How policy instruments can effectively promote private R&D is an important issue for the economy to maintain innovation vitality. Most of the existing researches focus on the impact of policies on private R&D from the time dimension, and less from the space dimension. Based on the panel data of 20 countries in 2001-2016, this paper introduces the interaction of government subsidy and preferential tax from the time dimension to explore the comprehensive impact of the two policy instruments. Secondly, the spatial lag is introduced to study the impact of domestic and foreign government subsidies and preferential tax on private R&D from both time and space dimensions. The results show that: first, there is a substitution effect between domestic government subsidies and preferential tax; second, the implementation of foreign policies weakens the effect of the domestic government subsidy and preferential tax on domestic private R&D, as well as the substitution effects; third, foreign government subsidies have a positive impact on domestic private R&D, foreign preferential tax have a negative impact on domestic private R&D.