A global malmquist productivity index of athletics performance in olympic games
提出一种基于数据包络分析的方法，结合固定产出约束和加权切比雪夫法，构建全球马尔奎斯特生产率指数，评估2008至2024年五届奥运会各国田径表现的生产率变化，发现少数国家超高效而多数国家效率轨迹不规则。
• DEA-based approach with a fixed-sum output constraint and Weighted Tchebycheff method • Global Malmquist Productivity Index (GMPI) to capture inter-Olympic productivity changes • Both a convex and a non-convex DEA technology variant are formulated • A few super-efficient and a majority with irregular efficiency and productivity change trajectories • Strong correlation between the points earned in Athletics events and efficiency scores This paper introduces a novel approach to evaluate the efficiency and productivity change of nations competing in Athletics events across the last five Summer Olympic Games, from Beijing 2008 to Paris 2024. Each nation's success is measured using a points-based system that assigns decreasing scores to the top eight finishers in each event, while population and GDP per capita are considered non-discretionary inputs. The proposed methodology builds on a three-step Data Envelopment Analysis (DEA) framework. First, an output-oriented intertemporal DEA model with variable returns to scale is used to estimate each nation's ideal performance benchmark. Second, the Weighted Tchebycheff method is applied, imposing that the total number of points awarded remains fixed in each Games, aligning the model with the constant-sum nature of Olympic competitions. Finally, a Global Malmquist Productivity Index (GMPI) is computed to capture productivity changes over time. The empirical results reveal a small group of relatively super-efficient countries, i.e. countries that outperform the others in relative terms, while the majority exhibit irregular efficiency and productivity change trajectories. The approach also shows a strong correlation between the points earned and computed efficiency scores. Additionally, a variant of the model under a non-convex technology was also developed, producing comparable results and confirming the robustness of the framework.