General purpose technologies (GPTs) like AI enable and require significant complementary investments. These investments are often intangible and poorly measured in national accounts. We develop a model that shows how this can lead to underestimation of productivity growth in a new GPTs early years and, later, when the benefits of intangible investments are harvested, productivity growth overestimation. We call this phenomenon the Productivity J-curve. We apply our method to US data and find that adjusting for intangibles related to computer hardware and software yields a TFP level that is 15.9 percent higher than official measures by the end of 2017. (JEL E22, E23, G31, L63, L86)