Foreign Direct Investment is theoretically expected to facilitate the transfer of knowledge from the home country to the host country, however, the empirical evidence on the subject is mixed. Some studies have shown that, on one hand, as competition grows, the incentive to innovate reduces with the decrease in monopoly rents (Schumpeterian effect). On the other hand, market competition can also boost investments in R&D activities incentivized by incremental profits (Escape-Competition effect). Therefore, this study aims to explore which of these two effects dominates in the selected group of countries. This study also identifies the moderators of the relationship between FDI stock and domestic innovation. It examines the role of absorptive capacity, quality of regulations, and property rights protection in the innovative activities of the host countries. Generalized Method of Moments is used to estimate the parameters of the multivariate regression equation. The analysis is based on panel data consisting of 49 countries over 14 years. The results show that FDI has a negative relationship with domestic innovation, indicating the presence of the Schumpeterian effect. The extensions of the main models show that FDI positively affects domestic innovation in countries with higher absorptive capacity, the superior quality of regulation, and stronger protection of property rights. This study shows that the positive relationship between FDI and domestic innovation is conditional on the ability to absorb knowledge and quality of governance in the recipient countries.