Statistical precision of Malmquist Productivity Index and DEA: A bootstrap application to OECD healthcare

Data Envelopment Analysis (DEA) is a non-parametric mathematical programming that uses multi inputs to produce multi outputs. It is investigated whether the decision-making unit is effective or not. However, it has been debated for years that the results obtained from DEA do not provide statistical inference. Simar and Wilson (1998) develop a bootstrap procedure which may be used to estimate confidence intervals for distance functions used to measure technical efficiency, and demonstrate that the key to statistically consistent estimation of these confidence intervals lies in the replication of the unobserved datagenerating process. This paper examines to the case of Malmquist indices constructed from nonparametric distance function estimates using data of OECD countries during the period of 2010 through 2014. We used DEA to derive efficiency scores, Malmquist indices to assess productivity growth, second-stage bootstrapping to determine the accuracy of estimators and whether conclusions would change after considering this statistical information. According to the study, due to the widespread return among countries, the most appropriate scale of operational health services should be investigated instead of treatment centered on people and focused on disease prevention.