The Theoretical Comparison of Malmquist and Luenberg Productivity Indices & Empirical Analysis

Background: We measured productivity changes of regional public hospitals using both global Malmquist productivity index-based on global production possibility set over all the periods-and the traditional Malmquist productivity index and analyzed the factors of productivity change. Methods: The data used in this study is two annual inputs and two annual outputs of 32 regional public hospitals in Korea from 2005 to 2009 and the results such as distances and Malmquist productivity index and global Malmquist productivity index are obtained by an R program written for this study. Results: The results can be summarized as follows. Firstly, technical efficiencies of regional public hospitals are affected largely by scale efficiency than pure technical efficiency. Second, productivity progressed and technological change has more significant influence on productivity advance over the period between 2005 and 2009. Third, the circularity problem of the traditional Malmquist index is confirmed, and so the global Malmquist index without this problem are valid for the analysis. Conclusion: Though this study also has some limitations with the data of regional public hospitals with a short time span, it is the first study of hospitals using global Malmquist productivity index and later it can be expanded to private hospitals and longer time periods.