How and to what extent does cyber risk impact firms in the modern data economy? When firms face a high risk of losing their data and algorithms, this unequivocally leads to reduced knowledge stocks, decreased productivity, and slower overall economic growth. Notwithstanding, the empirical analysis pursued in this study suggests that cyber risk may also mitigate some of its own adverse effects as it ex-ante prompts digitally-savvy firms to pursue digital innovation that can enhance productivity in other domains. We observe increased innovation rates in response to higher cyber risk, driven primarily by data-intensive firms and by firms which intensively pursue in-house cyber security protection rather than third-party cyber security delegation. In a second stage, we develop a structural heterogeneous-firm growth model of the data economy to illustrate and explain the channels through which cyber risk exerts influence over firms' productivity, profits and growth.