PhD graduates can help companies transfer knowledge from universities to firms. Scholars have analysed the determinants of PhD recruitment by firms and its effects on their innovation activities. However, little is known about what happens when a firm loses employees with PhDs. The aim of this paper is to compare the effects on the relationships of firms with universities when these firms lose PhDs versus when they hire PhDs to work in R&D. These effects may be symmetrical or non-symmetrical depending on the abilities of firms to retain the connections and knowledge acquired by hiring PhDs. We consider four types of relationships: collaboration with universities, universities as a source of innovation, academic journals as a source of innovation and the purchase of R&D services from universities. We use data from the Spanish Technological Innovation Panel (PITEC) for the period 2006 to 2015. The results illustrate the central role of PhDs in the linkages between industry and academia. The recruitment of PhDs has a positive effect on collaboration between firms and universities and on the purchase of R&D services from universities. By contrast, the loss of PhDs has a negative effect on collaboration with universities but not on the acquisition of R&D.