The growing importance of citation-based bibliometric indicators in shaping the prospects of academic careers incentivizes scientists to boost the numbers of citations they receive. Whereas the exploitation of self-citations has been extensively documented, the impact of reciprocated citations has not yet been studied. We study reciprocity in a citation network of authors, and compare it with the average reciprocity computed in an ensemble of null network models. We show that obtaining citations through reciprocity correlates negatively with a successful career in the long term. Nevertheless, at the aggregate level we show evidence of a steady increase in reciprocity over the years, largely fuelled by the exchange of citations between coauthors. Our results characterize the structure of author networks in a time of increasing emphasis on citation-based indicators, and we discuss their implications towards a fairer assessment of academic impact.