The Economic Theory of Index Numbers and the Measurement of Input, Output, and Productivity

Efficiency Measurement of Malaysian Agriculture Firms

“…where D represents the inverse of the distance function introduced by Caves et al (1982). M is the geometric mean of two ratios of input inverse distance functions.…”

Application of Window Malmquist Index for Examination of Efficiency Change of Czech Commercial Banks

“…This index was introduced into the DEA literature by Caves et al (1982) and is based on Malmquist's proposal to construct quantity indices as ratios of distance functions for use in consumption analysis 7 . Distance functions are representations of multi-output multi-input technologies which require data only on input and output quantities (Fare et al, 1994).…”

“…The original idea of the Malmquist index was proposed by Malmquist (1953), who suggested comparing the input of a firm at two different points of time in terms of the maximum factor by which the input in one period could be decreased such that the firm could still produce the same output level of the other time period. Caves et al (1982) extended the original Malmquist input index and introduced the first type of the Malmquist index, and then Fare et al (1992) showed that the Malmquist index can be calculated using a nonparametric DEA-like approach, given that suitable panel data are available and they applied DEA for measuring the Malmquist index. They assumed constant returns to scale and identified the technological change and the change of technical efficiency as two components of the productivity changes over time.…”

“…The above measure is actually the geometric mean of two Caves et al (1982) Malmquist productivity indexes. Fare et al (1992) define that M I > 1 indicates productivity gain; M I < 1 indicates productivity loss; and M I = 1 means no change in productivity from time t to s. Relaxing Caves et al (1982) assumption that D t I (y t , x t ) and D s I (y t , x t ) should equal to one, and allowing for technical inefficiency, Fare et al (1992) decompose their Malmquist productivity index into two components: Fare et al (1992Fare et al ( , 1994 point out that a value of TCC > 1 indicates a positive shift or technical progress, a value of TCC < 1 indicates a negative shift or technical regress, and value of TCC = 1 indicates no shift in technology frontier. In this paper we use the decomposition of Malmquist index into two components, namely technological change…”

Malmquist Productivity Index In Ratio Data Envelopment Analysis

“…The MPI was first introduced by Malmquist in 1953 as a general index to be used in the analysis of the consumption of inputs [5]. Fare et al [6] combined the Farrell's measures of efficiency and Cave et al's measures of productivity [7], and expressed the MPI as the result of the multiplication of efficiency changes by technological changes. In fact, this index maintains that the regression or progress of a unit, under evaluation, from one period to the next depends on not only its efficiency changes during these two assumed periods, but also technological changes of the population, or boundary shift of the evaluated population in the same periods.…”