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Statistical Inference for Aggregation of Malmquist Productivity Indices

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Abstract

The Malmquist Productivity Index (MPI) has gained popularity amongst studies on dynamic change of productivity of decision making units (DMUs). In practice, this index is frequently reported at aggregate levels (e.g., public and private rms) in the form of simple equally-weighted arithmetic or geometric means of individual MPIs. A number of studies have emphasized that it is necessary to account for the relative importance of individual DMUs in the aggregations of indices in general and of MPI in particular. While 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 con dence intervals and hypothesis testing. In this paper, we will ll this gap by developing a full asymptotic theory for an appealing aggregation of MPIs. On the basis of this, some meaningful statistical inferences are proposed and their nite-sample performances are veri ed via extensive Monte Carlo experiments.

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  • Manh D. Pham & Léopold Simar & Valentin Zelenyuk, 2019. "Statistical Inference for Aggregation of Malmquist Productivity Indices," CEPA Working Papers Series WP082019, School of Economics, University of Queensland, Australia.
  • Handle: RePEc:qld:uqcepa:138
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    File URL: https://economics.uq.edu.au/files/15442/WP082019.pdf
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    Keywords

    aggregation; asymptotics; DEA; hypothesis test; inference; Malmquist index; productivity;

    JEL classification:

    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • C44 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics - - - Operations Research; Statistical Decision Theory
    • C51 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Construction and Estimation
    • D24 - Microeconomics - - Production and Organizations - - - Production; Cost; Capital; Capital, Total Factor, and Multifactor Productivity; Capacity
    • M11 - Business Administration and Business Economics; Marketing; Accounting; Personnel Economics - - Business Administration - - - Production Management

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