Many countries aim to efficiently allocate limited national research and development resources to produce optimal research. A proportion of limited national research and development (R&D) budgets is invested in technologies that are highly publicly available to create public benefits. However, unlike general technology, it is not easy to generate profits through the commercialization of public technology; therefore, instead of using existing methodologies, it is necessary to analyze the efficiency of public technologies from a qualitative point of view. In this study, a two-stage network data envelopment analysis was conducted to analyze the stages involved in knowledge diffusion and application and the efficiency of conducting public technology R&D activities with respect to knowledge spillover. Cross-country comparisons were conducted to understand the factors that generate differences in R&D efficiency. The results of the return to scale analysis imply that countries with a high frequency of earthquakes should increase or at least maintain the number of studies conducted on earthquakes, whereas countries characterized by fewer earthquakes should focus their R&D strategy on a particular research area. In addition, in the two-stage network data envelopment analysis, the USA, France, New Zealand, and South Korea exhibited efficient performance in both stages. Japan performed poorly in the knowledge diffusion stage due to its national characteristics; however, the earthquake reduction effects were prominent because Japan responded effectively at the knowledge application stage. In contrast, well-diffused research results in Turkey, Iran, and China were not efficiently utilized, which resulted in low knowledge application-level efficiencies.