Statistical Inference for Aggregation of Malmquist Productivity Indices.

A Comprehensive Set of Asymptotic Properties for a Meaningful Aggregation of Malmquist Indices The Malmquist productivity index (MPI) has become one of the most widely used tools for analyzing dynamic performance of decision-making units. Whereas accounting for economic weights of individual units in aggregations of indices is emphasized in the literature, statistical theory for constructing confidence intervals and performing hypothesis tests based on weighted aggregation of the MPI are still unavailable. In "Statistical Inference for Aggregation of Malmquist Productivity Indices," Pham, Simar, and Zelenyuk use a novel approach (based on the uniform delta method) to develop new asymptotic theory (including new central limit theorems) for aggregate MPIs as the basis for the statistical inference and test. They also verify the finite-sample performance of their approach via extensive Monte Carlo experiments and provide an illustration using real-world data. The Malmquist productivity index (MPI) has gained popularity among studies on the dynamic change of productivity of decision-making units (DMUs). In practice, this index is frequently reported at aggregate levels (e.g., public and private firms) in the form of simple, equally weighted arithmetic or geometric means of individual MPIs. A number of studies emphasize that it is necessary to account for the relative importance of individual DMUs in the aggregations of indices in general and of the MPI in particular. Whereas more suitable aggregations of MPIs have been introduced in the literature, their statistical properties have not been revealed yet, preventing applied researchers from making essential statistical inferences, such as confidence intervals and hypothesis testing. In this paper, we fill this gap by developing a full asymptotic theory for an appealing aggregation of MPIs. On the basis of this, meaningful statistical inferences are proposed, their finite-sample performances are verified via extensive Monte Carlo experiments, and the importance of the proposed theoretical developments is illustrated with an empirical application to real data. Funding: M. Pham acknowledges support from an Australian Government Research Training Program Scholarship. V. Zelenyuk acknowledges financial support from the University of Queensland and the Australian Research Council [Grant FT170100401]. Supplemental Material: The e-companion is available at https://doi.org/10.1287/opre.2022.2424. [ABSTRACT FROM AUTHOR]