Statistical Inference for Aggregation of Malmquist Productivity Indices

Manh Pham (), Leopold Simar and Valentin Zelenyuk
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Manh Pham: School of Economics, The University of Queensland, Brisbane QLD 4072, Australia

Operations Research, 2024, vol. 72, issue 4, 1615-1629

Abstract: 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.

Keywords: Optimization; aggregation; asymptotics; DEA; hypothesis test; inference; Malmquist index; productivity (search for similar items in EconPapers)
Date: 2024
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http://dx.doi.org/10.1287/opre.2022.2424 (application/pdf)

Related works:
Working Paper: Statistical Inference for Aggregation of Malmquist Productivity Indices (2023)
Working Paper: Statistical Inference for Aggregation of Malmquist Productivity Indices (2022)
Working Paper: Statistical Inference for Aggregation of Malmquist Productivity Indices (2019)
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