructed dataset which collects the journal publications of all Italian academics working in universities. We find that individual researchers respond to incentives in the manner predicted by the theoretical model: more capable researchers respond to increases in the importance of the measurable determinants of promotion and in the competitiveness of the scientific sector by exerting more effort; less able researchers do the opposite.