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The biennial Malmquist productivity change index

Jesús T. Pastor, Mette Asmild and C. Knox Lovell

Socio-Economic Planning Sciences, 2011, vol. 45, issue 1, pages 10-15

Abstract: In this paper we introduce a new Malmquist productivity index that has three attractive features: it avoids linear programming infeasibilities under variable returns to scale, it allows for technical regress, and it does not need to be recomputed when a new time period is added to the data set. The proposed index is compared to both the adjacent Malmquist index and the global Malmquist index in an empirical example, which highlights the drawbacks of the existing indexes compared to the proposed biennial Malmquist index. Our results show that 13% of the observations in the data set may have to be ignored due to infeasibilities when decomposing the adjacent Malmquist index. Using only this reduced data set does at times lead to quite different results than those generated by applying the proposed biennial Malmquist index to the entire data set. The empirical example also shows that productivity change estimated between two time periods using the global Malmquist index change substantially when a third time period is added to the data set, whereas the proposed biennial Malmquist index is immune to this problem.

Measurement of Productivity Changes: Two Malmquist Index Approaches
Rikard Althin
Journal of Productivity Analysis
September 2001, Volume 16, Issue 2, pp 107-128

The adjacent Malmquist productivity index is compared to the more recently suggested base period Malmquist productivity index. The two index approaches are evaluated with respect to base period dependency, the circular test, and with respect to a set of additional classical index tests. In addition it is shown that the base period index is independent of base period if and only if the marginal rate of substitution of inputs is independent of time. Finally, the adjacent and the base period indexes are put through a Monte Carlo (bootstrap) test to see if they yield similar results when applied to a panel of Swedish pharmacy data.



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