This study develops an R&D-based growth model with vertical and horizontal innovation to shed some light on the current debate on whether patent protection stimulates or stifles innovation. We analyze the effects of patent protection in the form of blocking patents. We show that patent protection changes the direction of innovation by having asymmetric effects on vertical innovation (i.e., quality improvement) and horizontal innovation (i.e., variety expansion). Calibrating the model and simulating transition dynamics, we find that strengthening the effect of blocking patents stifles vertical innovation and decreases economic growth but increases social welfare due to an increase in horizontal innovation. In light of this finding, we argue that in order to properly analyze the growth and welfare implications of patents, it is important to consider their often neglected compositional effects on vertical and horizontal innovation.