Dynamic Probabilistic Indices - Probabilistic Composition of Preferences, Theory and Applications - page 63

Chapter 7
Dynamic Probabilistic Indices

Abstract A DEA approach to access the evolution of productivity along time
exploring the idea of the Malmquist index involves calculating the ratio between the
distances to the production frontier of 2 years of evaluation of the alternative being
evaluated: one representing the observed production during the year to which the
frontier is built and the other representing the observed production of the next or the
previous year. The same type of substitution is here applied with a probabilistic
composition algorithm to generate probabilistic Malmquist indices.

Keywords Malmquist index DEA Malmquist index Probabilistic Malmquist

index

7.1 Malmquist Indices

The Malmquist Index, as conceived by Malmquist ( 1953 ), aimed to assess the
evolution of consumer behavior. Caves et al. ( 1982 ) proposed the use of the same
idea in an index to assess the evolution of productivity. A DEA approach to the
Malmquist index was developed by Fare et al. ( 1994 ).
The Malmquist DEA indices apply the algorithms of linear programming of
DEA to the calculation of the Malmquist evolution of productivity. The basic
concept involves calculating the ratio between the distances to the production
frontier of 2 years of evaluation of the alternative being evaluated: the rst repre-

senting the observed production during the year to which the frontier is built, and
the other representing the observed production of the next or the previous year. The
same type of substitution can be applied with a probabilistic composition algorithm
instead of a DEA algorithm.