Energy innovation plays an important role in the transition to a zero-carbon economy. Governments in IEA member countries are investing in the R&D, demonstration, and deployment of new energy technologies as part of their energy and climate policies. However, government subsidies for energy innovation are not always efficient in achieving climate policy goals. This paper proposes a two-stage Data Envelopment Analysis model with shared inputs to determine the optimal allocation of public funds for the energy innovation process. The innovation process is divided into two stages: the R&D stage and the commercialization stage. The inputs to the model (budget expenditures for energy innovations) are distributed between the first and second stages. As intermediate products, we use the number of patents in clean energy and hydrocarbon energy. The outputs of the model are the changes in carbon intensity and energy efficiency. This model can be used to assess the effectiveness of government spending on energy innovation. The results show that some IEA member countries should allocate a large part of the fossil fuel technology budget (more than 70%) to the research and development phase. The proposed model can support decision making at the international level to increase the effectiveness of public policies in achieving decarbonization and energy efficiency goals.