How much horizontal innovation is consistent with vertical innovation?

R&D-driven growth theory emphasizes vertical and horizontal innovation activities for long run growth. In this paper, we show that the real world co-existence of both innovative activities restricts the admissible laws of motion for horizontal innovation, thereby allowing to test the admissible range of intertemporal horizontal R&D spillovers. Private arbitrage between manufacturing and vertically innovating makes quality improving R&D profitable if and only if the horizontal innovation rate does not exceed the population growth rate. Hence, the mere observation of positive vertical innovation suggests that the number of new sectors has not been increasing faster than population.